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Development and application of a momentum dispersive multichannel electron momentum spectrometer Lermer, Noah 1995

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DEVELOPMENT AND APPLICATION OF A MOMENTUM DISPERSIVEMIJLTICHANNEL ELECTRON MOMENTUM SPECTROMETERbyNoah LermerB. Sc., University of Lethbridge, 1989A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF CHEMISTRYWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAMarch 1995© Noah Lermer, 1995In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. it is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)_________________________Department of_____________The University of British CóumbiaVancouver, CanadaDate ) /995DE-6 (2188)AbstractThe design, evaluation, and application of a momentum dispersive multichannelspectrometer for electron momentum spectroscopy (EMS) is reported. The spectrometeremploys a microchannel plate/resistive anode position sensitive detector and a channel electronmultiplier, situated on the exit circle of a cylindrical mirror electron energy analyzer, tosimultaneously measure (e,2e) coincidence events over a ± 300 range of azimuthal angle. Anovel coincidence detection system based on the ‘pile-up’ of pulses from the detectors hasbeen developed to provide prompt detection of coincidence events. This spectrometerprovides an improvement of one to two orders of magnitude in sensitivity over typical singlechannel instruments.The performance of the new spectrometer has been characterized through measurementsof the binding energy spectra and experimental momentum profiles (XMPs) of the valenceelectrons of Ne, Ar, Kr, Xe, CH4 and SiH4. These measurements show significantly higherstatistical precision than any previously reported EMS work. Consistent with earlier studies,the present multichannel XMPs exhibit very good agreement with theoretical momentumprofiles calculated using high quality wavefunctions.The momentum profiles of the helium atom for the transitions to the ground (nt1) andthe excited (n=2, n=3) He final ion states have been obtained with considerably greaterIIprecision than previously reported. The experimental momentum profiles of H2 and D2 fortransitions to the ground and excited (2po, 2sag) ion states have also been measured to highprecision. While the XMPs for the transitions to the ground ion states of each system arefound to be in good agreement with theory, the XMPs for the transitions to the excited ionstates show significant deviations from theoretical profiles calculated with very accuratecorrelated wavefunctions. It is suggested that these discrepancies arise from contributions ofhigher order collision processes neglected in the plane wave impulse description of the (e,2e)scattering event normally used in the theoretical interpretation of EMS experiments. Whilethese additional processes have been discussed with regard to other photon, electron andproton impact studies of two-electron transitions (i.e. ionization plus excitation, doubleionization), they have not been previously considered in the context of EMS studies.ifiTable of ContentsAbstract iiTable of Contents ivList of Figures viiiList of Abbreviations xiiAcknowledgments xiiiChapter 1 Introduction 11.1 Electron Momentum Spectroscopy 21.2 Early Instrumental Developments 61.3 Experimental Studies by EMS 91.4 Multichannel Instrumental Developments 141.5 Context and Organization of this Work 17Chapter 2 Theoretical Background 222.1 The EMS Scattering Cross Section 222.2 The Calculation of Electronic Wavefunctions 322.2.1 The Hartree-Fock Method 342.2.2 The Method of Configuration Interaction 37ivChapter 3 The Momentum Dispersive Multichannel EMS Spectrometer 403.1 The Electron Source and Analyzer 413.1.1 The Electron Beam Assembly 453.1.2 The CMA Baseplate 463.1.3 The Collision Chamber 463.1.4 The Conical Lenses 473.1.5 The Cylindrical Mirror Analyzer 483.1.6 Preliminary Results 513.2 The Detector Assembly 533.2.1 The Channel Electron Multiplier 543.2.2 The Microchannel Plate/Resistive Anode Assembly 553.3 Coincidence Timing and Data Acquisition Electronics 613.3.1 Signal Processing 613.3.2 The Spectrometer Time Response 623.3.3 The Coincidence Detection System 663.3.4 The Pulse-Pile-Up Coincidence Circuitry 713.3.5 The Accidental Flag Circuitry 793.3.6 Data Acquisition 803.4 Characterization of the Instrument 843.4.1 TheCMA 853.4.2 The Channel Electron Multiplier 873.4.3 The Microchannel Plate/Resistive Anode Operating Voltages 92V3.4.4 The MCPIRAE Position Calibration and Uniformity 953.4.5 Linearity of the Detectors 1003.4.6 The Coincidence Timing Windows 1023.5 Experimental Results 105Chapter 4 Momentum Dispersive Multichannel EMS Measurements 1144.1 Neon 1164.2 Krypton 1224.3 Xenon 1254.4 A Summary of the Noble Gas Measurements 1284.5 Multichannel EMS of Methane and Silane 1304.6 Conclusions 137Chapter 5 EMS of Two Electron Systems: Helium 1385.1 Background 1385.2 A Momentum Dispersive Multichannel EMS Investigation of Helium 1475.2.1 Theoretical Momentum Profiles 1485.2.2 Multichannel Binding Energy Spectra and Momentum 151Distributions5.3 Discussion 1615.4 Conclusions 170viChapter 6 EMS of Two Electron Systems: Molecular Hydrogen 172and Deuterium6.1 Background 1726.2 Theoretical Momentum Profiles of Molecular Hydrogen 1746.3 Multichannel BES Spectra and Momentum Profiles of H2 1766.4 Multichannel BES Spectra and Momentum Profiles of D2 1876.5 Discussion 1926.6 Conclusions 195Chapter 7 Closing Remarks 197Bibliography 202vuList of Figures1.1 The symmetric non-coplanar (e,2e) scattering geometry 41.2 A schematic of a single channel symmetric non-coplanar 8(e,2e) spectrometer2.1 The Mott scattering cross section 253.1 Photographs of the multichannel spectrometer 423.2 A break-away schematic of the spectrometer 433.3 A schematic of the momentum dispersive spectrometer 443.4 A schematic of the collision chamber and conical lenses 493.5 Preliminary single channel EMS measurements 523.6 The CEM signal coupling circuitry 563.7 A typical CEM timing pulse 563.8 The MCP/RAE assembly 603.9 A typical MCP timing pulse 603.10 CEM pulse distribution and bipolar CFD pulses 633.11 Multichannel spectrometer timing spectrum 643.12 The PPU coincidence detection method 673.13 A block diagram of the coincidence detection system 703.14 A schematic of the coincidence detection circuit board 733.15 The PPU coincidence detection and gating circuit diagram 743.16 Waveform sequence through the coincidence circuitry 75VIM3.17 Position computer gating pulses 763.18 The accidental flag circuit diagram 813.19 Waveform sequence for the accidental flag signal 823.20 Characterization of the CMA energy resolution 863.21 CEM saturation 883.22 CEM and coincidence count rate variation with CEM front bias potential 893.23 Simulation of electron trajectory in the CEM 913.24 MCP and coincidence count rate variation with MCP back bias potential 943.25 Calibration of the MCPIRAE angle information 973.26 Angular distribution of electrons at the MCPIRAE 993.27 Variation of CEM I MCP / (e,2e) count rates with incident beam current 1013.28 The coincidence timing window 1043.29 The coincidence count rate variation with MCP / CEM signal delay 1043.30 A 15-minute multichannel binding energy spectrum of argon 1063.31 A 15-minute multichannel Ar 3p ç’-distribution 1073.32 A 46.5 hour single channel Ar 3p p-distribution 1073.33 A high precision multichannel BES of the argon valence region 1093.34 A high precision multichannel p-distribution and p-distribution of argon 1103.35 An impact energy I p-distribution surface— 2D-EMS 1134.1 A binding energy spectrum of the valence region of neon 1174.2 Experimental and theoretical momentum proffles of the neon 2p electron 119ix4.3 XMPs of the neon 2p and 2s electrons with DWIA and PWIA. 121theoretical profiles.4.4 A binding energy spectrum of the valence region of krypton 1234.5 Experimental and theoretical momentum profiles of the 4.p 124and 4s electrons of krypton.4.6 A binding energy spectrum of the valence region of xenon 1264.7 Experimental and theoretical momentum profiles of the 5p 127and 5s electrons of krypton.4.8 q- and p-distributions of the noble gases Ne, Ar, Kr, and Xe 1294.9 A binding energy spectrum of the valence region of methane 1324.10 Experimental and theoretical momentum profiles of the it2 and 2ai 133electrons of methane.4.11 A binding energy spectrum of the valence region of silane 1354.12 Experimental and theoretical momentum profiles of the 2t and 3a1 136electron of methane.5.1 Experimental and theoretical momentum profiles of helium reported 141by Cook et al. [26].5.2 Experimental and theoretical n=2 to n=1 cross section ratios reported 145by Labmam-Bennani et al. [74]5.3 Theoretical momentum profiles for helium 1495.4 A binding energy spectrum of helium showing double scattering effects 1515.5 A binding energy spectrum of helium measured following the modification 156of the collision chamber.5.6 XMPs and TMPs for the (e,2e) ionization of helium to the n=1, n=2 and 158n=3 final ion states.6.1 TMPs for the (e,2e) ionization of molecular hydrogen to the l5Gg 1742PGu, 2pit, and 2sGg final ion states.x6.2 The potential energy curves of the H2 ground state and the H2 ion states 1616.3 A binding energy spectrum of molecular hydrogen 1786.4 The H2 BES in the region of the transitions to the excited ion states 1796.5 XMPs and TMPs for the (e,2e) ionization of H2 to the lsag, 2pa 184and2SGg final ion states.6.6 XMPs -- corrected for the overlap of neighbouring transitions-- and TMPs ... 185for the (e,2e) ionization of H2 to the 1 sa5, 2pa,and2sag final ion states.6.7 A binding energy spectrum of deuterium 1896.8 The comparison of XMPs for H2 and D2 190xList of AbbreviationsBES binding energy spectrumCEM channel electron multiplier or channeltronCFD constant fraction discriminatorCI configuration interactionCMA cylindrical mirror analyzerDAC digital-to-analog converterDWIA distorted wave impulse approximationDWBA distorted wave Born approximationECL emitter coupled logicEMS electron momentum spectroscopyFWHIvI full width at half maximumIP ionization potentialGTO Gaussian type orbitalGW-PG Gaussian-weighted planar gridMCP microchannel plateMR-SDCI multireference singles and doubles CIOVD overlap distributionPES photoelectron spectroscopyPPU pulse-pile-upPWLk plane wave impulse approximationPWBA plane wave Born approximationRAE resistive anode encoderSCF self-consistent-fieldTAC time-to-amplitude converterTMP theoretical momentum profileTS two-step collision processTTL transistor-transistor logicXMP experimental momentum profilexuAcknowledgmentsThe research presented in this thesis would not be complete were it not for thecontributions of a number of individuals whose efforts I would like to acknowledge.It was the vision of Dr. Chris Brion, my research supervisor, that initiated, fueled andadvanced the development of the new momentum dispersive multichannel spectrometer. Aspecial note of gratitude is given to Dr. Brion for his advice, support, assistance, and patiencethroughout the study.The contributions of Dr. Bruce Todd, a post-doctoral fellow with whom I worked onthe development of the spectrometer, are recognized and very much appreciated. Dr. Todd’selectrical and mechanical expertise were of paramount importance to the success of theproject. Specific note should be made of his introduction of the pulse-pile-up technique forcoincidence detection. My heartfelt gratitude is expressed to Dr. Todd for his assistance,guidance and friendship during the course of the project.Dr. Natalie Cairn provided calculations of the theoretical momentum profiles for heliumusing a very accurate explicitly correlated wavefunction. Additionally, I would like to thankDr. Cann for discussions regarding the He and H2 measurements and for her friendship andadvice during the latter stages of my research. Dr. E. R. Davidson and S. Chakravorty ofIndiana University also provided theoretical profiles for helium, calculated with a very highquality correlated wavefunction.Ed Gomm, from the Department of Chemistry machine shop, skillfully fabricated manyof the individual components of the spectrometer. The care and exacting standards of Mr.Gomm are reflected in the successful operation of the instrument. Brian Greene, from theDepartment of Chemistry electronics division, constructed many of the supporting electroniccomponents of the instrument including the electrometers, the vacuum safety system, and theCEM amplifier. Additionally Mr. Greene freely offered advice and promptly executedemergency repairs when necessary.The assistance of every member of the electronic and the mechanical divisions of thechemistry department was called upon at one point or another during the project, and Iexpress my warmest thanks to Brian Greene, Joseph Sallos, Mike Hatton, Milan Cocshizza,David Tonkin, Zoltan German, Tom Markus, Ed Gomm, Bill Henderson, Ron Marwick, BrianSnapkauskas, Brin Powell, Oscar Greiner and Des Lovrity. As well, the friendly aid of thefront office personnel is affectionately acknowledged. In particular, I am grateful to CarolynC. Joyce for proofreading this manuscript.xmThanks are also due to Prof. N. Jaeger, Dr. Hiroshi Kato and Ken Madore of the Centrefor Advanced Technology in Microelectronics of the Department of Electrical Engineering,UBC, who kindly offered their services in the photolithographic etching of the MCP/RAEresolution mask.Helpful discussions with Mike Mellon of Quantar Technologies, Lorenzo Avaldi of the IMAIInstitute of CNDR (Italy), and Prof. I. E. McCarthy of Flinders University of South Australiaare gratefully acknowledged.The photographs of the spectrometer presented in chapter 3 were kindly provided by MankeeMah.I am also grateful for the many people who offered advice and support, and who togethercreated a challenging, dynamic and entertaining research environment. These include BruceHollebone, Patrick Duffy, Mark Casida, Terry Olney, Glyn Cooper, Gord Burton, Wing FatChan, John Neville, Steve Clark, Jennifer Au, Jim Roilce, Prof. D.P. Chong, and Dr. Y Zheng.The Natural Sciences and Energy Research Council and the Alberta Heritage Trust forproviding financial assistance during the course of the study is gratefully acknowledged.Finally, I would like to thank my family and friends for their support throughout my graduatestudies.xivChapter OneIntroductionAdvances in our understanding of nature are often gained through the development ofnew and creative instrumental techniques. Experimental tools have ‘made it possible toobserve, in unprecedented detail, a whole new world of small dimensions.” An appropriateexample of this is provided in the first unambiguous experimental measurements of thedistribution of momenta of electrons in atoms, obtained by DuMond and Kirkpatrick over 60years ago [1,2]. Their measurements showed that the linewidth of inelastically scattered Xrays, i.e. the Compton profile, originates from the Doppler broadening of the X-rays by themotion of the electrons in the target [3]. Difficulties arising from the weakness of theCompton signal were overcome through the development of a multicrystal spectrograph [4]that used 50 calcite crystals to analyze the wavelengths of X-rays scattered from a target at awell defined angle. In the late 1960s and early 1970s a new experimental technique for themeasurement of momentum distributions of electrons was proposed and developed. Thetechnique, originally known as binary (e,2e) spectroscopy, is now more commonly referred toas electron momentum spectroscopy or EMS. Unlike Compton scattering, in which the total1Professor Sture Forsdn, discussing the invention of the microscope, on the occasion of the awarding of theNobel prize in Chemistry to Dr. R. Ernst, 1991 [175].1Chapter One Introduction 2momentum distribution of all the electrons in the target is measured, EMS allows themomentum distribution of electrons associated with well defined energy states (i.e. orbitals inthe language of the independent particle model) to be determined. However, energyspecificity is not achieved without a commensurate loss of signal and increased difficulty ofmeasurement. This dissertation describes the development and application of a newspectrometer for the measurement of momentum distributions using electron momentumspectroscopy. As in the developments of DuMond and Kirkpatrick, this project attempted tomitigate the difficulties imposed by low signal rates through improved efficiency ofinstrumentation. The new spectrometer employs multichannel electron detection and noveltiming circuitry to enhance the collection efficiency by approximately two orders of magnitudeover conventional single channel EMS spectrometers.1.1 Electron Momentum SpectroscopyThe method of electron momentum spectroscopy is conceptually quite simple. It isbased on the idea that the momentum pg of a target object can be determined by a collisionwith another object of known momentum Po and observation of the direction and speed, that isthe momenta (labeled Pe and s for ejected and scattered), of both objects following thecollision. Conservation of momentum requires thatPt PePsPo (1.1)Chapter One Introduction 3In an EMS experiment, a beam of high energy electrons (typically 1200 eV) is directedinto a gas cell. The vast majority of the electrons passes through the region with nointeraction with the target species. Occasionally, an electron will “collide” with an electron ina bound state of the target atom or molecule in such a way that both electrons are scatteredinto large polar angles 9, relative to the direction of the incident electron. These largemomentum transfer collisions are the events of interest in EMS. The large polar angle andhigh (equal) energies of the outgoing electrons observed ensure that the collision can bemodeled by the direct collision of the two electrons with trajectories that can be well describedclassically. As shown by equation (1.1), the direction and speed of the two outgoing electronsshould reflect the initial momentum of the bound target electron.A favorable experimental configuration for the detection of these (e,2e) scattering events(i.e. one electron in, two electrons out) is the symmetric non-coplanar geometry [5,6,7],presented in figure 1.1. In this geometry, only those events in which both outgoing electronshave equal energies E5 = Ee and polar angles of Os = 9e = 45° are detected. The collisionprocess can be summarized bye + [e + M] —* e + + MEnergy E0 E5 Ee (1.2)Momentum p0, q] Ps Pe qwhere e0, e and ee represent the incident, scattered and ejected electron respectively, erepresents the target electron prior to the collision event, and M represents the final ion.Chapter One Introduction 4DetectionCirclee600 eVee600 eVTarget1200 eV+IP (E0)eFigure 1.1: The symmetric non-coplanar (e,2e) scattering geometry.Chapter One Introduction 5Under the conditions typically used in EMS, the target species, depicted by the terms in squarebrackets, may be assumed to be at rest. As well, the ion can be thought to be spectator of thecollision event, having a recoil momentum q equal in magnitude and opposite in direction tothe momentum of the target electron. If the very small recoil energy of the ion is neglected,the binding energy or ionization potential (IP) of the target electron is given by the energydifference of the neutral target and the final ion species. This energy must be equal to thedifference of the incident and outgoing electron energies in an ionizing collisionIP = Eo — E5— Ee. (1.3)The momentum of the ejected electron prior to the collision is given by equation (1.1) which,in the non-coplanar symmetric geometry at °e = Os = 45°, can be expressed asPt = J(2pe_po)2 +2psin(p/2). (1.4)The probability of detecting two outgoing electrons of equal energy from an ionization event,at polar angles of 45° and relative azimuthal angle q, is directly proportional to the probabilityof the target electron having the initial momentum given by equation (1.4). By measuring thisprobability at a number of relative azimuthal angles and at the appropriate impact energy, themomentum distribution of a binding energy selected electron in the target is obtained.The distributions measured in EMS are often referred to as experimental momentumprofiles (XMPs). The strength of EMS lies in the fact that the XMPs of valence electrons are,Chapter One Introduction 6to a very good approximation, proportional to the square of the momentum spacewavefunction of the respective target electrons. In a more rigorous treatment, the momentumprofile is calculated by the overlap of the total electronic wavefunctions of the ion and neutralspecies. Thus the measurement of the experimental momentum profiles gives a unique meanswith which to examine and evaluate theoretical electronic wavefunctions of atomic andmolecular systems and their ions.1.2 Early Instrumental DevelopmentsThe first instrument developed to measure (e,2e) scattering was reported by Ehrhardt etat. [8] in 1969. This instrument was designed to observe the scattering of slow (-.100 eV)electrons from a gas in a coplanar geometry, to provide a test for theories of low energyelectron impact ionization. In the same year, Amaldi et at. [9] reported the development of ahigh impact energy (14.6 keV) symmetric coplanar instrument designed to measure themomentum distributions of electrons in thin film targets, via the (e,2e) reaction. This work [9]presented binding energy spectra of the carbon is electron, obtained at 0 = 0e = = 45° andO = 410 corresponding to two values of initial target electron momentum. These initial studieswere followed by measurements of the angular distributions (i.e. momentum profiles) of thecarbon K shell (is orbital) and L shell (2s and 2p orbitals) by Camilloni et at. [10]. Theexperimental energy resolution in the studies by Amaldi et al. and Camilloni et at., (135 and64 eV FWHIvI respectively) was not sufficient to permit the valence structure of the targetspecies to be resolved. In 1973, Weigold et at. [11] reported the development of anChapter One Introduction 7instrument configured to observe symmetric non-coplanar scattering on gas phase targets.With an energy resolution of 4.3 eV [12], the momentum profiles of the outer valence regioncould be measured for the first time. A similar instrument to that of Weigold et al. wasdeveloped shortly thereafter at the University of British Columbia [13].The design of the ‘first generation’ of symmetric non-coplanar spectrometers ispresented schematically in figure 1.2. The polar (0) and azimuthal (q) angles of observed(e,2e) scattering events are selected by apertures positioned at the entrance of each of a pair ofenergy analyzers. The analyzers disperse the electrons on the basis of their energies by meansof a potential difference applied across the inner and outer surfaces. An aperture at the exit ofeach analyzer passes only those electrons having energies within a narrow range. The energyand angle selected electrons are detected by single channel electron multipliers (CEMs). Withthe appropriate circuitry, these devices permit individual electron detection [14,15] via anelectron cascade initiated by the impact of an electron having sufficient energy. In these ‘firstgeneration’ instruments, one of the assemblies consisting of entrance and exit apertures,energy analyzer, and detector, is able to rotate about the azimuth while the other is fixed inposition.Coincidence timing is used to identify an (e,2e) collision event. In all EMS experimentsto date, timing information has been provided by a time-to-amplitude converter (TAC), whichgives an output voltage signal proportional to the time delay between two pulses. A singlechannel analyzer is typically employed in conjunction with a TAC to detect coincidence eventsChapter One Introduction 8Figure 1.2: A schematic of a single channel symmetric non-coplanar (e,2e)spectrometer. The right side shows a cross sectional view of a stationary analyzer,while the left side displays a three-dimensional outline of a movable analyzer at arelative azimuthal angle q. The polar (0) and azimuthal (p) angles of electronsscattered from the collision region are selected by the lower circular apertures ofthe analyzers. Electrons in the analyzers are deflected by the applied potential, andthose having the appropriate energy will pass through the upper apertures, wherethey may be detected by the CEMs.(Chapter One Introduction 9occurring within a set time window. The instruments are operated in two modes. A bindingenergy spectrum is obtained at a fixed position of the analyzers by accumulating coincidenceevents while the incident electron energy E0 is scanned. The measurement of a momentumprofile of electrons having a particular IP is performed by counting coincidence events at theappropriate impact energy while sequentially stepping the movable detector assembly througha range of azimuthal angles (typically 00 to ±30° at E0 = (1200 eV + IP)).1.3 Experimental Studies by EMSThe application of the fully kinematically determined (e,2e) scattering experiment to theinvestigation of electron momentum distributions was first explored theoretically byNeudachin et at. [16,17] and these ideas were developed further by Glasgold and lalongo[1811. Following the thin film measurements of Amaldi et at. [9] and Camilloni et at. [10], thefirst measurements of the valence orbitals of gas phase atoms (Argon 3p,3s) [11] andmolecules (H2 i5Gg [19], CH4 it2 and 2a1 [12]) were reported in 1973. In the two decadessince these landmark measurements, EMS has developed into a sensitive technique with whichto investigate electronic structure. Recent reviews [7,20,21,22] give a good overview of themeasurements of the more than 70 atomic and molecular species that have been investigatedwith EMS. A brief discussion of a few particularly significant EMS studies is given below.1t should be noted that an earlier reference to the extension of the (p,2p) scattering technique to atomic andmolecular systems was made by Baker, McCarthy, and Porter in 1960 [1761Chapter One Introduction 10Perhaps the most fundamental EMS investigation is the study of the hydrogen atom byLohmann and Weigold [23]. Atomic hydrogen was formed by the dissociation of H2 in a dcdischarge tube. As the ground state of atomic hydrogen has an ionization potential (13.6 eV)well separated from that of molecular hydrogen (- 16 eV), its momentum profile could bemeasured despite the abundance of H2 in the collision region. The wavefunction of thehydrogen atom is known exactly, and the experimental momentum profile should be directlyproportional to the square of the is orbital momentum space wavefunction given byIw1(p)I2=8it_2(1+p2Y. (1.5)Excellent agreement between theory and experiment was observed, providing a directexperimental verification of the solution of the Schrodinger equation for the ground state ofthe hydrogen atom.As the simplest system in which electron correlation is present, helium is an interestingsystem for study by EMS. The transition of the helium atom to the ground state of the ioncorresponds to an ionization potential of 24.6 eV. The momentum profile measured at thisbinding energy is well described by the theoretical profile using a near SCF limit wavefunction1[5,24,25,26]. The transition from the ground state of helium to the first excited ion state (P =65.4 eV) is experimentally and theoretically more complex. Early studies [5,27] of themomentum profiles for this transition indicated that the inclusion of electron correlation in thewavefunction of the atom was required in the calculation of theoretical momentum profiles. A1 A description of SCF and CI wavefunctions is given in chapter 2.Chapter One Introduction 11number of theoretical profiles for this transition have been calculated using very accurate CIwavefunctions [26,28,29] and have exhibited a significant variation, reflecting the sensitivity ofthe EMS scattering process to initial state electron correlation and to wavefunction quality.However, the transition to the excited ion state has a much lower cross section than thetransition to the ground ion state, and accurate measurement of the shapes and relativeintensities of the momentum profiles for these transitions is difficult. The statistical precisionof the experimental momentum profiles of the initial and subsequent investigations [26,30,311,is insufficient to clearly distinguish amongst the various theoretical profiles, calculated withdifferent correlated wavefunctions.The momentum profiles of the molecular hydrides of second and third row heavy atoms(Cm, NH3H20, HF; SiH4,PH3,H2S, HC1) have been the subject of extensive investigationby EMS [13,32-451. Experimental momentum profiles (XMPs) for the outer valence orbitalsof water, reported by Bawagan et at. in 1985 [36], showed a remarkable discrepancy withtheoretical profiles obtained using what were considered to be high quality SCF calculations.In particular, the XMPs of the lb1 and 3a1 orbitals exhibited increased intensity at lowmomentum relative to the theoretical momentum profiles. Interestingly, results for the otherhighly polar second-row hydrides, FLF [42] and N}13 [13], showed similar discrepancies withtheoretical momentum profiles using SCF wavefunctions, while the corresponding third rowhydrides HC1 [42], H2S [46], and PH3 [47], were well described by theoretical profiles at thislevel of theory. One suggestion for the observed discrepancy in water [36] was theChapter One Introduction 12inadequacy of the variationally determined wavefunction to describe the long range behaviourof the molecular systems. The momentum profiles obtained by EMS investigate the lowmomentum region of molecules which corresponds to larger distances from the nuclei.Indeed, further investigations involving the addition of extra diffuse and polarization functionsto the basis set of the SCF calculations produced theoretical momentum profiles exhibitingsignificantly improved agreement with the XMPs of water [37]. Importantly, very littlechange in the total electronic energy of the SCF wavefunction was observed with thisenhancement of the basis set. The inclusion of electron correlation and relaxation effects byusing CI wavefunctions for the ion and neutral species, built with the diffuse and saturatedGaussian basis sets developed in the SCF calculations, was also found to have a significanteffect on the shape of the theoretical momentum profile, and adequate treatment of theseeffects was required to obtain good agreement with experimental EMS results. Additionally,these studies have revealed the need for an accurate accounting of momentum (angular)resolution effects in comparing theory and experiment. Small discrepancies were still observedat low momentum when the high quality theoretical momentum profiles were folded with asingle Gaussian momentum resolution function. These discrepancies were eliminated [20]when the experimental resolutions in the polar and azimuthal angles (z and Ap) were takeninto account separately [48,49].With a recent reinvestigation of HF [44] and HC1 [45], the disagreement between thetheoretical and experimental momentum profiles has been resolved for the row two and threeChapter One Introduction 13hydrides. The studies indicate that the highly polar second row hydrides HF, H20 and NH3each require a large degree of polarization and extremely diffuse functions in highly saturatedbasis sets to properly describe the low momentum (outer spatial regions) of the molecule.Furthermore, the use of highly correlated wavefunctions for both the neutral and ion species isrequired in the theoretical calculation of momentum profiles. The EMS study of water andother second row hydrides revealed the power of EMS to provide information on thechemically important outer spatial regions of molecular charge distributions, where changes inelectron density have little effect on the variationally determined electronic energies. Thesestudies have also aided in the development of improved molecular wavefunctions that yieldextremely accurate one-electron properties [20,37,50,511.The first EMS study of an oriented and excited target was recently reported by Zheng etal. [52]. In this experiment sodium atoms were excited by circularly polarized light. With thez axis selected to be along the direction of the incident electron beam, the 3p (m1 = + 1) state,was populated while the 3p (mi = 0) state (i.e. 3Pz) remained unoccupied. The binding energyof the 3p electron is sufficiently less than that of the Na 3s electron to enable the ionization ofthe 3p electrons of the excited atoms to be distinguished from ionization of the ground stateatoms, and momentum profile of these electrons was obtained. Good agreement was foundbetween the Na 3p XMP and the theoretical momentum profile using the Hartree-Fock 3p(mj = +1) wavefunction. Momentum profiles calculated for the unoriented Na 3p (m1 = 0, ±1)states gave significantly poorer agreement with the experimental data. While this studyChapter One Introduction 14involves a relatively simple system, it portends the likely direction of future EMS studiestowards prepared and more well defined target species.1.4 Multichannel Instrumental DevelopmentsThe mo4ern architecture of EMS spectrometers has evolved from ‘first generation’instrumental designs. The early EMS instruments described above are termed single channel,as they measure (within experimental resolution) scattering events for a single binding energyand a single relative azimuthal angle (it - q) between the outgoing electrons. However, valid(e,2e) collision events from all the target valence electrons occur at all angles of full 2iuazimuth. The vast majority of these scattering events is not measured with a single channelinstrument. The natural progression from the first generation instrumentation was theapplication of multichannel or multiparameter techniques to observe simultaneously as many(e,2e) events as possible. Two approaches were taken: one to sample a range of energies, theother to sample a range of azimuthal angles.The first momentum (azimuthal angle) dispersive multichannel spectrometer wasdeveloped by Moore et at. [53]. This instrument uses a single truncated spherical analyzer toprovide energy analysis over a large range of azimuthal angles. Detection of electrons at anumber of angles is achieved by 14 channel electron multipliers [54] (increased from theoriginal 10 CEMs [53]) that are dispersed in two banks of seven; one bank in a narrow angularspread, the other more widely dispersed on the opposite side of the detection circle.Chapter One Introduction 15Coincidence events are determined via a TAC using the start pulse from any one of thechanneltrons in one bank, while the stop is given by any one of the channeltrons of theopposing bank. With the appropriate signal processing, this arrangement gives thesimultaneous measurement of 49 relative azimuthal angles, and hence a possible enhancementof 49 in collection rate. In practice however, the use of an array of channeltrons formultichannel detection has limited the effectiveness of this instrumental design, since the gainsof individual CEMs are different from device to device and are subject to variation with timeand experimental conditions [54,55,56]. Frequent calibration of the instrument to a singlechannel measurement of the argon 3p orbital is required to circumvent this difficulty [54]. Inpractice, the statistical precision of the data obtained with this multichannel instrument [54]has been little different from that achieved in single channel instruments.The energy dispersive multichannel approach has been pioneered and developed byWeigold et at. [7,26,57]. An improvement of approximately an order of magnitude incollection efficiency is achieved by the simultaneous measurement of a range of outgoingelectron energies. The general design is similar to that of single channel instruments, shown infigure 1.2. A pair of hemispherical analyzers is used to disperse the outgoing electrons, and aslit aperture is used in place of the typical circular aperture in the exit plane of the analyzer. Amicrochannel plate/resistive anode encoder (MCPIRAE) assembly provides electronmultiplication and positional determination of the electrons in the exit plane of the analyzers.The radial position of an electron at the exit plane of the analyzer is approximately a linearChapter One Introduction 16function of the electron energy [57]. Thus a spread of outgoing energies can be measuredsimultaneously while maintaining the required energy resolution. As in single channelinstruments, a complete binding energy spectrum is obtained by sweeping the energy of theincident electrons through the desired range of binding energies, and a momentum profile ismeasured by scanning one hemispherical analyzer about the azimuthal detection circle. ATAC is used for the determination of coincidence events, and improved timing is provided bysoftware correction for the variation in transit times of different electron paths through theanalyzers [57].Following the initial (e,2e) measurements on solid targets [9,101, the attention of EMSstudies in the past 20 years has been primarily directed towards gas phase systems. EMSmeasurements on solid targets are obviously of great interest, but such studies are hamperedby the often high (background) accidental coincidence count rate, and by the necessity formuch larger (-.20-25 keV) electron impact energies to minimize multiple scattering effects.This significantly reduces the (e,2e) coincidence count rate, and increases the experimentaldemands on energy and momentum resolution [58,59]. A new spectrometer for the study ofthin (<100 A)solid films has recently been developed by Storer et al. [60], that combineslimited ranges of both energy and momentum dispersive multichannel operation. Thisinstrument [60] employs a toroidal analyzer and a hemispherical analyzer in an asymmetricgeometry, with both analyzers designed to accept electrons from a range of azimuthal angles.Two-dimensional MCPIRAE detectors positioned at the exit plane of each analyzer provideChapter One Introduction 17energy and angular information. An asymmetric geometry was chosen to take advantage ofthe higher cross section of asymmetric (e,2e) scattering over the symmetric case [61]. Bindingenergy spectra of the valence region of carbon have been presented as a function ofmomentum [60] and illustrate the potential of the new instrument to study the electronicstructure of thin films.1.5 Context and Organization of this WorkElectron momentum spectroscopy provides unique insight into the electronic structureof atomic and molecular systems, and fruitful collaborations with theoretical groups havedeveloped in recent years. Future directions in EMS will involve the study of more interestingand complex target systems. Larger molecules of chemical and biochemical importance, vander Waals complexes, oriented molecules [62], molecules oriented on a surface [63], as well asexcited molecules, free radicals and ions are all on the EMS ‘wish list’. However, relative tosmall atoms and molecules, many of these systems have more closely spaced valence energylevels, and can only be produced with low number densities (three to five orders of magnitudeless than common gas targets). Both the required improvement of energy resolution and thenecessarily low target densities will dramatically reduce the count rate of EMS coincidenceevents. Significant improvements in the detection efficiency of (e,2e) spectrometers aretherefore required before measurements for these systems become feasible.Chapter One Introduction 18The earlier multichannel developments offer some insight into potential avenues for theimprovement of EMS detection capabilities. The energy dispersive multichannel EMSspectrometer [26] has effected an order of magnitude improvement in sensitivity (i.e. detectionefficiency), and has been quite successful in the measurement of relatively small, gas phasetargets. However, the design suffers from the complexity involved in physically rotating andreproducibly positioning one of the energy analyzers to scan a range of momentum. Thesequential scanning requires that experimental conditions (i.e. the incident electron gun currentand target number density) remain constant during a measurement period, and additionally,necessitates significant analysis and reassembly of the experimental data to extract theindividual orbital momentum profiles of the target. As well, only a relatively narrow range ofbinding energies can be sampled simultaneously, and the potential for further development ofthe instrumentation to improve sensitivity is limited. The momentum dispersive approachoffers the advantage of using a single analyzer with no moving parts. The relatively simpledesign allows for greater precision in the construction and alignment of the spectrometer.Furthermore, such an instrument can be designed to simultaneously detect events over a widerange of azimuthal angles, permitting the complete XMP (i.e.— 0-2.5 a.u.) to be measured forany selected binding energy. Accordingly, the XMP measurements are relatively insensitive tofluctuations in experimental conditions. However, the instrumental design requires uniformdetection efficiency of electrons over the observed azimuthal range. In this respect, the use ofindividual channeltrons to provide detection about the azimuth has proven to be problematic[54].Chapter One Introduction 19This thesis presents the development and application of a new momentum dispersivemultichannel electron momentum spectrometer incorporating several new design features inboth the spectrometer hardware and the coincidence detection electronics. The spectrometeremploys a single cylindrical mirror analyzer (CMA) to provide energy analysis of (e,2e)electrons over a wide range of azimuthal angle. A two-dimensional microchannelplate/resistive anode encoder position sensitive detector and a single channel electronmultiplier at the exit of the CMA gives parallel detection of electrons over a ± 300 range ofazimuth. Furthennore, a novel technique for the determination of (e,2e) coincidence eventshas been implemented. Based on the discrimination of pulse-pile-up of pairs of detector timingpulses, this coincidence detection scheme possesses distinct advantages over conventionalTAC-based coincidence timing techniques. With such a design, the spectrometer shouldprovide an improvement of one to two orders of magnitude in sensitivity relative to singlechannel instrumentation.The development of the new multichannel spectrometer is the focus of chapter 3. Thedesign, operation and testing of the electron source, collision region, lens system, cylindricalmirror analyzer, CEM and MCPIRAE detectors, coincidence timing electronics, and the dataacquisition system are discussed in some detail. Proof-of-concept test measurements of argon,exhibiting the enhanced performance of the new spectrometer, are presented. Additionally,the two-dimensional surface displaying the angular (momentum) intensity as a function ofChapter One Introduction 20binding energy for the valence electrons of argon is presented. A description of the newinstrument and some proof-of-concept results have appeared in the literature as:B.R. Todd, N. Lermer, and C. E. Brion, Rev. Sci. Instrum. 65 (1994) 349.Prior to the description of the spectrometer in chapter 3, the theoretical analysis of the(e,2e) cross sections measured in EMS is briefly discussed in chapter 2. Since detailed reviewsof the scattering theory and the approximations used in the development of the theoreticalmomentum profiles have been published [64,65], only a summary is provided here.Additionally, a short comment on the more common approaches to calculating the electronicwavefunction of atoms and molecules is presented.In chapter 4, binding energy spectra and experimental momentum profiles of the outervalence orbitals of Ne, Ar, Kr, and Xe, and of the molecular systems of CH4 and SiH4 areshown. These measurements provide a thorough examination of the performance and angularresolution of the new instrument. As well, the XMPs represent the most statistically precisemeasurements of these systems to date. The profiles are compared to earlier EMSmeasurements and to theoretical momentum profiles calculated using wavefunctions of variouslevels of quality.Measurements of the (e,2e) ionization of helium and molecular hydrogen are presentedin chapters 5 and 6 respectively. Momentum profiles are presented for the ionization of theChapter One Introduction 21ground state neutral target to the ground state of the ion, as well as for ionization to excitedion states. As the final states of each of these systems have only one electron, the ionwavefunctions can be expressed exactly (within the Born-Oppenheimer approximation in thecase of H2). Hence, these systems are ideal for the detailed study of ground state electronicwavefunctions, and in particular, electron correlation effects. Previous investigations of Heand H2 have been hampered by the extremely low cross sections for ionization to the excitedion states. The improved detection efficiency of the new multichannel instrument haspermitted detailed measurements of these systems. The experimental profiles of He arecompared with momentum profiles based on extremely high quality correlated wavefunctions,including an explicitly correlated calculation by N. Cairn here at UBC, and very large CIcalculations performed by E.R. Davidson of Indiana University. The XMPs of H2 arecompared to ground and excited state momentum profiles calculated by J.W. Liu and V.J.Smith Jr. [66]. To examine the influence of molecular vibration, the multichannel XMPs of D2for the transitions to the excited ion states are compared to the H2 measurements. Differencesobserved between the experimental and theoretical results are discussed.It should be noted that throughout this thesis experimental momentum profiles arepresented in atomic units (a.u.) where 1 a.u. of momentum is equivalent tol.9929x1024Kg rn/s. Additionally, the total electronic energies associated with thewavefunctions used in the calculation of theoretical profiles are presented in atomic units ofenergy, where 1 a.u. is equivalent to 27 .212 eV.Chapter TwoTheoretical Background2.1 The EMS Scattering Cross SectionThe ionization of atoms and molecules by electron impact is an important physicalprocess that continues to be an area of considerable interest and investigation bothexperimentally and theoretically [65,67,68]. The probability of a given outcome of an electronimpact ionization is expressed by the scattering cross section, which, ideally, accounts for theinteraction of an incoming electron with all of the electrons and nuclei of the target system.However, approximations are required to describe this many-body interaction. The particularapproach used to simplify the cross section calculation is dependent on the scatteringkinematics: principally the energies of the incident and outgoing electrons, and the momentumtransfer. The momentum transfer, K = Po - Ps, is related to the classical concept of the impactparameter, with a small momentum transfer suggesting a soft or glancing coliision, while alarge momentum transfer suggests a hard or direct collision [69]. In electron momentumspectroscopy, the experiment is designed to observe ionizing collisions having high momentumtransfer and high kinetic energies such that the description of the complex scattering process isgreatly simplified. Ideally, measurements in EMS are a direct reflection of the target22Chapter Two Theoretical Background 23properties rather than the scattering physics. The theoretical treatment of the EMS scatteringcross section has been investigated in detail by McCarthy and Weigold [5,7,64,701. A briefoverview is given below.The triple differential cross section for an (e,2e) reaction can be written as [7,711d3cY= (21t)4.IMfI2 (2.1)e 0 avewhere E is the energy of the ejected (or scattered) electron, 2 and 2e are the outgoingelectron solid angles, and Mf is the scattering amplitude, given byMf =(xxqi4-l T(E) ‘Vx,j. (2.2)In this equation, represent wavefunctions of the incident (+) and outgoing (-) electrons inthe target scattering potential, T is the transition operator, and ‘P and {J represent thetotal wavefunctions of the ion and neutral species respectively. The high electron energies andlarge momentum transfer permit the scattering process to be viewed as an impulsive, binarycollision of the incident and target electrons. A nice physical picture of the impulseapproximation has been recently given by Hall, Reading and Ford [721:During the collision the (target) electron does not move very far, if at all. Ittherefore has no time to sense the forces binding it to the target nucleus; theymerely determine some distribution of electronic momenta and position. Duringthe collision the electron can be considered as recoiling freely. The simplifyingnature of this assumption is that this problem now reduces to a two-body collision,which is soluble if we know the projectile-electron t-matrix.Chapter Two Theoretical Background 24In the binary encounter approximation, the operator T depends only on the coordinates of theincident and target electron, and commutes with the ion wavefunction to giveMf =(xx IT(E)I (‘frI “)xj. (2.3)If the wavefunctions of the incident and outgoing electrons are represented as distorted waves,the cross section using equation (2.3) is referred to as the distorted wave impulseapproximation (DWIA); however, the calculation of the transition amplitude using thisequation is prohibitively difficult [73]. At sufficiently high impact energies, plane waves maybe used to represent the incident and outgoing electrons. In the plane wave impulseapproximation (PWIA), the scattering amplitude may be factorized into a collision term and astructure term, to giveMf = (k’It(E)Ik)(Xx ‘i’) x) (2.4)where t(E) is the two electron t-matrix, and k = (p0—p) and k’ = (p—are the relativemomenta of the two electrons before and after the collision.The square of the first term in equation (2.4) is the (half-off-shell) Mott scattering crosssection GMott, which describes the Coulomb scattering of two electrons including the possibilityof exchange. This term can be expressed exactly, and has a simple form in the symmetric noncoplanar geometry [25]. In figure 2.1, the variation of the Mott cross section with azimuthalangle, using typical values of 0 = 450 and E = Ee = 600 eV, is presented for impact energies ofChapter Two Theoretical BackgroundCC,,Cl)Cl)0L)0Figure 2.1: The Mott scattering cross section for symmetric non-coplanarkinematics with 8 = 45°, E1 = E2 = 600 eV, for three values of impact energy.2510864200 20 40 60 80 100 120Relative Azimuthal Angle 0140 160 180Chapter Two Theoretical Background 261215.8, 1224.6 and 1265.4 eV. These energies (less 1200 eV) correspond to the ionization ofan electron from the argon 3p orbital, and to the transitions from the ground state of He to theground and first excited states of the He ion. While the decrease in cross section is small formeasurement over the outer valence region of atoms and molecules, the change must beconsidered when, as for some experiments in the present work (chapter 5), a large range ofbinding energies is investigated. It is most important to note that, for a given impact energy,the Mott cross section is essentially constant over the range of ( angles at which observationsare made in an EMS experiment. This is in contrast with the large variation of the Mott crosssection inherent to the symmetric coplanar geometry (ci = 00, Oe = O) [741.The plane waves in the structure term of equation (2.4) are given by 2& =e’ andsince Pt = Pe + Ps - Po (eqn. 1.1), the equation can be rewritten asIMf 2aM0(ePt’ N9 N)2 (2.5)such that the (e,2e) scattering cross section in the PWIA is:aEMS dE dsd2e= (2ic) PePs E (ePtv9’2. (2.6)The term denotes the average over degenerate initial states and the sum over unresolvedavefinal ion states. Thus, as GMOtt is effectively constant at a given impact energy, the crosssection observed in an EMS experiment is explicitly dependent on the overlap of the initialChapter Two Theoretical Background 27target and fmal ion wavefunctions. A theoretical momentum profile evaluated using the crosssection expression of equation (2.6) is often referred to as an overlap distribution (OVD).In the case of molecular targets, the molecular and ionic wavefunctions are expressed(using the Born-Oppenheimer approximation) as products of electronic, vibrational androtational functions. Since vibrational and rotational states are not resolved in typical EMSexperiments, the cross section is summed over the final rotational and vibrational states, andthe final rotational and vibrational wavefunctions are removed from the cross sectionexpression (via a closure relation) [7,64]. The rotation of the (randomly oriented) gaseoustarget species is accounted for by spherically averaging over the nuclear coordinates (2) orequivalently by spherically averaging over the direction of the target electron momentum. Thevibrational motion of the target molecule requires that the cross section be integrated over thevibrational coordinates, with the electronic terms evaluated at each nuclear geometry andweighted by the absolute square of the vibrational wavefunction [7]. However, the influenceof vibrational motion on the cross section is commonly approximated by evaluating theelectronic overlap at the equilibrium geometry of the target molecule (see section 6.4). ThePWIA EMS cross section for molecular species is now given asGEMS = (2it)4 P;Ps GMott fd (e’Jt’2(2.7)where p’ and ‘p are the ion and neutral electronic wavefunctions.Chapter Two Theoretical Background 28Often the target Hartree-Fock approximation (THFA) is employed, which permits asimplification of the form of the ion-neutral overlap (e1Pt PN). If the targetwavefunction is approximated by an antisymmetrized product of one-electron wavefunctions(i.e. canonical Hartree-Fock orbitals), the integral over the coordinates of the target electroncan be separated from the integral over the coordinates of the remaining electrons. This gives(eit’ ‘{J’ ‘i’) =(P’ _1) Je1P (r) dr (2.8)where is the Hartree-Fock wavefunction of the target, with an electron removed fromthe orbital . The square of the overlap (‘P9 F_1) is termed the spectroscopic factor s.The integral on the right hand side of equation (2.8) is just the Fourier transform of theposition space canonical Hartree-Fock orbital Thus, in the THFA, the EMS cross sectionis expressed asGEMS= constant S Jdp ø(P)2. (2.9)Within the framework of the PWIA and TI{FA, the experimental momentum profile is directlyproportional to the spherically averaged square of the momentum space orbital occupied bythe target electron before the ionization process.The experimental (e,2e) coincidence count rate is related to the atomic or molecular(e,2e) cross section (equation 2.6 or 2.7) byN =nIaEMs M2a Acb LEa LEb EoEaEbIP) (2.10)Chapter Two Theoretical Background 29where A2 and AE are the solid angles and resolution of the energy analyzers labeled a and b, nis the number of target species in the collision region, and I is the rate of incident electronsthrough the collision region [5]. Typically in EMS studies the measured cross sections are notabsolute, since neither n nor I are usually determined. However, the experimental parametersof equation (2.10) are (essentially) constant over the valence region of the target species, andthe EMS momentum profiles are measured with the correct relative intensities. Only onenormalization of theory and experiment is required for the valence region of a given species.Hence, the normalization of an XMP of one orbital to a corresponding theoretical profiledetermines the relative intensities of the XMPs of other valence electrons.The comparison of the theoretical and experimental momentum profiles for inner valenceelectrons may be complicated by the often significant splitting of the main peak intensity to thesatellite peaks that arises from electron correlation effects (primarily final state correlation).However, the sum of the spectroscopic factors is governed by the sum rule5t.1 (2.11)fwhere the summation is over the final ion states associated with the ionization of an electronfrom orbital Ø (i.e. over the symmetry manifold t). As the spectroscopic factors are reflectedin the relative peak areas of the binding energy spectra, the sum of the peak areas over mainand satellite transitions permits a direct comparison to the theoretical cross sections, using aspectroscopic value of unity (see chapter 4).Chapter Two Theoretical Background 30The viability of the plane wave impulse approximation is crucial for the application ofEMS to investigations of electronic structure. As the approximation is based on the neglect ofthe interactions of the free (incoming and outgoing) electrons with the neutral target and finalion, the PWIA is expected to be increasingly valid at higher impact energies. A convincingtest of the approximation is given in the EMS measurements of atomic hydrogen [231discussed in chapter 1. The XMP measurements at impact energies of 400, 800 and 1200 eVshow very good agreement with each other as well as with the theoretical momentum profilecalculated in the PWIA using the exact wavefunction of the hydrogen atom. Experience hasindicated that the PWIA analysis is valid for the EMS investigation of the outer valenceregions of atoms and molecules in the momentum region from 0 a.u. to —1.5 a.u., provided theelectron impact energy is greater than 1000 eV [6,64,75]. This range covers the majority ofthe momentum region typically observed in an EMS experiment.At higher values of momenta ( 1.5 eV) the PWIA often underestimates theexperimental intensity. This effect is not unreasonable, since the higher momentum regioncorresponds to ionization from regions closer to the nuclei, where distortion of the incidentand outgoing electron waves by the target and ion potentials is expected to be larger [30]. Inthe case of atoms, the influence of the ionltarget potentials on the (e,2e) cross sections can bepartially restored by the use of the factorized distorted wave impulse approximation (DWIA)[27,73]. In this approximation, the factorized form of the scattering amplitude shown inChapter Two Theoretical Background 31equation (2.3) is retained, and distorted waves,calculated in the static potential of thetarget and the ion, represent the incoming and outgoing electrons. Although the factorizationof the scattering amplitude is not exact in this approximation, it has been shown to be valid forscattering in the symmetric non-coplanar geometry [73]. In studies of the noble gas atoms, thetheoretical cross sections evaluated in the (factorized) DWIA have shown improved agreementwith experimental momentum profiles, in the higher momentum region [27,76].The direct comparison of experimental and theoretical momentum requires aconsideration of the necessarily fmite experimental angular resolution. This is achieved by‘folding’ the estimated experimental resolution into the theoretical profile. The ip method is aprocedure that has been used to account for the instrumental resolution by folding thetheoretical cross section with a singleGaussian momentum resolution function. However,such a resolution function is unphysical [48,49] as the experimental resolution originates fromthe uncertainty (experimental spread) in angular coordinates, rather than in momentumcoordinates. An improved resolution-folding procedure, titled the Gaussian-weighted planargrid (GW-PG) method, has recently been reported by Duffy et al. [49]. This method is anextension of the momentum-averaged Gaussian-weighted (MAGW) formalism [48], which isitself a modification of the uniformly weighted planar grid (UW-PG) technique [35,77]. Incontrast to the Ap method, the GW-PG method uses individual Gaussian resolution functionsfor the azimuthal (p) and polar (0) coordinates in the calculation of p-dependent momentumresolution functions. At low values of p, the GW-PG momentum resolution function is non-Chapter Two Theoretical Background 32symmetric and has a tail extending to higher momenta. At higher values of momentum, amore symmetric, Gaussian-shaped function is generated (see fig. 3 of ref. [49]). Theoreticalmomentum profiles folded with such a procedure show an increase in the intensity at lowmomentum relative to the Ap method, and comparison of GW-PG folded TMPs calculatedusing very accurate wavefunctions, have exhibited significantly improved agreement withexperimental measurements for a wide range of systems. [20,49]. With a few notedexceptions, the TMPs presented throughout this thesis have been folded with the GW-PGprocedure.2.2 The Calculation of Electronic WavefunctionsIn 1959, Professor Charles Coulson2gave the closing address to participants of theConference on Molecular Quantum Mechanics held in Boulder, Colorado. Commenting onclues into the direction of future work, he suggested that “the most important clue seems tome to be the recognition that the energy is not the only criterion of goodness of a wavefunction. In the past we have been preoccupied with energy”. The preceding section hasshown the EMS cross section to be directly proportional to the overlap of the ion and neutralelectronic wavefunctions, which, in the THFA, is proportional to the square of the momentumspace orbital of the target electron. As the EMS momentum profiles investigate the lowmomentum, spatially diffuse regions of a wavefunction that have only small influence on the2j should be noted that C.A. Coulson, along with W.E. Duncanson, wrote a series of landmark papers[177-1821 in the early 1940’s, pioneering the investigation of the chemical bond from the perspective of momentumspace, rather than position space.Chapter Two Theoretical Background 33total electronic energy, EMS measurements are able to provide an additional “criterion ofgoodness” [78] for the assessment of an atomic or molecular wavefunction.The most common techniques for the calculation of wavefunctions are based on thevariational principle. Given the equation Yi = lo C1o where Y€ is the Hamiltonian, cI is theexact ground state wavefunction, and lo is the corresponding energy, then the expectationvalue of the Hamiltonian of a normalized wavefunction IWo) is an upper bound to the exactground state energy(‘p0IY€I’v)eo. (2.11)Thus in the variational method, the wavefunction that is assumed to be the best approximationto the exact wavefunction is the one calculated to have the lowest energy. The capability ofthe wavefunction to yield accurate atomic or molecular properties, including the momentumdistribution, depends on both the computational technique, as well as the quality of buildingblocks, or basis set, used in the calculation. As suggested by Shavitt [79], “it is a truism thatno calculated wave function can be better than the basis set from which it is constructed.”In the following sections the computational methods of Hartree-Fock andConfiguration Interaction, which are referred to throughout the thesis, are discussed. Onlybrief outlines are given as these computational techniques are well described in most modernquantum chemistry texts (see for example Levine [51], or Szabo and Ostlund [80]).Chapter Two Theoretical Background 342.2.1 The Hartree-Fock MethodThe (non-relativistic) electronic Hamiltonian operator for an N-electron system with Mnuclei can be written in atomic units asN NMZ NN1Y=_v12—+— (2.12)A=1 nA i=1 rwhere the first term represents the kinetic energy operator, the second the attraction betweenelectrons and nuclei, and the third the mutual repulsion of electrons. The difficulty of solvingfor the eigenfunctions of the Hamiltonian arises from the term since as a result of this termthe Schrodinger equation is non-separable. The Hartree-Fock approach circumvents thisdifficulty by averaging over the individual electron-electron interactions.In the Hartree-Fock approximation, the wavefunction of an N-electron system isdescribed by a single Slater determinant.(2.13)where the spin-orbitals are functions of the coordinates and spin of electron i. It can beshown that the wavefunction of this form that minimizes the energy given by (‘v0 Y€I ‘p0) is theSlater determinant composed of one-electron functions that are eigenfunctions of the HartreeFock equationf(1) X(1)) = g x(1)) (2.14)Chapter Two Theoretical Background 35wheref is the one-electron Fock operator. The Fock operator can be written as(2.15)2 AriAto emphasize the treatment of the electron interaction by an average potential of the otherelectrons of the systems,v. This potential is written more explicitly asvHi(l)=j(1)—XJ(l) (2.16)where is the coulomb operator given byr, (2.17)is the exchange operator defined byX(1)X(1)=[$dx2X(2)rXi(2)]j(1) (2.18)and where x2 represents the space and spin coordinates of an electron, labeled here as electron2.The Hartree-Fock orbitals are expressed as the sum of a set of basis functions, eachscaled by a coefficient:X=CviØ,. (2.19)Chapter Two Theoretical Background 36As the Fock operator itself is dependent on the one-electron functions, the solution of theHartree-Fock equation involves the iterative calculation of the basis function coefficients. Aninitial set of orbitals is used to evaluate a new set of orbitals, and the process repeated until theorbital coefficients no longer change, a procedure referred to as the self-consistent-field (SCF)method. The energy obtained from this procedure is dependent on the size and nature of theset of basis functions, or basis set, and as the basis size is increased, the wavefunction andenergy will approach the Hartree-Fock limit.Two types of basis functions are common: Gaussian-type and Slater-type orbitals.Slater-type orbitals (STOs) are written in spherical polar coordinates asønlm N r’1eYim(O ) (2.20)where N is the normalization constant, n is a positive integer, 1 and m are angular momentumquantum numbers, and , the orbital exponent, determines the diffuseness of the basisfunction. A collection of atomic near-Hartree-Fock limit wavefunctions has been tabulated byClementi and Roetti [811. Theoretical momentum profiles of noble gas atoms, calculatedusing these wavefunctions, are presented in chapter 5. Cartesian Gaussian-type orbitals(GTOs) are very popular for molecular calculations as the integrals required in thewavefunction calculation are easily evaluated. The Cartesian GTOs are defined by=Nxkymzrze_Cr2. (2.21)kmnChapter Two Theoretical Background 37where N and are as above, and k, m, n are (nonnegative) indices. A good overview of basissets and techniques used to ensure the efficient calculation of atomic and molecularwavefunctions is provided by Davidson and Feller [82].As shown in the previous section, in the target Hartree-Fock approximation the EMScross section is proportional to the spherically averaged square of the momentum space orbitalof the target electron. Since a Hartree-Fock calculation generally gives position spaceorbitals, the Fourier transform of these orbitals()(p) = (2it) Je()(r) dr (2.22)must be calculated. A FORTRAN program (HEMS), developed in this laboratory and basedon equations reported by Kaijser and Smith Jr.[83], perfonus the necessary transformationsand evaluates the spherically averaged momentum profiles from a Hartree-Fock wavefunction.Originally written and revised by A. Hamnett, J.Cook, K.T. Leung, and A.O. Bawagan, thisprogram was extensively modified during the course of the present study, and has recentlybeen further expanded by N.M. Cann.2.2.2 The Method of Configuration InteractionThe mutual repulsion of electrons gives rise to the correlation of their motion in anatomic or molecular system. Accordingly, the probability of fmding two electrons very closetogether should be small. The Hartree-Fock method neglects this Coulombic correlation, andChapter Two Theoretical Background 38the difference between the exact non-relativistic energy of a system and the Hartree-Fock limitenergy is termed the correlation energy. Many theoretical techniques have been developed tocalculate correlated wavefunctions. On small systems the correlation of electrons may beintroduced by explicitly expressing the interparticle coordinates r1 in the wavefunction [84].Indeed, explicitly correlated wavefunctions for helium are used in the calculation of OVDspresented in chapter 5. Larger systems require the use of other methods, the most general andconceptually straightforward being that of Configuration Interaction (CI) [79].Any many-electron wavefunction, including the exact wavefunction, can be written asthe sum of a series of Slater determinants constructed from a complete set of one-electronfunctions [84]. This is the foundation of the CI method, in which the exact wavefunction isapproximated by‘1ci=EcI,) (2.23)where I) are Slater determinants representing the ground state, and the singly and multiplyexcited configurations. The expansion coefficients c1 are chosen such that the expectationvalue given by Fci I ‘Pci) is a minimum. Singles and doubles CI (SDCI) is a commontechnique in which the CI expansion is restricted to include only singly and doubly excitedconfigurations. Doubly excited configurations are particularly important as they mix directlywith the ground state configuration; that is the CI matrix element given by (c1o1 I ci) whereID is a doubly excited configuration, is not zero. Singly excited configurations do not coupleChapter Two Theoretical Background 39with the ground state; however they enter the CI expansion through the indirect coupling withthe doubly excited configurations. Additionally, the inclusion of singly excited configurationsis important in the description of the one-electron properties of the system [79,80].An extension of the SDCI method is the multireference singles and doubles CI (MRSDCI) technique. In this approach, a SDCI calculation is performed first, and the significantconfigurations are used as the initial reference of a further calculation involving single anddouble excitations of each of the reference configurations. In this manner, the MR-SDCIwavefunction includes some triply and quadruply excited configurations [51]. A goodexample is provided in the MR-SDCI wavefunction for the ground state of water [36,50),calculated to investigate the outer valence momentum profiles as discussed in chapter 1. Abasis of 109-GTOs, designed to give both a good energy (the lowest SCF energy reported atthe time) and to saturate the diffuse basis function limit, was used in the calculation of theHartree-Fock wavefunction. From a SDCI calculation, a reference wavefunction of 15configurations was obtained. In the subsequent MR-SDCI calculation, 11011 configurationswere used in the description of the final CI wavefunction. This wavefunction was estimated torecover 83% of the correlation energy of H20 [36].Chapter ThreeThe Momentum Dispersive Multichannel EMS SpectrometerThe new momentum dispersive multichannel electron momentum spectrometer isdescribed in considerable detail in the following sections. The development of the instrument,incorporating a microchannel plate/resistive anode (MCP/RAE) position sensitive detectoralong with a conventional channel electron multiplier (CEM) detector, has provided the abilityto simultaneously detect (e,2e) events occurring over an azimuthal range of ± 300. Therealization of the full gain in sensitivity offered by such an instrumental design demanded greatcare in the construction and evaluation of the instrument. Particular attention was given to thealignment and symmetry of the analyzer, the implementation of the detectors for time andposition information, and the detection of coincidence events.The description of the spectrometer is separated into five sections encompassing i) thevacuum system, electron gun, and analyzer assembly; ii) the detectors; iii) the coincidenceelectronics and data acquisition; iv) the characterization and operation of the instrument, andv) proof-of-concept (e,2e) measurements of the valence region of argon.40Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 413.1 The Electron Source and AnalyzerIn order to offer a sufficiently complete picture of the design of the spectrometer, threedifferent views are presented in the following figures. Figures 3.la and 3.lb are photographsof the instrument showing (from the bottom up) the spectrometer mounting plate (with one ofthe pumping apertures visible on the right hand side), the analyzer base plate and supportpillars, the analyzer end corrector rings, and the inner and outer cylinder of the cylindricalmirror analyzer (CMA). An aluminum vacuum chamber rests on the 0-ring in thespectrometer mounting plate. The chamber is evacuated by two 360 1/sec turbomolecularpumps (Leybold-Heraeus) to a base pressure of 2x107 torn Differential pumping of theelectron gun chamber is provided by a 150 1/sec turbomolecular pump (LH-150). As themotion of an electron is affected by a magnetic field, the stray magnetic field strength withinthe spectrometer is reduced by a hydrogen annealed mu-metal enclosure surrounding thevacuum chamber. Also out of consideration of magnetic fields, the components of thespectrometer are constructed primarily of aluminum or brass. To reduce the backscatter ofelectrons, the inner surfaces of the gun and analyzer assemblies are coated with benzene soot.Figure 3.2 is a schematic showing the principal components of the spectrometer. Thegeneral order of assembly of the collision region, retarding lenses, CMA, and detector isdisplayed. A cross sectional schematic of the spectrometer is presented in figure 3.3. Each ofthe components presented in these figures is described in the following sections.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 42Figure 3. 1: Photographs of the spectrometer. The spectrometer base, CMA hiscplate, end correctors and inner cylinder are displayed in the top photograph. Theouter cylinder is in place in the lower photograph.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 43Outer CylinderDetector AssemblyInner CylinderConical LensesCollision ChamberCMA BaseplateSpectrometer Mounting PlateFigure 3.2: A break-away schematic of the spectrometer.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 44Figure 3.3: A schematic of the momentum dispersive spectrometer.QD=quadruple plate deflector, SP=spray plate aperture, FC=Faraday cup,MCP=microchannel plate, RAE=resistive anode encoder, CEM=channel electronmultiplier, CC=collision chamber, TH=top hat of CC.OuterCylinderCMABaseplateTurbo Pump StackElectronGunChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 453.1.1 The Electron Beam AssemblyA 0.125-mm thoriated tungsten (Goodfellow Metals W055300) “hairpin” filament,heated by a regulated (constant current) power supply (Lambda LK341) provides a stablesource of electrons. The filament is maintained at a negative potential (- -1200 V with respectto ground) with a DC power supply (Fluke 415B) that has been modified to allow computercontrol. The electron beam from the filament is accelerated and focused with a commerciallyavailable electron gun body (Cliftronics CE5AH) consisting of a grid, anode, and three-element electrostatic lens (see figure 3.3). As the third lens element and the collision chamberare at ground potential, the energy of the electron beam is determined by the potential appliedto the filament. The electron gun assembly is mounted below and aligned with the central holein the spectrometer mounting plate. The position of the filament mount may be manuallyadjusted, while under vacuum, to center the filament tip with respect to the grid aperture.Two pairs of parallel plate deflectors, provide additional control over the alignment of theelectron beam. The collimation and alignment of the beam are monitored usingmicroammeters that measure the current from molybdenum “spray plate” apertures, and fromthe Faraday cup. In the vicinity of the collision region, the electron beam is estimated to havea diameter of 1 mm.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 463.1.2 The CMA BaseplateThe CMA baseplate supports all of the major components of the spectrometer, andalignment of the baseplate to the axis defined by the electron beam is critical. The baseplate ispositioned with the aid of a jig that aligns its central hole with that of the spectrometermounting plate. The baseplate rests on three pillars (see figures 3.1 and 3.2) that may bemoved slightly with respect to the mounting plate. With the jig in place, the support pillars arefastened to the mounting plate and define the position of CMA baseplate. As long as thepillars remain fixed, the baseplate may be removed and replaced reproducibly.3.1.3 The Collision ChamberThe collision chamber consists of a brass tube and an alignment flange that rests in theCMA baseplate. With a molybdenum aperture (1.8-mm) at the bottom end, and the Faradaycup and spray plate (2.0-mm aperture) at the top , the chamber acts as a sample gas cell. Twoslots have been cut on opposing sides of the tube, and brass collars have been positioned todefine the location and size of the slot opening (1.76-mm). The slot spacing helps to definethe collision region, i.e., the volume of the interaction of the electron beam and target samplefrom which electrons may be scattered into the CMA.The design of the collision chamber was modified part way through this work, to reducethe distance from the collision chamber entrance to the collision region. The design of theChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 47original collision chamber is shown in figure 3.2, while the cross section of the modifiedchamber is shown in figure 3.3. The change was found to be necessary after binding energyspectra measurements for the very low intensity final excited ion states of He and H2 (seechapters 5 and 6) revealed weak structure originating from the interaction of the electronbeam with the sample gas prior to, as well as within, the collision region (i.e. doublescattering). These effects were inconsequential for conventional studies used to test theinstrument. To reduce this pre-collision interaction, the bottom of the collision chamber wascut off, and a “top-hat” (TH - fig. 3.3) shaped tube supporting the entrance aperture waspress-fit into the alignment flange. In the new design, the aperture is positioned approximately5 mm below the collision region, and the gas supply is introduced into the collision chamberthrough a small hole in the side wall of the “top-hat”. A wire mesh replaces the tube below thealignment flange to provide a ground plane shield for the electron beam, while allowingimproved pumping of gas away from the vicinity of the beam.3.1.4 The Conical LensesThe energy resolution of a cylindrical mirror analyzer is approximately a linear functionof the electron pass energy [85,86], and to improve the instrumental energy resolution adeceleration stage is often used prior to the entrance to the CMA. In the present instrument,an eight-element conical lens assembly is positioned about the collision chamber (see figures3.2 and 3.3). This lens assembly was designed by Dr. Tim Reddish, a former postdoctoralfellow in the group of C.E. Brion, to permit deceleration of the electrons exiting the collisionChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 48region over the full ± 300 azimuthal range. Initial test measurements using the lenses exhibitedan improved energy resolution (1.6 eV FWHM with 100 eV pass energy); however, extensivefocusing/defocusing of electrons in the azimuthal coordinate was also observed, due to “endeffects” in the ± 30° slot apertures. This effect destroys the azimuthal angular scatteringinformation central to the experimental measurement of electron momentum profiles. Futuredevelopment of the instrument will involve correcting this problem, either by the use of gridson the lens elements or by widening the azimuthal angular range of the lens slits. In thepresent application of the instrument, all of the lens elements are set to ground potential, andact only to define the range of poiar angles of electrons entering the CMA. Figure 3.4 showsthe cross section of the conical lenses and collision region. In addition to the size of exit slits(S1) of the collision chamber, the angular spread of electrons into the CMA and length of thecollision region are defined by the slits (S2) of the fifth lens element.3.1.5 The Cylindrical Mirror AnalyzerThe design of the CMA is based on the characterization of CMA performance by Risley[86]. The cylindrical mirror analyzer consists of two concentric cylinders with a voltageapplied between them. The resulting electric field between the cylinders disperses theelectrons on the basis of their kinetic energies. Ideally, the CMA would exhibit first andsecond order focusing characteristics [86] in which - -= 0 where z is the central theaxis of symmetry of the analyzer (i.e. the vertical axis in the present CMA). However, sizeChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 49Figure 3.4: A cross sectional schematic of the collision chamber and conicallenses, that, together with the electron beam diameter, define the size of thecollision region.±1.44°beamThe CollisionRegionChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 50restrictions and the 45° entrance (0) angle limit the focusing characteristics of the presentanalyzer. In practice this has not presented a serious impediment to the analyzer resolution.Considerable attention was given to the alignment of the inner and outer cylinders. Aflange on the bottom of the inner cylinder (see figure 3.2) has alignment holes that mate withholes in the CMA base plate. Precision ruby balls (5-mm diameter), placed between the pairsof alignment holes, position the inner cylinder to be coaxial and perpendicular to the CMAbase plate. Similarly, holes in the outer cylinder and CMA base plate are aligned using rubyballs (8-mm diameter), allowing the outer cylinder to be reproducibly positioned. The innerand outer cylinders have diameters of 126.4 and 254.0 mm, respectively. Measurements of thegap between the inner cylinder and outer cylinder are consistent around the full 2n circle,having a maximum deviation of less than 0.3 mm (0.011”).As the CMA has a finite length (the height of the outer cylinder is 235.2 mm), endcorrector rings at the base and the top of the CMA are used to minimize the fringing ofelectric fields. The voltages are applied to the rings by a resistive divider network between theinner and outer cylinders.The electron trajectories shown in figure 3.3 were calculated by a PASCAL programthat was written to emulate the operation of the analyzer. In the simulation of the motion ofan electron within the CMA, the program used the electric field strength of an ideal cylindricalcapacitor [87]Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 51VE_rln(a/b) (3.1)where V is the voltage across the cylinders, r is the radial distance of the electron, and a and bare the inner and outer cylinder radii. Commencing with an electron entering the CMA with600 eV and 0 = 450, the simulation determines the position, velocity, and acceleration of theelectron in the CMA in increments of 2 picoseconds. In this fashion, an outer cylinder voltageof -535.3 V was predicted to deflect a 600-eV electron to the exit slit of the analyzer. This isin very good agreement with the experimentally determined value of -538.0 V.3.1.6 Preliminary ResultsAs a simple check of the operation of the instrument in a (single channel) coincidencecounting mode, two channeltrons were employed, one fixed in position and the other able tobe manually rotated through an 0-ring-sealed plexiglass plate on the top of the vacuumchamber. Coincident (e,2e) events were determined using a method that was a precursor tothe final coincidence detection technique. The CEM signals (after constant fractiondiscrimination) were added using a power combiner, and discrimination of double heightoutput pulses, indicative of a coincidence event (i.e. pulse-pile-up--see section 3.3.3), wasprovided by a 2440 Tektronix Digital Oscilloscope with the appropriate trigger threshold.Figure 3.5a presents a binding energy spectrum of argon obtained at a fixed position of themovable analyzer, by manually changing the voltage of the cathode power supply. Figure 3.5bshows the angular distribution of coincidence events obtained with the cathode voltage set toChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 52500(a) I400 fCID0C..) 300II)c)0L)1000I I I I1210.0 1212.5 1215.0 1217.5 1220.0 1222.5 1225.0Cathode potential600(b)3500___________ç)400C.)II)C.)II)C.)CC2001000 I160 180 200Angle of Movable CEMFigure 3.5: Preliminary single channel EMS measurements using two CEMdetectors and a rudimentary PPU coincidence detection system. (a) a bindingenergy (cathode potential) spectrum for the 3p electron of argon at q=8°. (b) anazimuthal angle distribution with the cathode potential set to the peak of the 3pbinding energy.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 53observe ionization of the 3p electron of argon. The symmetric distribution of the data aboutthe position opposing the fixed analyzer (1800) gives a good indication of the alignment of thegun, collision region, lens, and CMA assemblies.3.2 The Detector AssemblyA momentum dispersive multichannel electron momentum spectrometer requires themeans to detect, in parallel, the coincident arrival of pairs of energy analyzed electrons over arange of azimuthal angles. Microchannel plate (MCP) electron multipliers have becomepopular devices for the detection of single electrons (or ions or photons) over large areas, andare well suited for use in EMS. A myriad of detector designs [881 has been developed to giveone or two dimensional position information of the MCP electron cloud. The use of a set ofdiscrete anodes is a conceptually simple method; however, the requirement of an amplifier anddiscriminator for each channel limits the practicality of such a detection system for EMS at thistime. In the present system, a single resistive anode position encoder (RAE) is used toprovide positional information over a wide azimuthal range. The detection of coincident(e,2e) events occurring between this detector and a single channel electron multiplierpositioned directly across the detection circle, allows the full momentum range of interest tobe observed simultaneously.Both the channeltron and MCPJRAE detectors are mounted on a plate that rests in theinner cylinder, just above the analyzer exit slits. Additionally, the detectors are housed inChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 54grounded metal enclosures (see figure 3.2), which help to eliminate stray electron signals andcross talk between the devices.3.2.1 The Channel Electron MultiplierThe channeltron is fabricated of glass and coated with a semiconducting layer that, uponimpact of an electron of sufficient energy, emits a number of secondary electrons. Acceleratedby a positive bias voltage applied to the exit of the channeltron, the secondary electrons collidewith the wall of the channeltron to produce additional electrons. If a sufficient bias potential isapplied, the avalanche of electrons continues down the length of the CEM until the density ofelectrons reaches a saturated level. At this point, the charge of the electron cloud in the CEMrepels any additional electrons emitted from the CEM surface, causing them to strike the wallbefore they are sufficiently accelerated to give the further emission of secondary electrons[89,90]. The CEM in this state operates in the saturated, pulse counting mode, having anelectron gain on the order of 108 [89,911. The gain variation for each incident electron givesrise to output pulses that have a Gaussian pulse height distribution [55,89,92]. Theappropriate setting of the threshold of a discriminator enables the detection of the (amplified)CEM pulses with an efficiency that is relatively invariant to changes in gain that may resultfrom a variation of the incident electron current, or ageing of the CEM [55,56].The CEM is curved to suppress the effects of ion feedback, in which a positive ionformed at the rear of the detector is accelerated towards the cone where collision with the sideChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 55wall may generate a spurious electron cascade [14,891. The curvature limits the accelerationof the ion before a collision with a wall, such that the ion velocity is insufficient to begin adetectable cascade.In the present application, a single channeltron (CEM -Phillips B318 ALIO1) isconfigured to detect individual electrons. Two high voltage power supplies (ITP 6516)provide front and back bias potentials. The output pulse from the CEM is capacitivelydecoupled as shown in figure 3.6. Presented in figure 3.7 is a typical CEM pulse’, having awidth of 5.0 ns FWHM and rise time (10-90%) of 3.4 ns. Details of the channeltron operationand performance are given in section 3.4.2.3.2.2 The Microchannel PlateIResistive Anode AssemblyA microchannel plate consists of an array of parallel tubes, typically 10- 40 jim indiameter, capable of providing electron multiplication in a manner similar to the CEM. Asmicrochannel plates are readily available with active areas on the order of 1 - 10 cm indiameter, it is possible to detect single electrons over a large spatial range. To furnishsufficient gain, a number of plates are typically employed in a variety of stackingarrangements. The fmal configuration used in this instrument was achieved after much trialand error. The original detector was a five-plate (40-mm diameter) device (Surface ScienceAll of the waveforms presents in this chapter were acquired using a Tektronix 2440 Digital Oscilloscope.The scope has a sampling rate of 5x108 samples/see, and single-shot bandwidth of 250 MHz. Some attenuationand alteration (particularly of the rise and fall times) of the waveforms is likely. The waveform data weretransferred to a personal computer using a National Instruments GPIB board.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 56Figure 3.6: The CEM signal coupling circuitry.0.00-0.04-0.08-0.12-0.16End BiasPower SupplyTiming SignalFigure 3.7: A typical CEM timing pulse (after the 50X preamp), with a rise timeFront BiasPower Supply220pF 5021 Ons/divof 3.0 ns and width of 4.7 nsChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 57Laboratories’ (SSL) 3390SB), consisting of a two-plate first stage and a three-plate secondstage. While the image of the many background (non-coincidence) electrons from the RAEwas an intense and uniform arc, the image from the coincidence electrons was less satisfactory.Only the coincidence electrons appearing at the edges of the arc were detected. The poorimage of coincidence electrons was reasoned to be a result of the dead time of 10-2 seconds[90] for each channel of the MCP involved in a cascade. As each MCP is composed of manychannels, the inherent dead time of an individual channel does not generally present a problem[901. In the five-plate design however, each incident electron would produce many electronsfrom the first stack which, in turn, would initiate a cascade in a very large number of channelsof the second stack. If a sufficient number of channels were stimulated, the channel deadtimewould have caused a reduced electron gain, particularly in the region where the concentrationof uncorrelated electrons was greatest.The final arrangement used in the present instrument is the most commonly usedchevron configuration of two MCPs [94]. The detector design is essentially that of a SSL3390SA device, which, according to the manufacturer, should provide lower spatial resolutionthan the five-plate device. However, the use of the two-plate configuration has not appearedto limit the performance of the spectrometer. The chevron-shaped MCP cross section, shownin figure 3.8, mimics the curvature of the CEM to reduce the effect of ion feedback. A smallgap (.1 mm) between plates improves the gain by allowing a number of channels of the secondplate to be stimulated (Rogers and Malina [95] estimate 20-30 channels for a gap of .15 -11Surface Science Laboratories is now Quantar Technologies Inc.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 58mm). However, the gap must be sufficiently small that a large enough number of electronsenter each channel of the second plate to ensure saturation [90]. With a voltage ofapproximately 1 kV/plate, the electron gain using such a configuration is typically 106l08[90,95]. The position of the electron cloud from the MCP stack is determined by the resistiveanode encoder and associated electronics. The anode is of the Gear design— square withconcave sides — which provides approximately distortion-free imaging [96]. On impact of theelectron cloud, the anode, which is coated with a series of metalizations and conductive inks,gives a current at the four corners reflective of the position of the incident electrons. Apreamplifier unit (SSL 24011) shapes and amplifies the charge pulses from each corner. Aposition computer (SSL model 2401) subsequently determines the X-Y position of theelectron cloud through the analog computation of the relationships:B+C (3.2)A+B+C+DandA+B (33)A+B+C+Dwhere A,B,C,D are the heights of the pulses from the corners. In addition to the (2-ps wide)bipolar positional pulses from the RAE preamplifier unit, a ‘fast’ E pulse (350-ns wide),representing the sum of the four anode pulses, is also generated. On detection of the E pulseby the position computer, a digital E pulse is generated. This signal initiates a control logicsequence, beginning a position computation, and ultimately yielding X and Y analog outputChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 59levels as well as a (TTL) STROBE pulse to inform an external analog-to-digital converter(ADC) of an acceptable event.The rise time of the resistive anode output pulses precludes the use of these readilyavailable signals for coincidence timing information. Many alternative methods of obtainingnarrow timing pulses were investigated. These included the conventional approaches ofcapacitively [59,97], or inductively [26,98] coupling the signal induced by an electron cascadein the high voltage supply line at the exit of the MCP stack. In the present system the timingpulse is obtained from a molybdenum grid (Buckbee Mears 1-PC) of 0.001-inch-thick wiresspaced on 0.025-inch centers, inserted between the MCP stack and the RAE. This methodwas found to give faster response and less time jitter than the more conventional timingtechniques. A similar approach was taken by de Bruijn and Los [98] but was abandoned dueto a degradation of the positional information. A poor image was also observed in the presentsystem when a grid of 0.003-inch-thick wires on .020-inch centers (72% transmissive) wasemployed; however, the presently used mesh, with an open area of 92%, showed no distortionof the RAE image. The grid timing pulse is capacitively decoupled as shown in figure 3.8.The ferrite beads on the supply line are used to dampen the small (-7-10 mV) transientsoriginating from the switching power supply (Wenzel Ni 130-4). A typical grid timing pulse,having a width of 3.9 ns FWHM and rise time of 2.2 ns, is shown in figure 3.9.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer+1025v4—-50v60Resistive AnodePosition EncoderWire grid•_______— 0.6 mm gapChevron MCPs(0.1 mm gap)ifFigure 3.8: The microchannel plate/resistive anode encoder assembly.Figure 3.9: A typical MCP timing pulse from the grid (after the 100X preamp)with a rise time of 2.2 ns and FWHM of 3.9 ns.Pulseout+2250vFerritebeads+2450v1M 450 2 :iiiiii ,iiIIIIIIIIIIIIIIIIIIIIIiIIIlIiII1I1iiIIIII11I1IIIIIIIIIIIiiII11 i ‘ i0.00.0-0.2-0.3-0.4-0.51 Ons/divChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 613.3 Coincidence Timing and Data Acquisition Electronics3.3.1 Signal ProcessingThe output pulses of the channeltron are amplified by a preamplifier that was fabricatedin-house as a low cost replacement of the ORTEC 9301 preamp. The preamp has a two-stagedesign originally with a Mini-Circuits MAR-3 input stage (typ. gain 12.5 dB) and a Mini-Circuits MAR-7 output stage (typ. gain 13.5 dB), to give a measured amplification factor of20 (26 dB). As channeltron efficiency decreases with use [55,56], greater bias voltages acrossthe CEM are required to give pulse heights above the detection threshold. When themaximum bias voltage, limited by the power supply and by ion feedback, was reached in thepresent system, the preamp was modified in an attempt to delay replacement of thechanneltron. A MAR-6 (20 dB) input stage, and MAR-3 (12.5 dB) output stage was found togive a 50X amplification (34 dB), with no apparent change in the pulse characteristics. Thismodification permitted the continued operation of the channeltron at much lower biasvoltages.The grid timing pulse of the MCPIRAE detector is amplified by a bOX preamplifier(Photochemical Research Associates model 1763). Both the CEM and MCP timing pulses areinput into constant fraction discriminators (CFD - ORTEC 934) that provide improved timeresponse over a fixed threshold discriminator in the detection of the signals. A CFDaccomplishes this by splitting an input pulse, delaying and inverting one fraction whileChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 62attenuating the other, and recombining the two to generate a bipolar signal. As shown infigure 3.10, the detection of the zero crossing of the bipolar signal provides discrimination at apoint approximately independent of the amplitude of the input signal. The two CFDs havediscrimination thresholds set to (the minimum) -30 mV which is well above the noise levels onthe signal lines (<5 mV). The output of the CFDs are NIM level pulses (0 to -0.8 V) havingwidths of 50 and 80 ns for the CEM and MCP respectively. The length of the MCP-CFDpulse is more than sufficient to prevent generation of additional CFD pulses on the occasionalnoisy MCP timing pulse (i.e. after pulses, which are believed to be caused by ion feedback).3.3.2 The Spectrometer Time ResponseTo investigate the temporal characteristics of the instrument, a time spectrum wasobtained using a time-to-amplitude converter (TAC- Ortec 567). The TAC was configured togenerate a signal (0 - 10 V) proportional to the time delay between a CEM-CFD start pulseand a delayed MCP-CFD stop pulse. The time spectrum presented in figure 3.11 was acquiredby digitizing and accumulating the TAC output signals, while the spectrometer was set todetect (e,2e) ionization of argon 3p electrons. The effectively uniform background’ of thetime spectrum arises from the detection of uncorrelated (random) electrons at the CEM andMCP detectors. The peak in the time spectrum indicates a correlation in the arrival time of theelectrons at the MCP and CEM detectors, which originate from an (e,2e) collision event. The1As the background pulses from each detector are random in time, the delay times between the arrival of CEMstart pulses and MCP stop pulses have an exponential distribution characteristic of Poisson processes [183].However, over the short 50 ns time window, the probability of observing a particular delay time betweenpulses is essentially uniform.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 630.00-0.10I-0.20-0.300.060.050.04‘0.03I0.020.010.00-0.01Figure 3.10: a) A distribution of pulse heights from the CEM. b) Thecorresponding bipolar pulses produced by the CFD to give pulse height invariant5 ns/div5 ns/divtiming.Chapter Three The Momentum Dispersive Multichannel EMS SpectrometerFigure 3.11: A timing spectrum of the multichannel spectrometer acquiredusing a TAC. The peak in the spectrum corresponds to the coincident arrival ofelectrons at the MCP/RAE and CEM detectors.64I.(-)1500100050000 10 20 30 40Time (ns)50Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 65pulse width of 1.6 ns FWHM is considerably more narrow than those typical of EMSinstruments, which are generally on the order of 3-10 ns FWHM. A narrow coincidence pulsewidth is desirable since, as discussed by Lower and Weigold [57], both the signal-to-background ratio and the statistical uncertainty of coincidence measurements are improvedwith a smaller coincidence timing window.A number of factors contribute to the width of the coincidence peak in an (e,2e)experiment [99]. These include the time spread from different energies and trajectories ofelectrons passing though the analyzer, the time spread inherent to each detector, and the timejitter from the electronics components [99]. In the present instrument, the analyzer timespread is considered to be small, due in part to the relatively high energy (-. 600 eV) of thescattered electrons. As well, given the consistency of the timing pulse shapes and the use ofconstant fraction discrimination, the contribution from timing electronics is likely to benegligible. The principal factor influencing the coincidence width is the transit time variationof the electron charge cloud through the CEM, which may be as high as a 2-3 ns [99]. Amicrochannel plate detector exhibits considerably less time variation than a CEM [93], and theinevitable future development of an instrument in which the CEM is replaced by a stack ofMCPs should realize an improved coincidence time width over the present spectrometer.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 663.3.3 The Coincidence Detection SystemIn all of the EMS instruments developed to date, the detection of (e,2e) coincidenceevents has been based on systems incorporating a TAC, in a manner similar to that justdescribed. A timing window is set (often with thresholds of a single channel analyzer) aboutthe coincidence peak of the time spectrum to identifies both ‘true’ and ‘accidental’ coincidenceevents. Characterization of the level of background ‘accidental’ events is obtained fromanother window, positioned away from the coincidence peak. Subtraction of the accidentalpedestal yields the true coincidences.A different approach to coincidence detection was taken in the present system; figure3.12 illustrates the basis of the technique. The detector timing signals are first shortened andthen combined using a 2:1 radio-frequency power combiner. The coincident arrival ofelectrons at the two detectors is recognized by the pulse-pile-up (PPU) of their timing signals,as double-height pulses at the output of the power combiner are distinguished from theuncorrelated (single pulse height) events by means of a discriminator with an appropriately setthreshold level.TAC-based systems are significantly less demanding to implement than those based onPPU detection [100]. The motivation for the application of the PPU method to the presentsystem lies in its ability to quickly recognize coincidence events. This has permitted theposition computer to be gated, such that only the position of electrons that are part of aChapter Three The Momentum Dispersive Multichannel Spectrometer 67MCP Grid timing pulses CFD pulsesFigure 3.12: The pulse-pile-up (PPU) coincidence detection method. Individualtiming pulses are combined using a power combiner. Coincident input pulses yielddouble height output pulses that can be detected with a discriminator.PowerCombinerI-u LiChanneltron pulsesDouble heightpulse detectionChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 68coincidence event are calculated. This is important in the present system in which therelatively low coincidence count rate (typically 2-20 Hz) is somewhat overshadowed by thehigh count rate of uncorrelated electrons striking the MCPIRAE detector (typically 20-80 kHz). If the position computer was not gated, the dead time associated with calculatingthe location of uncorrelated electrons would significantly reduce the efficiency of detectingcoincidences.An xy-position computation is initiated by the detection of the fast E pulse from theRAE preamplifier, which occurs approximately 85 ns after the arrival of an electron at the faceof the MCP detector. By comparison, the time response of typical commercially availableTACs is on the order of 1-3 Jis, and discrimination of the coincidence timing windows furtherincreases the time period between the actual coincident event and recognition of it. Hence,using a TAC-based coincidence system, the computation of the position of an event at theMCPIRAE detector would be well underway by the time the nature (coincidence or non-coincidence) of the event is established. A TAC-based design which incorporates thecoincidence gating of the position computer would be difficult to achieve. In contrast to theTAC response, the presently developed PPU circuitry recognizes a coincidence event within50 ns of the arrival of the electrons at the detectors.It should be noted that a few commercial coincidence units using pulse-pile-up detectionare available (e.g. Canberra Model 2040 and EG&G Ortec 414A). However the minimumresolving time of these systems is greater than 10 ns, and the use of such units for the presentChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 69application would offer poor timing resolution relative to the narrow coincidence peak widthexhibited in the TAC spectrum in figure 3.11. In the present system, the PPU coincidencecircuit was designed to have resolving time of approximately ± 1.5 ns. The PPU coincidencecircuit is also an important evolutionary step towards the development of a system able todetect coincidences occurring between any two of a large number of detectors. The use ofmany discrete detectors is expected to be central to the design of future systems in whichcoincident pairs are detected around the complete 2it azimuth.The implementation of the PPU technique in the present instrument is outlined in figure3.13. The time response of the MCP detector is faster than that of the CEM, due to thegreater pulse transit time in the CEM. Hence, the CFD timing signal of the MCP is delayed by12.5 ns with respect to the CFD signal of the CEM, thereby ensuring that signals arising fromelectrons that were coincident at the exit of the CMA are coincident upon arrival at the pulsepile-up circuitry.The PPU circuitry has a bifurcated design, with one branch configured to identify ‘true +accidental’ coincidence events, and the other to identify only ‘accidental’ events. As the CFDpulses are relatively wide and pulse-pile-up coincidence detection using these signals wouldgive a correspondingly wide coincidence window, the CFD pulses are compressed prior toinput to a pair of power combiners. The detection of a pulse-pile-up signal following thelower power combiner (2) indicates the coincident arrival of electrons at each of the detectors.Chapter Three The Momentum Dispersive Multichannel Spectrometer 70CEMFigure 3.13: A block diagram of the pulse-pile-up (PPU) coincidence detectionsystem.‘Accidentals”‘Trues’+‘Accidentals”ConstantFractionDiscriminatorsChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 71Prior to input to the upper power combiner (1) the CEM signal is delayed by 30 ns, therebydestroying the overlap of pulses from a true coincidence event. Pulse-pile-up events detectedin this channel correspond to the arrival of one electron at the CEM, followed --30 ns later bya second uncorrelated electron at the MCP. A TTL’ flag is set to identify the event as anaccidental. Observation of the accidental counts using this channel allows the removal of theaccidental background from the ‘true + accidental’ coincidence measurements.The detection of a coincidence in either branch generates a TTL coincidence signal thatis used to gate the position computer. The gating system operates by allowing the digital Epulse to initiate a position computation only when a coincidence signal is observed. Thus onlythe positions of the electrons at the MCP/RAE detector that give rise to the PPU coincidence(‘true + accidental’ or ‘accidental’) signal are calculated.3.3.4 The Pulse-Pile-Up Coincidence CircuitryThe high speed characteristics of ECL (Emitter Coupled Logic - 1OK/1OKH) integratedcircuits are exploited in the generation and discrimination of narrow pulses for coincidencedetection. These components, and additional TTL components, are mounted on a circuitboard positioned above the circuit board of the SSL position computer. The operatingvoltages required for the circuitry are acquired from the position computer. A schematic ofthe component layout and a circuit diagram of the coincidence detection and position1fl = transistor transistor logic (LO OV and HI 5V).Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 72computer gating electronics are presented in figure 3.14 and figure 3.15. The letters alongsidethe circuit correspond to the letters in figures 3.16 and 3.17, which display a series ofmeasurements following a pulse sequence through the coincidence circuitry. The waveforms,acquired with a Tektronix 2440 Digital Oscilloscope, should not be taken as absolute, as theaddition of the long oscilloscope probe effects the circuit performance and influences themagnitude, shape and ringing of the pulses. However, the measurements help to illustrate andclarify the operation of the circuitry.Following the MCP signal (A), the NIM logic (-0.8 toO V) pulse from the constantfraction discriminator is input to an ECL 1OH1 15 quad line receiver to generate acorresponding ECL pulse (logic levels : LO -1.8 V, HI -0.8 V) (B). A voltage of -0.4 V— near the mid range of the NIM pulse — is applied to the second input of the line receiver,which acts as differential amplifier. A pair of identical pulse compression circuits is used togenerate two short timing pulses, one for the ‘true + accidental’ branch, and the other for the‘accidental’ branch. In each branch, the long ECL pulse is inverted and delayed by a 10102NOR gate. A further delay is added by approximately 6” (—1 ns) of RG174 coaxial cable.This delayed and inverted pulse (C) is sent to one input of an OR gate (10103), with theundelayed pulse sent to the other input. A LO output pulse from the OR gate is generatedwhen both inputs are LO, a situation occurring only during the short delay time of the originalpulse. In this manner, short ECL pulses (-4 ns FWHM fig 3.16D) are generated on theleading edges of the CUD pulses. These short pulses are routed to the inputs of the radio-Chapter Three The Momentum Dispersive Multichannel Spectrometer 73CEM SignalInputsIOH 115Line Receiver10102Quad 2-InputECL NOR GateDDU-37VariableDelay(6-76ns)CoincidenceGate SignalOutPE-2 1217Delay 8OnsDDU-39FVariable Del7-25 ns74S74DualD Rip-Flops10H125ECL-to-TTLTranslaterE 10103Quad 2-InputECL OR GateE 2:1 Power CombinerPCOM 12:1 Power CombinerPCOM 24A1OHI1 BLine Receiver 0 C(Discrinuinatori 4 iy Accidental FLAG21220lOOns DelayEnEu10K74LS74 74L5221 74LS221Dual MonostableMultivibrators10103 /101031010310K Trimmer pots.to set PPU thresholdFigure 3.14: A schematic of the coincidence detection circuit board.Chapter Three The Momentum Dispersive Multichannel Spectrometer 74—C” U.0- to________ ______t... IU,C’J C’)E- I-JC) -_JC)cs iL1to to CD C?I...C’)Cu—o .o .0.0.0> I, >“ 8to >-J0 C)—cs iU 0)I____T TuJ’__ ___C)- ACD toC)C... CD 0Figure 3.15: The PPU coincidence detection and position computer gating circuitdiagram. IC pin connections are numbered, and small letters in the OR gates refer toICs in figure 3.14. Larger letters correspond to lettering in figures 3.16 and 3.17Chapter Three The Momentum Dispersive Multichannel Spectrometer 750.0-0.4-0.8-0.8-1.2-1.6-0.4-0.8-1.2-1.6-0.8-1.0-1.20.0-0.2-0.4-0.8-1.2-1.6-0.8-1.2-1.6-0.8-1.2-1.6Figure 3.16: A sequence of waveforms following an MCP timing pulse through thecoincidence detection circuitry. The pulse shapes should be taken as qualitative.Lettering corresponds to points in figure 3.15. The vertical axes are in volts.42010 ns/div— CDCDç)CD-CDCD -tCDoCD•CDCD-t. CDCD-t-00CD 0OCD c,CDCDq3..<CD0CDC) CD CD -t CD 0 CD C’, CD 00F’.)0F)0F’.).01’.).0F’.)—aChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 77frequency power combiners (Mini-Circuits PSC-2-Wl). Figure 3.16E displays a typical singleheight pulse and a double height PPU pulse after the power combiners.The output of each power combiner is detected by another 1 OH 115 line receiver,operating as a discriminator with a threshold voltage at the non-inverting input set by a 10-Kvariable resistor. The threshold is set above (more negative than) the level of a single heightpulse, such that an output signal is given only for large pulses resulting from an overlap of twotiming signals at the power combiner. The output of the first 1OH1 15 discriminator is ‘cleanedup’ by a subsequent 1OH1 15 IC (F). Early designs of the circuitry attempted to discriminatethe PPU pulses using a SP93802 sub-nanosecond comparator (Plessey Semiconductors), butthe approach was unsuccessful. The comparator was unable to discriminate between thesingle and double height PPU pulses. While the 1OH1 15 IC is not specifically designed for useas a discriminator, it has proven to be effective in the detection of the double height pulse-pileup signals.The next stage in the coincidence circuitry is designed to lengthen the output signal ofthe discriminator. To accomplish this, a similar process to the pulse compression at the inputis used. The output signal is split, with one signal being delayed (fig. 3.16 G) by thepropagation time of two ECL 10103 OR gates (typically 1.0 ns per gate [101]). This delayedpulse is then input into another OR gate with the undelayed pulse at the second input, yieldinga broadened ECL pulse (H).Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 78As shown in figure 3.15 the ‘true + accidental’ and the ‘accidental’ PPU discriminationcircuits are identically configured. The broadened outputs of both branches are directed toanother ECL OR gate such that an output signal from this gate indicates a coincidence ineither of the two timing windows. The ECL signal from this gate is converted to a TTL pulseusing a 10125 ECL - TTL translator, and the output TTh coincidence signal (figs. 3.161 and3.171) is subsequently used to gate the position computer.The remaining components of the circuit set the appropriate width and time of thecoincidence gate signal (COINC) relative to the digital £ pulse from the position computer. ATTL flip-flop (74S74) generates a lengthened1pulse that is subsequently delayed by a variabledigital delay unit (Data Delay Devices DDU-37F). The delay time determines the position ofthe COINC signal and has been adjusted appropriately (presently 16.5 ns). The delayed signal(fig. 3.17K) is sent to the clock of a second flip-flop that, on the rising edge of the signal,gives an output HI COINC signal. The output remains in the HI state until a LO level occursat the clear, the time of which is set by another variable delay (DDU-39F) that determines thewidth of the COINC signal. The positions of the COINC pulse and digital E pulse arepresented in figures 3.17L and 3.17M.In this manner, the PPU detection of a coincidence event generates a COINC signal,approximately 85-ns wide and positioned to coincide with the arrival of the digital E pulse.The COINC signal and the digital E pulse are input to a TTL NAND gate. An output pulse is‘The length of the pulse is determined by the delay between Q (pin 6) and CLR (pin 1).Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 79given only if both the COINC pulse (HI) and E pulse (111) are present. If no coincidence isdetected, the COINC signal is not generated, and the E pulse is blocked from the circuitry ofthe position computer. Should a coincidence occur, the overlap of the COINC pulse anddigital E pulse yields a gated E pulse that is routed to the position computer circuitry,permitting the calculation the (x, y) position of the event at the anode in its usual fashion.3.3.5 The Accidental Flag CircuitryThe accidental circuitry is designed to generate a TTL flag to identify PPU coincidenceevents occurring at the ‘accidental’ power combiner. The simple generation of an 8-10 j.isTTL pulse, is complicated by a few scenarios in which ‘true + accidental’ and ‘accidental’events would be misinterpreted. These troublesome situations arise from the requirement forresistive anode pulses to satisfy upper and lower thresholds (internal to the position computer)for a position computation to occur. Consequently the detection of a PPU coincidence andsubsequent gating of the digital E pulse does not always lead to the output of X,Y andSTROBE signals by the position computer. Should an 8.5-us accidental flag (ACC) be setwithout the corresponding STROBE, a ‘true + accidental’ PPU event occurring shortlyafterwards may be interpreted as an ‘accidental’ event. Similarly, if the ACC flag is setwithout a STROBE, and an ‘accidental’ event occurs shortly afterwards, the ACC flag maybecome LO before digitization, causing the PPU event to be recognized as a ‘true +accidental’. Thus, to avoid these problems, the accidental circuitry is designed to generate aTTL ACC flag only if a corresponding STROBE signal has been given.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 80The accidental circuit diagram is presented in figure 3.18, and a pulse sequencefollowing the generation of the ACC flag is shown in figure 3.19. The accidental ECLcoincidence pulse is lengthened by an additional gate delay, and then converted to a TTh pulseusing a 10125 ECL-TTL translator. Similar to the gating of the E pulse, the T1’L accidentalsignal must be shaped and delayed to give a signal (GAF — for generate ACC flag) thatcoincides with the leading edge of the STROBE pulse. The accidental TTL pulse triggers amonostable (74221), and the falling edge of the output pulse triggers a second monostable thatgenerates the GAF signal. The width of the first monostable pulse determines the position ofthe GAF pulse, while the variable resistor of the second monostable sets the width.Meanwhile, the leading edge of the (inverted) STROBE signal from the position computertriggers a monostable to generate a 100-ns Short Strobe signal. The GAF pulse is set to arriveat one input of a fourth monostable prior to the expected time of arrival of the Short Strobesignal. If the falling edge of the Short Strobe pulse arrives at the second input of themonostable while the OAF signal is HI (see figure 3.19), an 8.5-jis TTL HI accidental flag isproduced. If the position computer fails to generate a STROBE signal, the flag is not set andthe accidental circuitry is ready to process the next event.3.3.6 Data AcquisitionThe end result of a valid coincidence event is the generation of an X,Y pair of analogsignals, a STROBE signal, and an ACC flag if the coincidence was an ‘accidental’. In themeasurement of a momentum profile or binding energy spectrum, the X,Y and ACC flagChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 81ECL AccidentalCoincidence SignalGAFVccVccAccidental Flag8.5 is ITL pulseV00Figure 3.18: The accidental flag (ACC) circuit diagram.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 822042042042042250 ns/divFigure 3.19: A series of waveforms depicting the generation of an ACCflag. The vertical axis are in volts. The T1’L accidental OAF signal must beHI upon the arrival of a short strobe signal, to generate the Accidental Flag.4Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 83signals are digitized using a slightly modified1 ISC-16 data acquisition board (R.C.Electronics), which interfaces with a 286 personal computer. With a 12-bit ADC (analog-todigital converter), the board provides sufficient digital resolution in the acquisition of theposition information. The detection of the STROBE pulse at the trigger input prepares theboard to acquire data. The STROBE pulse also causes a 74121 T1’L monostable to generatea 1-is external clock signal that initiates the ADC process. Following a setup time of 2-3 jis,each channel is digitized on l-j.ts intervals. To ensure that the X,Y and ACC flag informationis valid at the time of digitization, the output signals of the position computer and accidentalcircuitry have been extended to approximately 8 J.ts.2The monostable that generates the external clock pulse is located in a home-builtcoincidence counting unit. An array of 74390 decade counters, 7447 seven-segment displaydrivers and 10-mm seven-segment LED displays (MAN8640) were connected using wire wraptechniques in the construction of the counter. This inexpensive counter/clock pulse unit hasproven to be convenient in the real-time monitoring of coincidence events.The ISC-16 acquisition board also has a 12-bit DAC output channel that has been usedto provide variable control over the energy of the incident electron beam. The voltage level ofthis DAC is set by the acquisition computer and modifies the output of the Fluke 41 5B‘Each input channel of the board was designed with a low pass filter, which seriously affected the rise times ofthe input pulses. Input capacitors (to ground) were removed to remedy the problem.2 A pair of sample-and-hold amplifiers internal to the position computer were modified to enable adjustmentof the X and Y analog output durations.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 84cathode high voltage power supply. Calibration of the power supply has shown the cathodepotential to be very linear as a function of the DAC output over the available 133-V range(1189-1322 V). Within this range, any potential in increments of 33 mV can be established.A PASCAL program has been written to control the acquisition board in themeasurement of p-angle distributions and momentum profiles. This program requests userinput of the cathode potentials to be investigated and the accumulation time at each potential.The cathode potential is set by the DAC, and the board is signaled to acquire data, upon whicha BIOS Delay Interrupt (Tnt 15, Function 80) is called. This pauses the program for period oftime, typically 30-60 seconds, specified in microseconds. During a time delay, X, Y and ACCflag data for each coincidence event are stored in the buffer memory of the ISC- 16 acquisitionboard. On detection of each coincidence event, the ISC- 16 board also generates an IRQ3interrupt that advances an accumulator variable in a software interrupt handler routine. At theend of each time period, the program queries the ISC- 16 buffer memory and reads in thestored X, Y, FLAG data for each coincidence. If a range of binding energies is to be scanned,the program sets a new cathode potential, resets the buffer memory, and initiates a newacquisition period. At the end of each measurement period, an updated binding energyspectrum and momentum distribution are displayed on the computer monitor.3.4 Characterization of the InstrumentAs a chain is only as strong as its weakest link, so too is a spectrometer only as efficientas its ‘weakest’ component. To obtain the optimal (or close to optimal) performance of anyChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 85spectrometer, each of its individual components must be properly configured and operated.The sections presented below explore some of the measurements conducted to test andcharacterize each of the individual devices that together comprise the momentum dispersivemultichannel spectrometer.3.4.1 The CMAFor a particular setting of the CMA voltages, electrons within a range of energies andpoiar angles will pass through the CMA to the detectors. To characterize the energyresolution provided by the spectrometer, the transmission of elastically scattered electrons tothe MCP and CEM detectors was measured. The variation of the count rates of the detectorswith the energy of the incident electron beam is shown in figures 3.20a and 3.20b. The shapesand widths of the transmission peaks are slightly different, due to the different effectiveentrance apertures to the detectors. In addition to the intrinsic resolution of the analyzer, thewidths of the peaks include a contribution from the energy distribution of electrons in theincident beam [102]. Assuming Gaussian peak shapes with widths (FWHM) of 2.8 and 3.4 eVfor the CEM and the MCPIRAE respectively, a coincidence mode binding energy resolution of4.4 eV is anticipated. This is consistent with the measured value of 4.3 eV, exhibited in theBES of the argon 3p electron shown in figure 3.20c.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 8630 I I I Ia) MCP b) CEMN25 i xlO1:1)2015 3.4 eV - 2.8 eVfwhm fwhmriD ---.riD0 I• I •I . I. • I • I -,592 596 600 604 608 592 596 600 604 608 612Incident Electron Energy (eV)3000 I Ic) BES2500 - Ar3pCM2000 -U‘a)1500--— 4.3eVfwhm.-.4CU500--0 •‘.5 10 15 20 25Binding Energy (eV)Figure 3.20: Characterization of the CMA energy resolution: (a)Transmission of elastically scattered electrons to the MCP/RAE detector (b)to the CEM. (c) The (e,2e) coincidence energy resolution.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 873.4.2 The Channel Electron MultiplierFollowing techniques typically employed in this laboratory, the CEM was positionedsuch that the electrons passing through the analyzer would strike the horn of the CEM. Aswell, a retarding bias voltage of -500 V with respect to the (grounded) inner cylinder wasoriginally applied to the horn to help reduce the detection of stray electrons. Subsequenttesting of the operation of the CEM has revealed an interesting dependence of the count rateon the front bias potential. Figure 3.21 presents saturation curves, depicting the count ratefrom the CEM as a function of the rear bias potential, for a number of different front biasvalues. The explicit dependence on the front bias is more clearly displayed in figure 3.22 inwhich the total electron count rate from the CEM and the (e,2e) coincidence event rate areplotted as a function of the front bias voltage, with the total bias across the CEM heldconstant. It is apparent from these figures that the detection efficiency of both backgroundand coincidence electrons at the CEM is greatest for a front bias of -570 V. This appearedto be counter to the intuitive belief that the faster impact energy electrons would give a greateremission of secondary electrons and hence more efficient detection. Indeed, Seah [15] hasindicated that the maximum detection efficiency of the CEM occurs for electrons striking thehorn with an energy of 100-1000 eV.However, in addition to the incident electron energy, the efficiency of a channeltron hasbeen shown to be dependent on both the location and angle of impact [91,103]. In particular,Seth and Smith [91] have demonstrated that the efficiency of a channeltron is greater for anelectron striking the edge of the channel or entering directly into the channel, than for anChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 883000 —2500 -2000za)1500 -U500 -0—2000 2500 3000 3500Channeltron Back Bias (V)Figure 3.21: CEM saturation curves, depicting the count rate as a functionof the back bias potential, for a number of retarding front bias potentials.Spline curves are shown between the data points, to aid the eye.FrontBias (V)-590Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 892500 I I Ia)2000 -...1500-.1000- •.500-.O I300 400 500 600 700I I I Ib)5000-40003000 -.0.2000-.1000-.0 I I I300 400 500 600 700CEM Front Bias (-V)Figure 3.22: The variation with the retarding front CEM bias potential of(a) the total electron count rate from the CEM, (b) the (e,2e) coincidencecounts rate (5 minute collection time).Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 90electron striking the horn. Since an electron that directly enters the channel will initiate acascade closer to the end of the CEM than one striking the horn, fewer multiplication stageswill occur, giving a reduced output gain [91]. However, the overall detection efficiency maybe higher in this case, as the electron directly entering the channel is more likely to initiate acascade down the length of the channel than an electron striking on the horn, where scatteringof electrons or quenching of the cascade before entering the channel may occur. The mostefficient location of impact seems to be the intersection of the channel and horn, where theprobability of a cascade is high and the gain from the full cascade through the CEM isachieved [91].In the present system, the increase in detection efficiency with the retarding potential isbelieved to be caused by the deflection of electrons towards the channel opening, or into thechannel itself. To illustrate this effect, two simulations of the trajectory of a 600-eV electronentering a CEM are presented in figures 3.23a) and 3.23b). The simulations were performedusing SIMION (EG&G Idaho Inc.), a computer program for the modeling of motion ofcharged particles. The front biases on the CEMs of figures 3.23a and 3.23b are -500 V and-570 V respectively. As well, the potential from the horn edge towards the channel wasincreased slightly (— 2% of total bias at the channel edge) to account for the effect of thepositive back bias [91]. In both simulations, the electron is deflected towards the center of theCEM, although with a front bias of -500 V the deflection is small. The influence of the greaterretarding potential on the electron trajectory is quite dramatic, as the electron is deflected intoChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 91Figure 3.23: A simulation of the trajectories of 600 eV electrons at theentrance of the CEM, with a retarding potential of a) -500V and b) -570Vapplied to the CEM horn. The horizontal line to the left of each figurerepresents the electron trajectory. The curved, more vertical lines areequipotentials. The lower aperture in each figure is an artifact of thesimulations.A)B)Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 92the channel of the CEM. As this region gives more efficient detection, it follows that thecount rate of electrons with the higher front bias potential should be greater than lower bias, inaccord with the measurements of figure 3.22. A related effect has been discussed by Seah andHolboum [104], who noted that the CEM efficiency was found to decrease with theapplication of an increased (positive) cone bias. In their study, a grid was applied to the frontof the CEM to remove the distortion of the electric field in the horn, and a much more uniformCEM efficiency with applied front bias was obtained [104].As a result of the investigation of the influence of the front bias on CEM efficiency, theCEM is operated with a retarding front bias potential of -570 V. The positive bias at the backof the CEM is set to ensure CEM operation in the saturated pulse counting region (typically3100-3900 V across the CEM), exhibited by the plateau in the higher curves of figure 3.21.3.4.3 The Microchannel Plate / Resistive Anode Operating VoltagesThe operation of the MCPIRAE detector is inherently more complex than the operationof the CEM. For efficient performance, the pulse height distribution of the timing signals mustbe above the threshold of the constant fraction discriminator. As well, the distribution of RAEpulses must lie within an upper and lower threshold window determined by the positioncomputer electronics. Furthermore, the pulse height distributions of the anode pulses and thetiming pulses are both influenced by the bias potential across the MCP chevron. Anacceleration bias of 200 V from the back of the MCP chevron to the timing grid, and aChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 93subsequent 200-V accelerating bias to the RAE (as shown in figure 3.8) have been found togive both a sharp and narrow timing pulse and a high-contrast uniform image from the RAE.Presented in figure 3.24a are measurements of the count rates of the timing signals andposition computer STROBE signals as a function of the MCP bias potential, obtained whilemaintaining the 200-V grid and anode acceleration potentials. As the MCP bias potential isincreased, the count rate of the MCP timing signals (solid circles) rapidly increases and beginsto plateau. At higher potentials, the onset of ion feedback lead to a sharp rise in the timingsignal rate and a degradation of the anode image. The count rate of STROBE signals from theposition computer (open circles) also rises with increased bias, but only up to a maximum. Atbias potentials beyond this point, the larger anode pulses are rejected by the upper threshold ofthe position computer, and the STROBE count rate drops off. The lower count rate of theSTROBE signals relative to the timing signals is primarily due to the position computer deadtime. Presented in figure 3.24b is the number of coincidence events detected over a range ofMCP bias potentials. The coincidence count rate should be dependent on both the STROBEand CFD count rates, and indeed the coincidence count rate exhibits a similar rise and fall withMCP potential as observed for the STROBE count rate.Presently, the bias potential of the MCP stack is set to maximize the number ofcoincidence events. At this point, the grid timing pulses are on the leading edge of thesaturation plateau. Future developments may add an additional amplification stage for theMCP timing pulses, which should provide more flexibility to meet the threshold requirementsChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 9425000 i I I Ia).20000- • CFD0 STROBE ...N 5ooo00•0c 010000 0 0oc;_) 0 05000- 00 I1800 2000 2200 2400 2600I Ib)500-Come.ioo-0 I I I I1800 2000 2200 2400 2600MCP Back Bias Voltage (V)Figure 3.24: The influence of the MCP bias potential on the count rates of thea) grid timing pulse at the CFD and the STROBE signal after the positioncomputer b) coincidence events.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 95and may allow for some improvement in sensitivity. As well, some enhancement inperformance may be possible through the optimization of the thresholds for the anode pulsesat the position computer.3.4.4 The MCP/RAE Position Calibration and UniformityThe nature of an (e,2e) scattering reaction identified by the pulse-pile-up circuitry ischaracterized by the (x,y) coordinate of the electron impinging on the MCP. As theinformation of interest in EMS is the relative azimuthal angle between this electron and itscoincident partner at the channeltron, a method of transforming the (x,y) coordinate toq-angle must be employed. In principle the conversion could be based on the knowledge ofthe geometric positions of the MCP/RAE and CEM detectors. However, any non-linearitiesin the response of the RAE or different gains in the X and Y output channels of the positioncomputer would destroy the necessary one-to-one correspondence between the anode imageand the positions of electrons striking the incident face of the MCP. To calibrate the image ofthe RAE, an angular mask, with 1° slots spaced every other degree, was fabricated from0.002-inch thick beryllium copper shim stock. A photoreduced CAD (computer aided design)drawing of the mask was used in the photolithographic etching of the shim stock. Calibrationwas performed with the mask positioned in front of the incident face of the MCP stack andaligned relative to the CEM. An angular definition obtained in this manner negates the effectsof any distortion of the RAE image, since the image of the mask would be equally distorted.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 96Presented in figure 3.25a is an image of the mask obtained by accumulating (x,y)position coordinates of electrons elastically scattered from argon at 600 eV and striking theMCPIRAE detector. The slots in the mask are well defined in the image, although scatteringof electrons from the edges of the slots is suspected of slightly broadening the image of the 10slots relative to the 10 filled area of the mask. Figure 3 .25b displays a similar mask imagerepresenting the accumulated positional information of coincidence events, resulting from the(e,2e) ionization of argon 3p electrons. The variation of intensity of the image with phi angleis quite evident. As the different collision volumes for elastic scattering and (e,2e) scatteringhave an effect on the MCPIRAE image, the coincidence image is used to specify the angulardefinition.In formulating an angular definition of the image, a balance between individually defmingeach bin and fitting the entire image with a single arc was required. A good compromise wasobtained by using two arcs, having independent focal points and angular positions. One arc isused to describe the slot spacing on the inside of the mask image, while the other describes theslots at the outer region of the arc. An interactive computer program has been written tofacilitate the definition of the angular bins. The program permits a region of the mask imageto be magnified (on a computer monitor) and the parameters of the two arcs to be modified togive a description of the image. Joining the corresponding angles of the two arcs gives rise tothe angular definition presented in figure 3.25c. The mask is removed in the normal operationof the spectrometer, and the angular definition is used to assign an azimuthal coordinate toChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 97a) Elastics ImageCoincidence ImageFigure 3.25: Calibration of the MCPJRAE p-angle information: (a) image ofelectrons elastically scattered from argon, (b) image of coincident electrons fromthe ionization of the 3p electron of argon, (c) the definition of azimuthal anglebins.b)c) Angle DefinitionChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 98each (x,y) position of an (e,2e) coincidence event. At present, the positions are allocated into1° bins, which sets the azimuthal angular resolution of the MCPIRAE detector to zp = ±0.5°.An important requirement in the momentum dispersive design of the spectrometer is theuniform transmission and detection of electrons about the observed azimuthal range. Asdiscussed in chapter 1, an EMS instrument developed by Moore and colleagues [53,54] usingan array of CEM detectors, requires frequent calibration to account for the variation of theefficiency of each CEM. Significantly more uniform response should be provided by the useof an MCPIRAE detector. A recent study by Brigham et al. [1051 tested the characteristics ofan MCPIRAE detector similar to the device used here, and found the detector to have lessthan 1% deviation in the count rate at various positions over its surface. An indication of theresponse of the MCP/RAE detector employed in the present application is given in figure 3.26,in which a typical distribution of the background (i.e. non-coincidence) electrons impinging onthe MCP/RAE detector is presented. The distribution is very consistent over a p-range of± 26°, although outside of this angular window the intensity decreases. The drop in intensityat the larger angles is believed to be a result of a restriction in the transmission of the electronsnear the ends of the slits in the conical lenses. Presently these slits extend over a q-range of± 30°, and the widening of the slits to permit the deceleration of electrons without “endeffects” is also expected to improve the observed distribution at the larger angles. As a resultof the distortion at the larger p, the momentum profiles presented in this thesis are only shownChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 99I I I I I I I I I3000--2500 --2000 --1500--I.1000--500--0 I I I I I I I I-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30Azimuthal Angle (degrees)Figure 3.26: The angular distribution of background (non-coincidence) electronsat the MCP/RAE detector.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 100to ± 26°. However, the uniformity shown over this range is encouraging for the application ofthe detector to the measurement of the angular distribution of (e,2e) coincidence events.3.4.5 Linearity of the DetectorsThe saturated operation of the MCP and CEM detectors is important to ensure theiruniform response over a range of experimental conditions. The gain of each detectordecreases at higher rates of incident electrons [56]. If an increased incident flux causes theoutput pulse height distribution of a detector to pass below the discrimination threshold, themeasured count rate may decrease or register a smaller increase than expected. As a thoroughtest of the operation of the CEM and MCP detectors, a series of investigations (using heliumas the target gas) was performed in which the rates of electrons striking the detectors weredramatically varied. Figure 3.27 presents the CEM, the MCP (timing grid), and thecoincidence event count rates as a function of the electron beam current measured at theFaraday cup. The linear response of the CEM and MCP detectors is clearly displayed. Theobserved linearity of the coincidence count rate is also a reflection of the low dead time of thecoincidence and gated position computation circuitry. The count rates were also monitored asa function of the gas pressure and a similar linear response was obtained. It should be notedthat the variation of electron flux in these measurements represents extreme conditions. In thetypical measurement of a binding energy spectrum, the rate of electrons incident on thedetectors changes very slightly (< 3% for a change in cathode potential from 1224 eV toChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 101NCa)0UUNCUU1200Faraday Cup Current (hA)Figure 3.27: The response (count rate) of the detectors and coincidencedetection circuitry over a range of electron beam currents.0 10 20 30 40 50 60 70Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 1021265 eV), while during the determination of a momentum distribution at a given bindingenergy, the electron flux is essentially constant.3.4.6 The Coincidence Timing WindowsThe size of the coincidence timing windows of the pulse-pile-up circuitry is primarily afunction of the width of the pulses input into the power combiners and of the discriminatorlevels of the power combiner outputs. The widths of both the ‘true + accidental’ and the‘accidental’ windows were measured by splitting the signal from a pulse generator (HP8082A)and inputting the two pulses to the CFDs to simulate coincidence events. A fixed delay wasintroduced after one CFD, and a digital delay generator (Stanford Research Systems DG535),interfaced with the 286 PC using a GPIB board, was used to introduce a variable delay afterthe other CFD. The time delay between pulses was varied in short (typically 0.05 ns) stepsthrough the two timing windows, identifying the degree of overlap of timing pulses required togive a PPU coincidence detection. With this measurement procedure, the thresholds of bothchannels were adjusted to record coincidences on the condition of two pulses arriving at theinputs of the power combiner within ±1.5 ns of each other. Displayed in figure 3.28 is thesimulated coincidence count rate measured as the digital delay was swept through the‘true + accidental’ window.In a TAC-based system, the ‘true + accidental’ coincidence timing window is adjustedabout the peak in the TAC spectrum. In contrast, the present system requires the coincidenceChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 103peak to be adjusted to fit within the coincidence timing window. The appropriate delayrequired to align the coincidence peak and timing window has been determined by addingshort lengths of RG-174 coaxial cable to the output of the CFDs. Figure 3.29 displays thevariation of the coincidence count rate for the different lengths of delay line. The shape of thedistribution is effectively the convolution of the 3.02-ns coincidence timing window (figure3.28) by the coincidence peak shape (1.6 ns FWHM, see TAC spectrum figure 3.11). Tnnormal operation the delay is set to the middle of the distribution, ensuring that thecoincidence peak is centered in the timing window.The relative PPU detection efficiencies of the ‘true + accidental’ and ‘accidental’channels are periodically tested using a pulse generator (HP8082A) in place of the CEM signalto provide pulses of greater frequency (typically 20-40 kHz). As the simulated CEM and theMCP pulses are uncorrelated in this situation, both channels are subjected to the sameaccidental count rate, and the PPU coincidence count rate of each channel is indicative of itscoincidence detection efficiency. Additionally, during the course of an EMS measurement, thedetection efficiency of the channels is monitored by the relative counts of the channels whenthe cathode potential is set below the energy required for (e,2e) ionization of the sample. Therelative efficiencies are taken into account in removing the accidental background from thebinding energy and momentum profile measurements.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 104350, 3000250C)200150 E— 3.O2ns10050022 23 24 25 26 27 28Digital Delay (ns)Figure 3.28: The ‘true + accidental’ PPU coincidence timing window.5000 i40004-’o 3000c)C)0______3.Ons2000 FWHMIc-)I1000I0-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6CFD Delay(ns)Figure 3.29: The variation of coincidence counts with the addition of delay lineafter the CEM or MCP CFD. The solid points are ‘true + accidental’ coincidenceevents and the open circles are ‘accidental’ events.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 1053.5 Experimental ResultsThe stage is now set for the presentation of some proof-of-concept measurementsillustrating the capabilities of the momentum dispersive, multichannel spectrometer. Only the‘opening act’ is given in this section, as a more full presentation of the multichannel EMSinvestigation of a number of atomic and molecular systems is given in the following chapter.During the measurements presented in the figures below, argon was introduced to the collisionchamber through a Granville-Phillips leak valve to a pressure of 1.0x105 torr (measured withan ion gauge at the top of the vacuum chamber). Additionally, the electron beam current wasset to 60 jiA.The improved coincidence collection efficiency of the new instrument permits a largereduction in the acquisition time required for EMS measurements of a given statisticalprecision. This is clearly illustrated in figures 3.30 and 3.31, which respectively show abinding energy spectrum and momentum distribution of the argon 3p electron. Each point inthe binding energy spectrum was acquired for a period of 53 seconds, and represents the totalof coincidence counts collected over the ± 26° angular range of the MCPIRAE detector. Thetotal acquisition time of the spectrum was 15 minutes. The angular (p) distribution of argon3p presented in figure 3.31 was acquired at 53 angles simultaneously, over a period of 15minutes. Both spectra exhibit a high signal-to-noise ratio and a statistical quality comparableto many single channel results in the literature that required at least several days or weeks ofChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 106300• True+Accid. Come. ‘ Ar BES0 Accidental Coinc.250 -200- all 1angles150 --C.)CL)100--50- f-00 5 101520 25 30Binding Energy (eV)Figure 3.30: A binding energy spectrum of the argon 3p electron acquired in atotal of 15 minutes (— 53 seconds per point).CU0.)QCUChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 1071501209060300-30 -20 -10 0 10 20 30Azimuthal Angle (degrees)Figure 3.31: A momentum dispersive multichannel ( distribution of the 3pelectron of argon acquired in 15 minutes.300250200DCU0)00)0CUF150 H100500-30 -20 -10 0 10Azimuthal Angle (degrees)20 30Figure 3.32: A momentum distribution acquired in 46.5 hours using a singlechannel, p-angle scanning instrument [188].Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 108measuring time. The ability to measure binding energy spectra and momentum profiles isrelatively short periods of time has been described as “rapid orbital imaging”.To provide some perspective on the enhancement of sensitivity of the new instrument, amomentum profile of the Ar 3p electron obtained with a single channel instrument [188] (arecently retired predecessor of the present spectrometer) is shown in figure 3.32. The totalacquisition time of the 31 points in this spectrum was 46.5 hours. It is clear from acomparison with figure 3.31 that a very significant improvement in sensitivity has been realizedin the new multichannel instrument. A more detailed assessment of the degree ofimprovement would require consideration of many factors, including the operating conditions,detector performance, and energy resolution of both instruments.Measurements acquired over longer periods are presented below and permit a morequantitative evaluation of the instrumental performance. Figure 3.33 is a binding energyspectrum of the valence region of argon, acquired in 13.5 hours (15 mm/point). The spectrumexhibits peaks arising from ionization to the (3p)’ and (3sf’ states as well as a broad peakfrom ionization to (3s)’ satellite states that occur through electron correlation effects [761.The energy resolution exhibited in this spectrum is 4.3 eV.A typical high precision measurement of the phi-angle distribution of (e,2e) events fromthe argon 3p orbital, measured over a period of 6.2 hours, is displayed in figure 3.34a. TheChapter Three The Momentum Dispersive Multichannel EMS Spectrometer 10930003p I ‘Ar2500 BES20O011U 4.3 eV anglesl500 fwhm.— 3s().E1000CU500 Satellites0I0 10 20 30 40 50 60Binding Energy (eV)Figure 3.33: A high precision, q-angle integrated, binding energy spectrum ofargon acquired in 13.5 hours (15 mm. per point).Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 110Ar3pJTrue+Accid. Coin.0 Accidental Coin.aIII4IIIII1a.a.I0o000000000o0000000000000000000000000000000000C 000000-20 -10 0 10 20Azimuthal Angle (degrees)A) 35003000-_________2500-UI)2000 -a)0•E 15000U1000-5000B) 7000600040003000U2000100000.0Figure 3.34: (a) A high precision momentum dispersive multichannelp-distribution of the 3p electron of argon, acquired in 6.2 hours.(b) A high precision momentum profile of the 3p electron of argon, derived fromthe p-disthbution in (a).0.5 1.0 1.5 2.0Momentum (a.u.)Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 111accidental background (open circles) has been scaled by the relative sensitivities of the twoPPU channels (measured to be 1.37 ± 0.03), and exhibits an isotropic intensity distributionsimilar to that shown in figure 3.24. Subtraction of the background intensity, summation ofthe points at corresponding angles about q = 0°, and conversion from an angular to amomentum scale using equation (1.5), furnished the experimental momentum profile (XMP)displayed in figure 3.34b. Included in this figure is a theoretical momentum profile obtainedusing the ion-neutral overlap expression of the EMS cross section given in equation (2.6).The theoretical momentum profile was evaluated by E.R. Davidson using high level ion andneutral wavefunctions from an MRSD-CI calculation involving a basis set of 91 Gaussian-typefunctions [49,113]. For comparison to the XMP, the theoretical profile has been heightnormalized to the experimental data, and has been folded with the estimated instrumentalresponse function using the Gaussian-weighted planar grid method of Duffy et al. [49]. Witherror bars (one standard deviation) comparable to, or smaller than, the symbols representingthe data points, the profile exhibits significantly greater statistical precision than any previouslypublished work in the field of EMS. As well, the accuracy of the data is supported by theagreement with the high quality theoretical calculation in the momentum region below — 1.5a.u.. As discussed in chapter 2, the effects of distorted waves on the (e,2e) cross sectionbecome more pronounced at higher momenta. The degree of distortion observed in figure3.34b is of the same order as measurements and DWIA calculations reported by McCarthy etal. [76].Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 112It is clear from these measurements and a consideration of existing published work thatthe multichannel momentum dispersive spectrometer described in this chapter provides asignificant improvement in detection efficiency for EMS measurements. The application of amultichannel detector in a momentum dispersive architecture, and the development of a novelPPU coincidence detection system described herein, represents an important development asthe field of EMS strives to investigate increasingly complex systems and lower target densities.To conclude this chapter, a two-dimensional EMS measurement (2D-EMS)— the first of itskind— is presented in figure 3.35, giving a further illustration of the enhanced capabilities ofthe new instrument. The binding energyhp angle surface of argon for impact energies from1200 to 1260 eV, in 1eV increments, was obtained in 93.4 hours. Such a 2D-EMS surfacerepresents an alternative method of displaying EMS results and contains a wealth ofinformation regarding the intensities and symmetries of the various ionization transitions.Chapter Three The Momentum Dispersive Multichannel EMS Spectrometer 113Figure 3.35: Two dimensional electron momentum spectroscopy (2D-EMS): animpact energy I q’ angle distribution surface of argon, acquired in 93.4 hours.3pliteThChapter FourMomentum Dispersive Multichannel EMS MeasurementsThe binding energy spectra, the angular distributions, and the experimental momentumprofiles of the valence regions of the noble gases Ne, Kr and Xe, and of CH4 and SiH4 arepresented in this chapter. Argon results have afready been presented in chapter 3. Theprincipal motivation for these studies was to establish the quantitative response of themomentum dispersive multichannel spectrometer over the full valence region of a number ofsystems. The detailed characterization using relatively simple atomic and molecular systems isimportant for the application of the multichannel spectrometer to more demanding (in terms ofinstrumental performance) studies such as those presented in chapters 5 and 6. A secondmotivation was to obtain the most precise measurements to date, albeit at low energyresolution, of the experimental momentum profiles of these systems.As the noble gases have been thoroughly investigated in previous EMS studies, theypresent an excellent series of target systems for the quantitative evaluation of the multichannelinstrument. Earlier studies have investigated three general facets of the EMS scattering crosssection. The XMPs have been compared to the theoretical profiles calculated with a variety ofwavefunctions using a PWIA description of the collision process (see for example, Leung and114Chapter Four Momentum Dispersive Multichannel EMS Measurements 115Brion [25]). As well, the influence of distorted waves on the (e,2e) cross section has beeninvestigated [27,76,106,107]. Recently, much attention has focused on the EMS investigationof the satellite structure of the inner valence region of the binding energy spectra of noblegases [76,108,109,110,1111. This satellite structure arises from many-body (i.e. electroncorrelation) effects in the fmal-state (see for example, ref. [251). The EMS investigations havefound the shapes of the XMPs of the valence orbitals of the noble gases, obtained at impactenergies in the region of 1200 eV, to be well described at low momentum (< —1 to 1.5 a.u.) bytheoretical profiles using the PWIA and near-Hartree-Fock limit wavefunctions. However, therelative intensity of the inner valence (ns - where n is the principle quantum number) XMP tothe outermost (np) orbital XMP is generally overestimated by the PWIA cross section, whileimproved agreement is given by a distorted wave description [76,106,107]. This intensityvariation must be considered in the comparison of the momentum dispersive multichannelXMPs to PWL& theoretical profiles presented below.All of the PWIA theoretical momentum profiles presented in this chapter have beenfolded by the GW-PG method [49] using empirically determined angular resolution widths of= ±0.7° and Aq. = ±1.2°. A direct evaluation of the range of azimuthal and polar anglesassociated with the (e,2e) scattering events detected by the multichannel instrument isdifficult. However, the value of Aq is very consistent with the azimuthal resolution assignedto the RAE image, and the range of angles determined by the entrance aperture to the CEM.The value of AO is considerably smaller than the expected range of polar angles of electronsentering the cylindrical mirror analyzer, defined by the conical lens elements and collisionChapter Four Momentum Dispersive Multichannel EMS Measurements 116chamber slits (fig. 3.4). As the CMA is not expected to exhibit first or second order focusingof electrons to the exit slit, the range of polar angles of electrons detected by the MCPIRAEand CEM detectors should be smaller than the range entering the CMA. The poiar angleresolution used in the folding procedure is not inconsistent with these instrumentalconsiderations.Finally, it should be noted that in each of the experimental measurements presentedbelow, the ambient gas pressure was --1.0x105torr, and the incident electron beam current,measured at the Faraday cup, was maintained at —6O hA.4.1 NeonThe angle integrated (0- ±26°) binding energy spectrum of neon, obtained with themomentum dispersive multichannel EMS instrument, is presented in figure 4.1. To calibratethe energy scale, the lower energy peak, corresponding to the ionization of neon 2p electrons,has been positioned to the ionization potential of 21.57 eV, determined by PES measurements[112]. The second peak, corresponding to ionization of 2s electrons, is centered at 48.47 eVwhich is in good agreement with the IP of 48.46 eV measured by photoelectron spectroscopy[112], giving a good indication of the linear operation of the programmable high voltagepower supply used to scan the impact energy in the present instrument. Above the main 2speak, some low intensity sateffite structure is apparent, in agreement with the more detailedEMS investigation of this region of Samardzic et al. [110]. The solid line in the satelliteChapter Four Momentum Dispersive Multichannel EMS Measurements 117C2CUa)C.)a)C.)CU432100 10 20 30 40 50 60Binding Energy (eV)Figure 4.1: A multichannel (0 - ±26°) binding energy spectrum of the valenceregion of neon. The solid line represents the sum of Gaussian functions, fit to the2p and 2s peaks. Additional Gaussians, with intensities determined from the EMSmeasurement of Samardzic et al. [1101, are shown as dotted lines. The energyscale has been determined by setting energy of the 2p peak to the ionizationpotential identified by PES measurements [1121.é#Chapter Four Momentum Dispersive Multichannel EMS Measurements 118region of figure 4.1 (above the 2s main peak) represents the sum of Gaussian functionsdetermined from the energies and spectroscopic factors given by Samardzic et al. [110].The experimental momentum profile of the 2p electron is presented in figure 4.2. Theexperimental data are represented as solid circles, and the (one standard deviation) statisticalerror bars are similar to the point size. The single channel XMP (open circles) reported byLeung and Brion [251 is also shown in figure 4.2, and is in good agreement with themultichannel experimental profile. The improved statistical precision of the presentmultichannel measurements is readily apparent. Additionally, two theoretical momentumprofiles are also displayed: one based on a near-Hartree-Fock limit wavefunction [81] and theother an OVD determined from a MRSD-CI calculation using a 106-Gaussian basis set. Thetwo theoretical profiles have been individually normalized to the height of the multichannelXMP. While the single channel data have previously been reported to give good agreementwith the near-Hartree-Fock limit TMP [25], the present multichannel measurement indicatesthat both of the TMPs displayed in figure 4.2 overestimate the relative intensity momentum(>1 a.u.). This presented some confusion, since any discrepancy between theoretical profiles(using high-quality wavefunctions and the PWIA) and experimental profiles at high momentumvalues is typically in the opposite direction; the effects of distorted waves in the scatteringprocess generally cause the PWIA cross section to underestimate the EMS cross section inthis region. However, reported theoretical profiles of neon 2p, calculated using the DWIAChapter Four Momentum Dispersive Multichannel EMS Measurements 1190.0 0.5 1.0 1.5 2.0 2.5Momentum (a.u.)Figure 4.2: The multichannel experimental momentum profile for the 2pelectrons of neon (filled circles), compared to PWIA theoretical profiles calculatedwith an SCF wavefunction (dashed line) and with a CI wavefunction (solid line).The single channel XMP reported by Leung and Brion [25] is shown as opencircles.Neo Single channel• Multichannel——SCFCI••I I IChapter Four Momentum Dispersive Multichannel EMS Measurements 120[27] and the distorted wave Born approximation (DWBA) [106]’, exhibit a reduced intensityrelative to the PWIA profiles in the region above 1 a.u., consistent with the presentobservations. The variation of the profiles calculated in the plane wave and distorted waveapproximations is reasonably small, and an earlier experimental measurement of the neon 2pXMP by Braidwood et a!. [1061 (obtained at an impact energy of 1500 eV) was unable todistinguish between the PWBA and DWBA theoretical profiles. The present XMP of the neon2p electron is displayed in figure 4.3a with the digitized DWBA and PWBA theoreticalprofiles reported by Braidwood et a!. [106], and is clearly in better agreement with the TMPusing the distorted wave analysis. It should be noted that the PWBA profile has been scaledby 0.9 to match the peak intensity of the lower DWBA profile [106].The multichannel experimental profile for the 2s electron, normalized to the 2p XMPusing the relative areas of the 2p and main 2s binding energy peaks, is shown in figure 4.3b.The DWBA cross section from Braidwood et al. [106] is also shown, and has been scaled bythe spectroscopic factor of 0.85, as in the original work [106]. Reasonable agreement of thistheoretical profile with the present experimental data is obtained.The DWBA calculation uses an alternative description of the (e,2e) scattering process, and includes theinfluence of distorted wave effects in the calculation of EMS cross sections, as in the DWIA. For a description,see Braidwood et al [1061.Chapter Four Momentum Dispersive Multichannel EMS Measurements 121I21086422.0 2.5Figure 4.3: Experimental momentum profiles of the 2p and 2s electrons of neon.The solid and dashed lines are digitized theoretical profiles from Braidwood et al.[106]86400.0 0.5 1.0 1.5Momentum (a.u.)00.0 0.5 1.0 1.5 2.0 2.5Momentum (a.u.)Chapter Four Momentum Dispersive Multichannel EMS Measurements 122The PWBA and DWBA cross sections presented in figure 4.3 were folded in the originalstudy [105] using the angular resolution of the energy dispersive EMS spectrometer at theFlinders University of South Australia. The resolution is likely slightly different in the twoinstruments, and different folding parameters would influence the shapes of the theoreticalprofiles. However, because of their large breadth, the TMPs and XMPs of the Ne 2p and 2selectrons should be less sensitive to instrumental resolution effects than the narrower profilesof larger systems such as Kr and Xe, presented below.4.2 KryptonThe angle integrated (0- ±26°) momentum dispersive EMS binding energy spectrum ofkrypton is presented in figure 4.4. The dashed curves shown in this figure are Gaussianfunctions centered on the more intense lines of the Kr PES spectrum reported by Svensson etal. [112]. The energy scale of the present BES was set relative to the Gaussian curvepositioned on the 4s ionization potential. Experimental momentum profiles were obtained atthe energies of the 4.p and 4s binding energy peaks, and are presented in figure 4.5. Therelative areas of the 4.p and 4s XMPs have been normalized to the areas observed in thebinding energy spectrum, in which all of the satellite intensity was assigned to the 4s manifold.Excellent agreement between the 4.p XMP and the 4.p fliP calculated using a near-HartreeFock limit wavefunction [81] is obtained below -1.3 a.u.. The theoretical profile for the 4selectron, shown in figure 4.5b, has been scaled by 0.74 and is in good agreement with theshape of the XMP below -0.8 a.u.. The requirement of a scale factor is not unexpected, asChapter Four Momentum Dispersive Multichannel EMS Measurements 123CL)a)C.)CU864200 10 20 30 40 50 60Binding Energy (eV)Figure 4.4: A binding energy spectrum of the valence region of krypton.Dashed lines are Gaussian functions centered on the energies of the (more intense)PES transitions reported by Svensson et al. [1121.Chapter Four Momentum Dispersive Multichannel EMS Measurements 1241.2‘:1,. 0.60.30.00.01.20.9. 0.60.30.00.0 0.5 1.0 1.5Momentum (a.u.)Figure 4.5: Experimental momentum profiles of the 4p and 4s electrons ofkrypton. Solid lines are theoretical profiles calculated using the near-Hartree-Focklimit SCF calculation of Clementi and Roetti [811. The 4s TMP has been scaledby 0.74.0.5 1.0 1.5 2.0 2.5Momentum (a.u.)2.0 2.5Chapter Four Momentum Dispersive Multichannel EMS Measurements 125similar attenuation of the theoretical profiles obtained using the PWIA (or PWBA) wereneeded to fit the XIvIPs of the inner valence electrons of neon [1061, argon [76], and xenon[106] measured at similar electron impact energies to that used in the present study. Distortedwave cross section calculations for the inner valence electrons of these systems exhibitreduced intensities relative to the PWIA calculation at low momentum, and are in much betteragreement with the XMPs [76,106,107].4.3 XenonThe angle integrated (0- ±26°) binding energy spectrum of the valence region of xenonis presented in figure 4.6. The increase in the intensity of the satellite structure relative to Ne,Ar (fig. 3.31) and Kr is quite apparent, although the number of individual states in the Xe 5smanifold is impossible to determine, due to the relatively low energy resolution of the presentmeasurements. A higher energy resolution EMS investigation of xenon has recently beenreported by Braidwood et al. [111], and the transitions identified in this study were used in theanalysis of the present binding energy spectrum. To calibrate the energy scale, the 5p peakwas positioned to the summed intensity of two Gaussian functions, representing the 5p3,2’ and5pi,’ transitions, with positions and relative areas obtained from Braidwood et al.[1 111 TheGaussian functions (dotted lines) at higher energies have fixed positions and relative areas asgiven by the earlier study [111]. The summed intensity of the Gaussians is represented by thesolid line, and is in very good agreement with the present binding energy spectrum.Chapter Four Momentum Dispersive Multichannel EMS Measurements 126I10864200Figure 4.6: A momentum dispersive multichannel (0 - ±26°) binding energyspectrum of the valence region of xenon. The dotted lines are Gaussian functionswith energies and relative intensities determined from the EMS measurementreported by Braidwood et al. [1111.10 20 30 40 50 60Binding Energy (eV)Chapter Four Momentum Dispersive Multichannel EMS Measurements 1270.000.02.000.000.02.001.501.000.500.5 1.0 1.5 2.0Momentum (a.u.)2.51.501.000.50•10.5 1.0 1.5Momentum (a.u.)Figure 4.7: Experimental momentum profiles of the 5p and 5s electrons ofxenon. The PWIA theoretical profiles were obtained using the near-Hartree-Focklimit SCF calculation of Clementi and Roetti [811. The 5s TMP has been scaledby 0.62.2.0 2.5Chapter Four Momentum Dispersive Multichannel EMS Measurements 128The area of the 5p BES peak and the summed area of the 5s main peak and sateffiteintensity are used in the relative normalization of the experimental momentum profiles shownin figure 4.7. The shape of the 5p XMP is very well described by the theoretical profilecalculated in the PWIA, using the near-Hartree-Fock limit wavefunction of Clementi andRoetti [81]. The 5s TMP in figure 4.7b has been scaled by 0.62 and gives reasonableagreement to the low momentum region of the XMP. The 5s experimental profile exhibits arelatively large intensity at high momentum, indicating a considerable contribution fromdistorted wave effects. The EMS measurements of xenon by Cook et al. [107] andBraidwood et al. [1111 display a similarly large plateau in the 5s XMP at higher momentum,which is in agreement with distorted wave calculations presented in these studies.4.4 A Summary of the Noble Gas MeasurementsFigure 4.8 presents a collection of the momentum dispersive multichannel measurementsof the outer valence (np) momentum profiles of the noble gases. The azimuthal angulardistributions (0- ±26°) are displayed in the left-hand column. The distributions are verysymmetric about the central angle, providing further evidence of the uniform detectionefficiency of the MCPJRAE detector, as well as the uniform transmission of electrons throughthe analyzer, over the measured range of azimuth. The experimental momentum profilesobtained from these angular distributions are shown in the right-hand column of figure 4.8.The XMP for the 3p electron of argon is compared to the TMP calculated from a MRSD-CIwavefunction having a basis set of 190 GTOs, recently provided by E.R. Davidson [113].Chapter Four Momentum Dispersive Multichannel EMS Measurements 129-20 -10 0 10 20 0.5 1.0 1.5 2.0 2.5Azimuthal Angle MomentumFigure 4.8: The angular distributions and experimental momentum profiles forthe noble gases Ne-Xe. The Ne theoretical profiles (t) are from Cook et al. [107].The Ar 190-G(CI) OVD calculation was provided by E.R. Davdison [113]. The Krand Xe TMPs () were calculated using a Clementi and Roetti SCF wavefunction[81].Chapter Four Momentum Dispersive Multichannel EMS Measurements 130With the exception of neon (see above discussion), all of the TMPs shown in this figure havebeen folded using the GW-PG method [49] with angular resolution values of AG = ±0.7° andAq = ±1.2°. Very good agreement between the theoretical and experimental profiles isshown, below 1 to 1.5 a.u.. Finally, it is interesting to note that the column of XMPs in figure4.8 clearly exhibits the contraction in momentum space of the outermost orbital as the spatialextent of the orbital increases (i.e. with increasing principal quantum number). The reciprocalnature of the momentum and position space distributions is explored in detail by Leung andBrion [25].4.5 Multichannel EMS of Methane and SilaneThe noble gas measurements give a clear display of the ability of the new instrument toaccurately measure XMPs for a range of target systems. However, the influence of distortedwaves prevents the quantitative comparison of the inner valence experimental profiles totheoretical profiles calculated in the plane wave impulse approximation. A furtherinvestigation of the response of the new spectrometer to the measurement of XMPs, over thefull valence binding energy region of a target system, was performed by the study of themolecular target systems methane and silane. Previous EMS investigations of these systemshave shown the experimental momentum profiles for the outer and inner valence electrons tobe well described by TMPs obtained from near-Hartree-Fock or CI wavefunctions, in thePWIA representation of the scattering cross section [32,38]. The multichannel (0 - ±26°)binding energy spectrum of methane is presented in figure 4.9. Gaussian functions, havingChapter Four Momentum Dispersive Multichannel EMS Measurements 131widths estimated from the EMS measurements of Clark et al. [32] and a consideration of thedifferent instrumental energy resolution of the earlier [32] and present studies, were fitted tothe BES and are shown in figure 4.9. Calibration of the energy scale was performed bycentering the 2a1 peak to the vertical ionization potential of 23.05 eV given by photoelectronspectroscopy [114,115]. In accord with previous work [32], the satellite intensity above themain 2a1 peak has been assigned to the 2a1’ process.This assignment is reflected in the relative normalization of the it2 and 2a1 experimentalmomentum profiles, presented in figure 4.10. The (angular resolution folded) theoreticalmomentum profiles of both orbitals, calculated using 146-Gaussian basis function MRSD-CI(146-G(CI)) wavefunctions of the molecule and final ion [32], are also shown in this figure.The it2 XMP has been normalized to the height of the theoretical profile, and exhibits verygood agreement with the shape this profile. In terms of both shape, as well as intensity, thetheoretical profile of the 2a1 orbital corresponds very well with the 2a1 XMP. The excellentagreement between both the present and previous measurements with the i46-G(CI)theoretical profiles, confirms the quantitative accuracy of the new instrument.The only previous EMS investigation of the valence region of silane has been reportedby Clark et al. [38]. While a small, but significant, discrepancy was reported [38] between theXMP of the 2t orbital and the TMPs calculated from a 126-GTO SCF wavefunction and fromi26-G(CI) neutral and ion wavefunctions, this has since been shown to be due to inadequateaccounting for angular resolution effects in the original study [20]. The theoretical profiles ofChapter Four Momentum Dispersive Multichannel EMS Measurements108CCdDCU1)C.)CU200Binding Energy (eV)Figure 4.9: A multichannel (0 - ±26°) binding energy spectrum over the valenceregion of methane. The peak of the 2a1 transition has been set to the ionizationpotential of 23.05 eV [114,115] to calibrate the energy scale.13210 20 30 40 50 60Chapter Four Momentum Dispersive Multichannel EMS Measurements 133(a) I I CH4it21.0146-G(CI)10.50.0 I I I0.0 0.5 1.0 1.5 2.0 2.5Momentum (a.u.)I I I I(b)CH42.0 2a11.5•_146-G(CI)±10.5.••.0.0 •••.....I..0.0 0.5 1.0 1.5 2.0 2.5Momentum (a.u.)Figure 4.10: The multichannel momentum dispersive XMPs for the it2 and 2a1electrons of methane. The solid lines are the TMPs calculated using a 146-G(CI)wavefunction [32].Chapter Four Momentum Dispersive Multichannel EMS Measurements 134the 3a1 orbital exhibited a very similar shape to the XMP, although the TMPs were generally—1O% greater in intensity[38]. The present measurement of the momentum dispersivemultichannel binding energy spectrum of silane is displayed in figure 4.11. Using peak widthsestimated from the BES measurements of Clark et al. [38], the main 2t and 3a1 peaks werefitted by appropriate Gaussian functions. In accord with the earlier study [38], all of theintensity in the inner valence region has been attributed to the 3a1’ transition, in the relativenormalization of the XMPs.The multichannel experimental momentum profiles for 2t and 3a1 electrons of silane arepresented in figure 4.12. The 2t XMP has been height normalized to the 126-G(CI) TMP,and the agreement observed with the shape of the theoretical profile is reasonable. The XMPof the 3a1 electron also agrees well with the shape of the 3a1 TMP, although the experimentalcross section has slightly greater intensity. The X]VIP intensity at higher momentum valuessuggests the existence of distorted wave effects. Some of the intensity variation, particularlyat lower momentum, may be a result of the assignment of the BES satellite intensity to the3a1 transition. A Green’s function (ADC(4)) calculation of the pole strengths (spectroscopicfactors) in the silane BES reported by Clark et al.[38] suggests that some of the satelliteintensity arises from the 2t1 ionization process, with at least 2.4% of the intensity of the main2t peak appearing at transition energies above 20 eV. This would influence the height of the3a1 XMP, as the satellite intensity has been included in the relative normalization of the profileto the 2t XMP. Correcting the normalization for 2t satellites, using 2.4% of the main peakChapter Four Momentum Dispersive Multichannel EMS Measurements 135C0UC)I)C)• —CU1210864200 10 20 30 40 50 60Binding Energy (eV)Figure 4.11: A binding energy spectrum of the valence region of silane. Thewidths of the Gaussian functions fit to the 2t and 3a1 peaks have been estimatedfrom the higher energy resolution measurements of Clark et al. [38], and theenergy scale of the present BES has been determined relative to the two Gaussianfunctions. Additional Gaussians are included to fit the satellite intensity.Chapter Four Momentum Dispersive Multichannel EMS Measurements 136SiH‘-4Cl) 1.51 26-G(CI). 1.0aS0.5S....0.0 I ••.••S0.0 0.5 1.0 1.5 2.0 2.5Momentum (a.u.)(b) SiH43a14.030__126-G(CI)_xlO-.52.01.0-S0.0 I•OSiIIhII0.0 0.5 1.0 1.5 2.0 2.5Momentum (a.u.)Figure 4.12: The experimental and theoretical momentum profiles for the 2tand 3a1 electron of silane. The solid lines are the theoretical momentum profilesobtained from a l26-G(CI) wavefunction [38]. The dashed line is the 3a1 TMPscaled by 1.07.Chapter Four Momentum Dispersive Multichannel EMS Measurements 137intensity, requires the 3a1 XIvIP to be scaled down by approximately 95.6%. Alternatively, the3a1 theoretical profile may be scaled up by an additional 4.6%. The dashed line in figure 4.12brepresents TMP of the 3a1 electron scaled by a slightly larger value of 7% and is in goodagreement with the experimental cross section in the low momentum region. Hence, thepresent measurements offer support for the theoretical ADC(4) calculation, indicating a smallbut significant degree of splitting of the 2t main peak intensity.4.6 ConclusionsThe generally good agreement between the theoretical and experimental momentumprofiles for Ne, Ar, Kr, Xe, as well as for CH4 and SiFL1, together with the good overallconsistency with previous EMS measurements [32,38,76,105, 105j lends confidence to thequantitative accuracy of the presently reported momentum dispersive multichannel EMSinstrument. The agreement over the range of systems investigated also gives an indication ofthe reasonable characterization of the instrumental angular resolution effects.Chapter FiveEMS of Two Electron Systems: Helium5.1 BackgroundAs the simplest many-electron atom, helium is a particularly favorable system for theexperimental and theoretical investigation of electron correlation, or many-body, interactions.As early as 1929, Hylleraas [116] applied a formalism that explicitly included the interelectroncoordinate r12 to obtain a very accurate correlated wavefunction for the ground state ofhelium. This formalism is not easily extended to larger systems however, and since thispioneering work much attention has focused on alternative methods of accounting for electroncorrelation to permit an accurate description of the system (see chapter two). Early in thedevelopment of the EMS technique, it was shown [5,24] that the (e,2e) scattering crosssection for the ionization of helium from the ground state atom to the ground state ion wasalready well described by a theoretical profile calculated using a near-Hartree-Fock limitwavefunction, and subsequent studies [26,70] indicated that the inclusion of electroncorrelation in the description of the helium wavefunction had little effect on the theoreticalEMS profile. In contrast, the theoretical estimate of the cross section for the (e,2e) transitionto the n=2 excited final ion state of helium was shown to be much more sensitive to the effectsof electron correlation in the target wavefunction [117,118], indicating the possibility for138Chapter Five EMS of Two Electron Systems: Helium 139experimental measurement of these transitions to provide insight into the wavefunction of theneutral helium atom and the influence of initial state electron correlation.In the plane wave impulse approximation (PWIA), the EMS cross section isproportional to the momentum-space overlap of the neutral target and final ion wavefunctions(eqn. 2.6). As the wavefunction for the helium ion may be obtained exactly, the EMS crosssection provides a direct probe of the ground state atomic wavefunction. In the configurationinteraction formalism, the ground state wavefunction for helium is dominated by the HartreeFock configuration consisting of two electrons in a is orbital, with smaller contributions to thewavefunction given by singly and doubly excited configurations (see for example refs.[119,120]). Since the theoretical momentum profile corresponding to the (e,2e) ionizingtransition to the ground state ion is dominated by the overlap of the is ion wavefunction withthe primary Hartree-Fock configuration of the neutral atomic wavefunction, it is not verysensitive to initial state correlation. However, if the (e,2e) collision leaves the final ion in ann=2 or higher excited state, the overlap of the final ion wavefunction with the excitedconfigurations of the target atom wavefunction contribute significantly to the EMS crosssection. For such transitions to excited ion states, both the shape and magnitude of the EMScross sections are sensitive to the effects of initial state correlation.The accurate measurement of the experimental momentum profiles for the transitions tothe excited ion states is hampered by their relatively low cross sections. The investigation ofthe (e,2e) ionization to the ground and degenerate 2s and 2p excited ion states wereChapter Five EMS of Two Electron Systems: Helium 140investigated first in the symmetric coplanar geometry by McCarthy et at. [117], andsubsequently in the symmetric non-coplanar geometry by Dixon et at. [118]. As theseexperimental studies predated the development of multichannel EMS techniques, singlechannel instruments were employed and the (e,2e) cross sections were measured at a few(polar [117], and azimuthal [118]) angles with poor statistical precision. Nevertheless, thesestudies clearly indicated that the EMS cross section for the transition to the n=2 excited ionstate calculated using an SCF description of the helium atom gave an extremely poordescription of the experimental results, while significantly improved agreement was given by aTMP calculated with the correlated wavefunction of Joachain and Vanderpoorten (.TV) [121].Using an energy dispersive multichannel instrument, improved measurements wereobtained by Cook et at. [26], and their results are reproduced along with the reportedtheoretical profiles in figure 5.1. The XMP for the transition to the n= 1 ion state (fig 5.1 a) isin very good agreement with the (digitized) theoretical profile calculated using the JVcorrelated wavefunction, which, as expected, is very similar to the TMP obtained using a nearHartree-Fock limit wavefunction [26]. The wavefunction sensitivity of the cross section forthe (e,2e) transition to the n=2 ion state is evident in figure 5. lb. The n=2 theoretical profileobtained using a near Hartree-Fock limit wavefunction has the same shape as the TMP for thetransition to the n=1 fmal ion state, while the profile obtained with the correlated JVwavefunction, exhibits a much different cross section in both magnitude and shape. Theexperimental measurement of the n=2 cross section is clearly in much better agreement withChapter Five EMS of Two Electron Systems: Helium 1412.52.01.51.00.50.00.020CCo 0.016Cl)LIDLIZ 0.01220.0000.0040.0030.0020.0000.0000.0 0.5 1.0 1.5 2.5Momentum (a.u.)Figure 5.1: The EMS cross section for the ionization of helium to the n=1, n=2,n=3 final ion states. The experimental data (solid points) and theoretical profileshave been digitized from Cook et al. [26]. The dashed profile was calculated usingan SCF wavefunction while the solid profile used the correlated wavefunction ofJoachain and Vanderpoorten [121].2.0Chapter Five EMS of Two Electron Systems: Helium 142the JV profile than with the profile calculated from the SCF wavefunction. However, theagreement between the JV profile and the XMP is reasonable, particularly in the region below1 a.u.. In figure 5. ic the TMPs for the transition to the n=3 final ion state, calculated with acorrelated wavefunction [121] and a near Hartree-Fock limit wavefunction, are presented.Also shown on figure 5. ic are three experimental points, representing the EMS cross sectionmeasured by Cook et at. [26] at three relative azimuthal angles. These are the onlyexperimental values for the EMS transition to the n=3 ion state reported prior to the presentwork, and the size of the error bars gives an indication of the difficulty of measurement.Nevertheless, the data points strongly suggest the importance of electron correlation effects inthe transition to the n=3 state of He.Two additional experimental measurements of the EMS cross section for the ground andexcited final ion transitions of helium have been reported since the earlier work. Using amomentum dispersive multichannel spectrometer (see chapter one or ref. [53]), Smith et at.[30] investigated the n=1 and n=2 helium cross sections’. Unfortunately, both the n=1 andn=2 experimental cross sections reported by Smith et at. [30] were independently normalizedto theoretical profiles, preventing direct comparison of the magnitude of the n=2 XMP totheory or to other experimental measurements. A much more stringent investigation of then=2 theoretical cross section is permitted if the relative normalization of the n 1 and n=2experimental profiles is maintained. One point emphasized by Smith et at. [30] is the1 For convenience, the cross section for the (e,2e) transition of helium to the n=1 (2,3) final ion state is referredto throughout this chapter as the n=1(2,3) cross section.Chapter Five EMS of Two Electron Systems: Helium 143difference in distortion potentials for the n=1 and n=2 helium ion states, which influences theoutgoing electrons and gives rise to an increase in distorted wave effects in the n=2experimental cross section relative to the n= 1 cross section. Distorted wave effects wereshown to influence the shapes of the n=l and n=2 cross sections, particularly in the momentumregion above -.1.5 a.u. and —1.0 a.u. respectively [30]. However, an additional study ofdistorted waves effects in the EMS investigation of helium reported by McCarthy and Mitroy[122] indicated only a small influence on the cross sections of both the n=1 and n=2 transitionsat higher momentum.More recently, an asymmetric scattering geometry was employed by Labmam-Bennani etal. in an (e,2e) study of helium [31]. Asymmetric (e,2e) measurements offer some increase in(e,2e) cross section, and involve coincidence detection of a fast (-.5-10 keV) electron scatteredinto a small polar angle with respect to the incident beam direction, and a slower electrondetected over a range of polar angles. For sufficiently high energy of the ‘slow’ outgoingelectron it was earlier shown [74] that (e,2e) Bethe-ridge measurements in this geometrypermit a PWIA evaluation of the experimental momentum profile, as in the more conventionalmeasurements using the symmetric non-coplanar geometry. Additionally, using ‘slow’outgoing energies of 405 and 598 eV, experimental measurements in the asymmetric geometryhave been shown by Lahmam-Bennani et at. [74] to be less influenced by distorted waveeffects than XMPs measured with typical symmetric non-coplanar scattering kinematics. Inthe 1992 asymmetric (e,2e) study of helium [311, coincidence events were detected betweenfast electrons having energies of -P5500 eV, scattered into a polar angle of -.6.6 10, and ‘slow’Chapter Five EMS of Two Electron Systems: Helium 144electrons having (reasonably low) energies of —75 eV. Following a format used by Dixon etal. [118], and Cook et at. [26], these asymmetric scattering measurements [31] werepresented as the ratio of the cross sections for the n=2 and n= 1 transitions. This experimentalratio, along with that given by the data of Cook et at. (figure 5. la and 5. ib) is reproduced infigure 5.2. Also shown in this figure are the cross section ratios presented by LahmamBennani et at. [31], obtained from theoretical profiles calculated using an SCF wavefunction,and the four different CI wavefunctions of Tweed and Langlois (TL) [123], Taylor and Parr(TP) [119], Joachain and Vanderpoorten (JV) [121], and Nesbet and Watson (NW) [119].The percentage of the total correlation energy accounted for in each calculation, are shown inbrackets in figure 5.2. Although all of the wavefunctions recover a large fraction of thecorrelation energy, a significant variation in the theoretical nt2/n=1 cross section ratios ispresent. With the exception of a single point at 1.5 a.u., the data points of Lahma.m-Bennaniet at. [31] (solid circles in figure 5.2) are consistently lower than those of Cook et al. [26](open circles), and are in better agreement with the theoretical ratios calculated using thelower energy JV and NW wavefunctions. Lahmam-Bennani et at. [31] have suggested thattheir asymmetric measurements are less influenced by distorted wave effects than themeasurements of Cook et at. [26], giving rise to the lower experimental cross section ratio,particularly in the higher momentum region. Lahmam-Bennani et a!. [31] also noted thatwhile the TL theoretical cross section ratio is significantly higher than their data points atlarger momenta, the TL ratio gives an improved agreement over the JV and NW ratios to theexperimental data in the low momentum region (although the JV ratio appears to give quiteChapter Five EMS of Two Electron Systems: Helium 145Figure 5.2: The theoretical and experimental helium n=2 to n=1 cross sectionratios, digitized from ref. [31]. The solid points are the experimentalmeasurements of Labmam-Bennani et al. [74], and the open points represent themeasurement of Cook et al. [26]. The helium wavefunctions used in the evaluationof the theoretical profiles are identified on the right axis with the percentage of thecorrelation energy recovered by each wavefunction calculation. The wavefunctionsare: TL [123], TP [119], JV [121], NW [1201.% correlationTL94C.C.C)‘1.)rJCl)C,)CU0.070.060.050.040.030.020.010.000.0TP 85JV 98.0NW 97.7HF2.50.5 1.0 1.5 2.0Momentum (a.u.)Chapter Five EMS of Two Electron Systems: Helium 146good agreement to 0.5 a.u.). A more detailed evaluation of the theoretical cross section ratiosis limited by the statistical precision of the experimental measurements of both Cook et at.[26] and Lahmam-Bennani et al. [31].5.2 A Momentum Dispersive Multichannel EMS Investigation of HeliumIt is evident that the unambiguous assessment of the theoretical profiles calculated withthe various correlated wavefunctions requires a marked improvement in the measurement ofthe experimental profiles for the transitions to the n=2 and n=3 ion states. Data of higherstatistical precision and accuracy are clearly needed. In this regard, it was noted by McCarthyand Mitroy [122] that “further refinements to the (DWIA) calculation would be justified onlyif more-accurate experimental data are available”. The enhanced collection efficiency of thepresently reported multichannel EMS spectrometer should provide an opportunity to measurethe helium n= 1, 2, and 3 cross sections with significantly improved statistical precision andaccuracy, as well as with more data points, since all 53 azimuthal angles are sampledsimultaneously. At the outset of the study of helium, it was anticipated that the previousexperimental investigations, particularly that of Cook et at. [26], would provide a solidfoundation to aid in the interpretation of the present measurements. However, as will bediscussed below, the present measurements exhibit some significant differences from thepreviously reported experimental cross sections and also from the theoretical predictions.Chapter Five EMS of Two Electron Systems: Helium 1475.2.1 Theoretical Momentum ProfilesDespite the high quality of the correlated wavefunctions used in the calculation of thepreviously reported theoretical cross sections for the (e,2e) transition to the n=2 state of thehelium ion [26,28,29,3 1], the various theoretical profiles have shown a significant variation inboth shape and intensity. In an effort to identify a degree of convergence in the theoreticalprofiles, the n=1 and n=2 TMPs calculated with more accurate correlated wavefunctions havebeen obtained in the present work (see below). The theoretical momentum profiles for the(e,2e) ionization to the n= 1 and n=2 final ion states were first recalculated using the heliumwavefunction of Nesbet and Watson (NW) [1201 to provide a quantitative reference to earlierstudies [29,31]. The CI wavefunction consists of 20 Slater determinants and yields an energyof -2.90276 a.u., corresponding to 97.7 % of the correlation energy. As the 2s and 2p heliumion wavefunctions are (essentially) degenerate, the calculation of the n=2 TMP includes theoverlap of the NW wavefunction with both the 2s and the 2p helium ion wavefunctions.Theoretical momentum profiles were also calculated in the present work using the CIwavefunction of Weiss (W) [124]. This wavefunction consists of 35 Slater determinants andgives an energy of -2.90320 a.u., corresponding to 98.75% of the correlation energy.All of the theoretical momentum profiles for the helium transitions reported to date havebeen based on SCF or CI wavefunctions. It is well known, however, that even more accuratewavefunctions for the ground state of helium can and have been determined by alternativeapproaches. Therefore, in the present work, two profiles based on very high quality correlatedChapter Five EMS of Two Electron Systems: Helium 148wavefunctions have been obtained. First, the theoretical profile based on the explicitlycorrelated wavefunction of Cann and Thakkar (CT) [125] was calculated by N.M. Cann, apost-doctoral fellow in the research group of C.E. Brion. The 200-term wavefunction givesan energy of -2.903724376 a.u., which is less than 10 nHartree from the estimated limit for theexact nonrelativistic energy of the helium atom [1261, and hence accounts for greater than99.9999% of the correlation energy. Additionally, a theoretical profile obtained from anatomic natural orbital expansion of a 141-term Kinoshita-type wavefunction [127,128], wasprovided by S. Chakravorty and E.R. Davidson (CD) of the University of Indiana [129]. Theoriginal Kinoshita type wavefunction yielded an energy of -2.9037243667 a.u., similar to theCT wavefunction, and also accounting for greater than 99.9999% of the correlation energy.The four theoretical momentum profiles (NW, W, CT, CD) calculated in the presentwork for the transition to the n=1, and n=2 ion states, and convoluted with the instrumentalresolution (see chapter 4), are shown in figure 5.3. Additionally, the (resolution folded)theoretical profiles for the transition to the n=3 final ion state, calculated with the CT and CDwavefunctions, are shown in figure 5.3c. As expected, the n1 profiles are very similar to oneanother, with the CT and CD profiles slightly more intense than the profiles labeled W andNW. The momentum profiles for the transition to the first excited ion state are shown infigure 5.3b. It should be noted that each of the profiles includes a factor of 0.92 to account forthe variation of the kinematic terms of the EMS cross section [28] at the different impactenergies of the n=1 (1224.6 eV) and n=2 (1265.4 eV) transitions. This factor primarily reflectsChapter Five EMS of Two Electron Systems: Helium 1493.0 I I I(a)2.5 \ CT,CD He2.O1\ n=1w,Nw\1.51.00.5 -0.0(b)n=2CC(c)0.0030.002 CT,CD0.0010.000 I I I0.0 0.5 1.0 1.5 2.0 2.5Momentum (a.u.)Figure 5.3: Theoretical momentum profiles for the ionization of helium to then1, n=2, and n=3 final ion states. The cross sections have been obtained from thecorrelated wavefunctions of Weiss (W) [124], Nesbet and Watson (NW) [120],Cann and Thakkar (CT) [125], and Chakravorty and Davidson (CD) [1291.Chapter Five EMS of Two Electron Systems: Helium 150the change in the Moft scattering cross section at the higher impact energies (see figure 2.1).While the W and NW theoretical profiles, based on CI wavefunctions, continue to exhibitsome variation, the CT and CD profiles, each based on extremely accurate heliumwavefunctions, are essentially in exact agreement with each other, indicating that the variationin profiles has converged at this level of theory. These two profiles (CT,CD) thereforeprovide an excellent reference to assess the experimental measurements. The CT and CDprofiles for the transitions to the n=3 state, shown in figure 5.3c, are also in excellentagreement. Due to the change in the kinematic factors in the cross section for the n= 1(1224.6 eV) and n3 (1273.0 eV) transitions, the n=3 profiles have been scaled by a factor of0.91.5.2.2 Multichannel Binding Energy Spectra and Momentum DistributionsAn angle integrated (0- ±26°) binding energy spectrum of helium, exhibiting a largepeak corresponding to (e,2e) ionization to the n=1 final state, and a very small peak forionization to the n=2 final state, is shown in figure 5.4a. The n=2 region is expanded in figure5.4b. An initially unanticipated feature exhibited in the spectrum is the additional intensitybetween the helium n=1. and n=2 peaks. Careful investigation has shown that the extraintensity originates from multiple scattering effects. These effects, which involve theinteraction of an incident electron with two helium atoms in separate, sequential scatteringChapter Five EMS of Two Electron Systems: Helium 151150000100000L)00C0U 50000020001500U0C10000C0U5000Figure 5.4: (a) An angle integrated (0 - ±26°) binding energy spectrum ofhelium. (b) An expanded view of about the n=2 helium ion peak, exhibiting extraintensity from double scattering effects. The solid and open circles represent twoseparate measurements performed under similar conditions. The two data sets arenormalized on the n=1 peak.20 40 60 80Binding Energy (eV)40 50 60 70 80 90Binding Energy (eV)Chapter Five EMS of Two Electron Systems: Helium 152events along the incident electron beam direction, can be summarized as follows for the mostlikely double collision process:(i) e(1245.8eV)+He(1’S) -4 He(21P)+e_(1224.6eV)(5.1)(ii) e(1224,6eV)+He(1’S)—> He(n=1)+e-(600eV)+e-(600eV)The first interaction (eqn. 5. ii) is essentially a dipole (e,e) scattering event [130,1311 which ischaracterized by a low momentum transfer, forward scattering, collision along the incidentbeam path prior to the coincidence interaction region. The excitation of helium from theground state to the 2’P state is commensurate with an energy loss of an incident electron of21.2 eV (see for example refs. [125,1321). With the cathode potential set to yield an incidentelectron beam with a mean energy of 1245.8 eV, this energy loss process would give rise toelectrons with an energy of -.1224.6 eV in the ongoing incident electron beam. At thisreduced kinetic energy, the incident electrons may undergo an (e,2e) collision, ionizing ahelium atom (to the n=1 final ion state) in the coincidence interaction region (eqn. 5. lii), togive a detected ‘true’ coincidence event. In this manner, intensity corresponding to the (e,2e)ionization of helium (n=1) may be observed at (and at all energies above) an apparent bindingenergy of 45.8 eV (with a spread due to the -.4.5 eV FWHM energy resolution). Of course,the (e,e) excitation of helium represented in 5. ii, may also occur from the ground state to anyof the higher helium n’P states, as well as to the ionization continuum [132]. Intensity fromsuch double scattering processes may therefore be observed at any setting of the cathodepotential above approximately 1245 eV, corresponding to a binding energy of 45 eV (inChapter Five EMS of Two Electron Systems: Helium 153actuality above -40eV due to the energy resolution of -4.5 eV FWHM). Since the (e,e) crosssection producing He(n’P) is much larger than the (e,2e) cross section producing He (n=1),the (e,2e) signal resulting from electrons formed in such double collision processes canbecome significant compared with that for the, even lower cross section, (e,2e) production ofthe He n=2, and 3 excited ion states, as can be seen in figure 5.4b.The nature of the additional, unexpected intensity in the BES of figure 5.4b , and theabove hypothesis, were investigated by measuring the helium BES at a reduced sample gaspressure. The EMS scattering count rate (eqn. 2.10) is directly proportional to the numberdensity of target atoms, while the double scattering count rate should to be proportional to thesquare of the target density. Hence, intensity from the double scattering processes would beexpected to decrease relative to the intensity of the n=1 and n=2 peaks, at the reducedpressure. Indeed, such a reduced intensity was observed (see for example, figure5.5b) at thelower gas pressure, providing strong support for the proposed double scattering mechanism.Of particular concern for the present investigation of the helium XMPs, is the possibilityof a significant contribution from the double collision processes underlying the intensity of theHe n=2 transition at 65.4 eV. To evaluate this contribution, the variation of the intensityfrom the double collision processes with electron impact energy (E0) was estimated from thehighly accurate helium optical oscillator strength measurements obtained from low-momentumtransfer, electron impact (dipole (e,e)) spectroscopy by Chan et al [132]. The opticalChapter Five EMS of Two Electron Systems: Helium 154oscillator strength is proportional to the differential (forward) electron scattering cross sectionby a factor which varies as -E03 [133]. The dash-dot curve presented in figure 5 .4b is thecomplete excitation and ionization optical oscillator strength spectrum of Chan et al. (seefigure 7 of ref. [132]), scaled by E03, convoluted with the present energy resolution, andshifted to the appropriate energy scale by adding the ionization potential of helium (24.59 eV)to give a threshold of —41 eV. Normalized to the BES intensity at the left of the n=2 peak, thecurve reproduces the general trend of the double collision peak; however, the intensity at —47eV is underestimated. This may reflect a breakdown in the assumption that the first scatteringevent does not significantly alter the direction of the incident electron. Small momentumtransfer collisions involving (e,e) dipole forbidden energy loss transitions, may havecontributed to intensity arising from the double scattering processes.The contribution of the double collision processes is estimated from the optical oscillatorstrength (dash-dot) curve to be 4% of the maximum peak height of the n=2 transition.Experimental momentum profiles for the n=l and n=2 transitions were measured byaccumulating (e,2e) events at the maxima of the peaks in the BES. To correct for the smallcontribution of the double collision processes, a fraction of the n=l XMP, totaling 4% of thesummed intensity (0 to ±26°) of the n=2 XMP, was removed from the n=2 experimentalprofile. The correction had a very small influence on the shape and intensity of the n=2 XMP.To permit the relative intensities of the n= 1, n=2 and n=3 EMS cross sections to bedetermined in the absence of, or at least with a reduced contribution from the doubleChapter Five EMS of Two Electron Systems: Helium 155scattering processes, the multichannel EMS spectrometer was slightly modified. As discussedin section 3.1.3, the collision chamber was altered to reduce the length of the gas cell in frontof the (e,2e) collision region. In addition, a differential pumping enclosure, separating theCMA entrance and collision region from the rest of the analyzer and detector system, wasremoved to reduce the concentration of helium in the vicinity of the incident electron beamprior to the coincidence collision region. The binding energy spectrum of helium obtainedfollowing the modifications is shown in figures 5.5a and 5.5b. The solid circles in figure 5.5,represent the angle integrated (0 - ±26°) intensity obtained at a sample gas pressure of5.0x106torr (measured with an ion gauge at the top of the vacuum chamber). Relative to theBES measurements obtained prior to the modifications (fig 5.4), the intensity arising from thedouble collision processes is significantly reduced. The triangular symbols in figure 5.5represent measurements at a gas pressure of -.2. 1x10 torr, with the areas of the n=1 peaknormalized to the higher pressure data (fig. 5.5a). These low pressure measurements exhibit afurther significant reduction in the contribution from the double scattering processes.Importantly, the shape and area of the peak of the n=2 transition does not exhibit anydetectable pressure dependence, indicating that any contribution of the double collisionprocesses is negligible.The energy scale of the BES was determined by setting the peak of the n= 1 transition tothe ionization potential of 24.59 eV [134]. The n=2 and n=3 peaks were fit by Gaussianfunctions centered at transitions energies of 65.41 eV and 72.97 eV, determined from theChapter Five EMS of Two Electron Systems: Helium 1562500002000000UCl) 1500000)1000005000004040000U0.)020001000040Binding Energy (eV)Figure 5.5: An angle integrated (±26°) binding energy spectrum of heliumobtained measured following the modifications to the collision chamber, showingpeaks for a) the n=1 transition, and b) the n=2 and n>2 transitions. Triangularpoints are (scaled) BES measurements obtained at approximately half the gaspressure used in the measurements represented by the solid circles.10 15 20 25 30 35Binding Energy (eV)50 60 70 80Chapter Five EMS of Two Electron Systems: Helium 157calculated energy levels of the helium ion [135]. These values are in excellent agreement withthe PES studies of Svensson et al. [112], and Heimann et al.[135]. Additional Gaussians,centered on the transition energies for ionization to the n>3 ion states were added to accountfor the intensity at the higher binding energies. It is important to note that in the fittingprocedure to obtain the areas (i.e. relative intensities) of the n=2 and n=3 peaks, the energiesand widths of the Gaussian functions were fixed.The experimental momentum profile for the n=1 transition is shown in figure 5.6a and isin very good agreement with the theoretical profiles (solid lines) obtained using the correlatedwavefunctions of Cann and Thakkar (CT) and of Chakravorty and Davidson (CD). The smalldiscrepancy at higher momenta is due to distorted wave effects. The experimental momentumprofile for the transition to the n=2 ion state is presented in figure 5.6b together with thetheoretical profiles (NW), (W), (CT),and (CD). The n=2 XMP obtained prior to themodification of the instrument and corrected for double scattering, was found to be in goodagreement with the profile taken following the (collision chamber) modification. The XMPshown in figure 5.6b includes the experimental data from both measurements.It is immediately apparent from this figure that the experimental profile for the n=2transition is significantly more intense than all of the theoretical profiles. At low momentumvalues, the experimental measurements are estimated to be higher than the CT, CD profiles bya factor of 1.35 ± 0.05. These TMPs, scaled by 1.35 are also shown in figure 5.6b. While theChapter Five EMS of Two Electron Systems: Helium 1580.000.0041.0 1.5Momentum (a.u.)3.02.52.01.51.00.50.00.020.01I0.0030.0020.0010.0000.0 0.5 2.0Figure 5.6: The XMPs for the transitions from the helium ground state to then=1, n=2 and n=3 ion states, measured with the momentum dispersivemultichannel spectrometer (solid points). The open squares represent energydispersive multichannel measurements of Zheng and Neville [1361.2.5Chapter Five EMS of Two Electron Systems: Helium 159shape of the XMP is similar to the scaled TMP, the XMP exhibits increasing intensity at highervalues of momentum. This may indicate the effects of distorted waves, however the differencebetween the XMP and the scaled TMP is larger than predicted by the distorted wavecalculations of McCarthy and Mitroy [122].The XMP for the transition to the n=3 final ion state is shown in figure 5.6c, togetherwith the CT and CD theoretical profiles. It should be noted that the XMP was obtained at anenergy corresponding to the expected position of the n=3 peak in the BES. At this energy, asmall contribution from the n=4 transition (see figure 5.5) is anticipated; however, theinfluence on the shape of the XMP is expected to be small. Accordingly, the XMP isnormalized to the relative area of the n=3 Gaussian function in the BES spectrum (figure 5.5).As in the case of the n=2 results, the experimental momentum profile for the n=3 transition issignificantly higher (1.85 ± 0.30) than the n=3 theoretical profiles. The CT and CD profiles,scaled by 1.85 to give reasonable agreement to the experimental data below -0.9 a.u., are alsoshown in figure 5.6c. At higher momentum values, the n=3 experimental data points areconsistently higher than the scaled TMPs, as found in the n=2 results, although the limitedstatistics of the n=3 measurement prevents an accurate assessment of the divergence from(scaled) theory in this region.Chapter Five EMS of Two Electron Systems: Helium 1605.3 DiscussionThe disparity between the intensities of the XMPs for the n=2 and n=3 transitions andthe theoretical profiles is significant, and indicates a problem with either the experimentalmeasurement, or the calculation of the theoretical cross sections, or both. It should be notedthat the experimental cross section measurements for helium are normalized to theory byscaling the n= 1 XMP to the n= 1 TMPs. Therefore, if the coincidence detection efficiencyover the n=l peak was somehow reduced, or the efficiency about the n=2 and n=3 peaks wasincreased, the n=2 and n=3 XMPs would appear to be elevated. However, the thoroughcharacterization of the new multichannel instrument, outlined in chapters 3, was performed toensure the uniform detection efficiency of (e,2e) coincidence events over a much larger rangeof experimental conditions than typically experienced in normal operation. During the courseof the measurement of a binding energy spectrum or momentum distribution, the experimentalconditions change very little.The incident electron beam current collected by the Faraday cup exhibited a very smalldependence on the cathode potential. For a typical mean setting of —60 j..tA, the electron beamcurrent entering the Faraday cup increased by less than three percent over the range ofcathode potential from 1220 eV to 1265 eV. The actual change in the electron flux throughthe collision region was likely even smaller.Chapter Five EMS of Two Electron Systems: Helium 161The coincidence count rate obviously changed considerably during the measurementover the peaks of the transitions to the n=1, n=2 and n=3 final ion states, and the instrumentaldead time for coincidence detection should be considered. In the present system, theinstrumental dead time is essentially that required to process and store the positionalinformation from the MCPIRAE detector; approximately 8 microseconds per event. As theposition computer is gated on the PPU detection of a coincidence event, only the positions ofelectrons which are one-half of an (e,2e) coincidence pair are calculated. Even for themaximum coincidence count rate of 20 Hz obtained at the peak of the n=l transitions, theinstrumental dead time is negligible.The uniform (e,2e) coincidence detection efficiency of the present spectrometer over alarge variation in experimental conditions is most clearly and convincingly demonstrated by thetest measurements presented in figure 3.27 of chapter three. The non-coincidence (singles)electron count rates of the MCPIRAE and CEM detectors, as well as the (e,2e) coincidencecount rate were shown to vary linearly with the incident electron beam current over a rangefrom 0.1 to 70 .tA. This effectively rules out the possibility of any non-linearity in theinstrumental response over the range of electron impact energies and experimental conditionsin the measurement of the (e,2e) transitions of helium to the ground and excited ion states. Aswell, the study of the noble gases and of methane and silane presented in chapter 4 haveclearly demonstrated the quantitative response of the momentum dispersive spectrometer inthe measurement of the binding energy spectra and the outer and inner valence XMPs.Chapter Five EMS of Two Electron Systems: Helium 162As an independent test of the present momentum dispersive experimental results, theEMS cross sections for ionization of helium to the n=1 and n=2 final ion states have beenmeasured in this laboratory by Y. Zheng and J. Neville [136] at three azimuthal angle(momentum) values using a recently constructed energy dispersive multichannel spectrometerat the University of British Columbia. This instrument is very similar to that used in the earlierhelium study of Cook et a!. [26]. The energy dispersive data are represented in figure 5.6aand 5.6b as open squares. Normalized to the n=1 TMPs, the n=2 cross section measurementsexhibit an increased intensity by a factor of 1.20±0.05 compared to the CD and CTtheoretical profiles. While this measurement is somewhat lower than the present momentumdispersive multichannel results, both of the n=2 XMP measurements are significantly above then=2 theoretical profiles. This is in conflict with the XMP measurements of Cook et at. [26]and suggest that the n=2 (and n=3) profiles of the earlier reported energy dispersive studiesmay be too low. In connection with the energy dispersive multichannel EMS measurements, itshould be noted that Zheng and Neville used the much more accurate binning mode [137],rather than the less accurate non-binning mode employed by Cook et al. [26]. While the n=2experimental cross section measurement of Lahmam-Bennani et a!. [311 (presented as a ratioto the n= 1 cross section) is also lower that the present studies, this may be due to kinematiceffects resulting from the different geometry and outgoing energies employed in the study (seebelow). In addition, Lahmam-Bennani et at. [311 found it necessary to correct their n=2intensity for a long range binding energy ‘tail’ from the much larger n=1 signal [138]. Themagnitude of the correction was reported to be 10-20% of the n=2 intensity [31].Chapter Five EMS of Two Electron Systems: Helium 163While the presently reported EMS momentum profiles for the transition to the groundion state is in very good agreement with the shape of the theoretical profiles, the n=2 and n=3XMPs obtained using both the multichannel momentum dispersive and the multichannelenergy dispersive EMS instruments are significantly higher than the theoretical profiles basedon even the most highly correlated wavefunctions. As the profile labeled CT was calculatedusing a wavefunction which gives an energy within 10 nHartree [125] of the exact (nonrelativistic) energy for the ground state of helium [126], and is in agreement with the profileCD, which is based on a similarly high quality wavefunction, the discrepancy between theoryand experiment is not believed to arise from a deficiency in the helium wavefunctions. Moresuspect is the viability of the plane wave impulse approximation used to evaluate thetheoretical momentum profiles. In the theoretical description of the scattering cross sectionsfor the ionizing transitions to excited fmal ion states (ionization + excitation) it has beenassumed that the scattering process is identical to that for the transition to the ground ion state(ionization). With the exception of studies of distorted wave effects [30,122], the possiblebreakdown of this assumption has not been addressed in earlier EMS studies. This is likelybecause the scattering kinematics for EMS is specifically chosen to permit a plane wavedescription of the incoming and outgoing electrons as well as an impulsive binary encounterdescription of the scattering events.In the PWIA (or a first Born) treatment of the scattering, the excitation of the final ion isessentially a ‘shake-up’ process [139], in which the removal of one target electron modifiesChapter Five EMS of Two Electron Systems: Helium 164the potential of the second target electron which may relax into excited or a continuum(double ionization -‘shake-off’) state [139]. As discussed above, electron correlation in theinitial state has a considerable influence on the probability of an excited final ion statetransition. Recently, the role of other mechanisms which may contribute to the cross sectionof scattering processes involving two-electron transitions in the target ( for example,excitation - ionization, double ionization, double excitation) has been of much interest. Anexcellent review of the mechanisms contributing to two-electron processes has been presentedby Tweed [139] using the framework of the first and second Born approximations to describethe projectile scattering. Essentially, the first Born terms account for a single interaction ofthe projectile with the target electron, while the second Born terms account for twointeractions with the target, including double collision mechanisms involving two targetelectrons’ [139]. The second Born, double collision terms identified by Tweed are oftenreferred to as two-step (TS) processes, using nomenclature introduced by McGuire [140] andby Andersen et at. [141]. In the TS-1 process [141], the projectile undergoes a collision withone of the target electrons, which subsequently interacts with a second target electron. Asecond process, often labeled TS-2, involves the collision of the projectile with one targetelectron followed by a second collision of the projectile with another target electron.[141,142]. The neglect of these two processes in the calculations of the EMS cross sectionsfor the ionization of helium to excited ion states, is a possible cause of the discrepancy1It should be noted that, to avoid (or at least to minimize) confusion, the double processes referred to here andin the remainder of the chapter are termed double collision processes, while processes described earlier, inreference to the additional intensity in the helium BES at —45 eV, are termed double scattering processes.While the names are similar, the events they describe are significantly different.Chapter Five EMS of Two Electron Systems: Helium 165observed between the (correlated wavefunction) TMPs calculated in the PWIA, and thepresent experimental cross sections.A diverse array of experimental measurements of two-electron processes has beenperformed, and has indicated the importance of including two-step mechanisms in thedescription of the scattering cross sections. Almost thirty years ago, Carlson and Krause[143] suggested that the interaction (TS-1) of a photoelectron with the remaining electrons ofa target neon atom may influence the yield of multiply charged neon ions produced by X-rayphotoionization. More recently, Andersson and Burgdorfer [144] incorporated thecontribution of the TS-1 process in a calculation of the ratio of double to singlephotoionization cross sections of helium, and demonstrated a significant influence of the TS-1process on the ratio, particularly for photon energies below 5 keV. The investigation of thedouble ionization of helium by charged particle impact was particularly important in theelucidation of the contribution of these two-step processes [140,1411. Specifically, the (total)single ionization cross section for impact of electrons and protons were shown to giveidentical results and were in agreement with theory using the first Bornapproximation[ 140,1451. In contrast, the electron impact cross section for double ionizationof helium was found to be significantly greater than the proton impact cross section atequivalent velocities [140,145]. The charge dependence of the double ionization process wasconfirmed by measurement of the cross section using antiproton projectiles [141,146] whichwas shown to be in good agreement with the cross section using electron projectiles. In theChapter Five EMS of Two Electron Systems: Helium 166first Born approximation, the double ionization cross section is identical for positively ornegatively charged projectiles, and hence the first Born treatment cannot account for theexperimental results. The theoretical description of the enhanced double ionization crosssection for impact of negatively charged particles has received much attention [140,147,148,149,150]. While the details of the process are still the subject of some debate [1511, thetheoretical cross section has been shown to require the inclusion of the double collision(second Born) terms TS-1 and TS-2 to explain the experimental double ionization results[142,151]. The influence of two-step terms was also shown to be required to explainexperimental measurements of the cross section of ionization-excitation processes. The totalcross section for ionization of helium to excited final ion states, has been studied for electronand proton impact [152,153,154] by measuring the emission of Lyman radiation from theexcited helium ions (np — is). Similar to the double ionization process, the cross section forionization of helium to an excited (np) helium ion final state has been shown to be considerablyhigher (approximately a factor of 2 - 3 for projectile velocities of 3.5 - 8 a.u.) [152,153,154]for electron impact than for proton impact. These results cannot be explained using a firstorder (first Born) description of the scattering process.In the light of the above discussion, the two-step, TS- 1 and TS-2, scattering mechanismsare proposed to be the source of the discrepancy between the present measurements of theEMS cross sections for transitions from the ground state helium atom to the excited (n=2 andn=3) helium ion states, and the PWIA theoretical profiles (NC and CD) using highly accurateChapter Five EMS of Two Electron Systems: Helium 167correlated wavefunctions. In the present EMS kinematics, the two-step processes wouldentail a large momentum transfer, binary collision of an incident electron and target electron,with the subsequent interaction of either of the outgoing electrons with the second targetelectron. This second interaction is not considered in the PWIA formalism, and the additionalcontribution from the two-step processes to the EMS scattering cross section may account forobserved discrepancies. In parallel with the electron (and photon) impact studies discussedabove, the two-step processes may be expected to give an increased intensity of XMP for thetransitions to the excited n=2 and n=3 final ion states. As well, since the second collisionevent may influence the direction of one of the outgoing electrons, the angular relationship ofthe coincident (e,2e), and hence the experimental momentum profile, may be modified. In theextreme case of large deflections in the direction of the outgoing electron, the contributionfrom the double collision events may be expected to be homogeneous over the ±26° azimuthalangle, leading to a ‘flatter’ shape of the XMP. Both the increased intensity and modifiedshape of the profile expected from the double collision events, are in qualitative agreementwith the differences in the experimental and (PWIA) theoretical profiles presented in figure5.6.A significant difference between the EMS scattering process and the high energyelectron/proton impact studies (leading to double ionization) discussed above, exists in theenergies of the electrons ejected from the target. The ejected electrons in the electron/protonimpact, total cross section measurements may be expected to have relatively low energiesChapter Five EMS of Two Electron Systems: Helium 168[151], while the outgoing electron energies in EMS are relatively high (—600ev). However, inthe recent study of Andersson and Burgdorfer [144] described above, the theoreticaldescription of the double photoionization cross section indicated a significant contributionfrom the TS- 1 process, even at high photon energies corresponding to high outgoingphotoelectron velocities. As a result of the TS- 1 process, the calculated ratio of double tosingle ionization cross sections rises from the high energy limit (1.66%) by —10% at a photonenergy of 5 keV, and by —35% at a photon energy of 2.5 keV. The calculated ratio continuesto rise at lower photon energies [144]. This result offers additional support for the proposedcontribution of the two-step processes to the (e,2e) cross section, at the outgoing electronenergies detected in the present EMS measurements.The studies of double ionization and ionization with excitation, have primarily focusedon total cross section measurements. Differential measurements permit a much more detailedexamination of the collision dynamics, and would be of great value for the investigation of twoelectron transitions. In this respect, the nascent experimental technique of (e,3e) scattering[155], in which the energies and angles of three outgoing electrons are determined, mayprovide further insight into the double ionization scattering process. Unfortunately, thedifficulty associated with the experimental measurement of the (e,3e) cross sections has thusfar limited the effectiveness of the technique [155]. In the case of ionization+excitation of atarget system, the present measurement of the triple differential EMS cross sections forhelium should provide a basis for the theoretical examination of the two-step scatteringChapter Five EMS of Two Electron Systems: Helium 169process. The kinematics used in the present EMS study should permit a relatively simpledescription of the incident and outgoing electrons, as well as of the single and two-stepcoffision mechanisms. It is hoped that the present measurements will provide the impetus fornew investigations of the EMS scattering cross sections for transitions to the excited ionstates, at a level of theory which accounts for two-step processes.5.4 ConclusionsThe experimental momentum profiles for the ionization of helium to the n= 1, n=2 andn=3 fmal ion states have been measured with the high sensitivity of the recently developedmomentum dispersive multichannel spectrometer, to a greater statistical precision, and for anincreased number of data points, than previously reported. In addition, theoretical profilesbased on highly correlated wavefunctions have been obtained. Two of these profiles (NC,CD), calculated using extremely accurate helium wavefunctions, represent an effectivelyconverged limit to the cross section calculations using the PWIA. The XMP for the ionizationto the ground state ion is in good agreement with these theoretical profiles. In contrast, theXMPs for the transitions to the n=2 and n=3 final ion states are significantly larger than all ofthe theoretical profiles. It is proposed that the enhancement of the intensity of theexperimental cross sections relative to theory is due to the need to include second orderscattering effects in the evaluation of the theoretical cross sections. In particular, the two-stepprocesses (TS- 1 and TS-2) describing the interaction of the two outgoing electrons with thethird (helium ion) electron, have been identified as possible sources for the additional intensityChapter Five EMS of Two Electron Systems: Helium 170of the experimental measurements. These processes have recently received much attention inexperimental and theoretical studies of the total cross sections for the ionization-excitation,and double ionization, of helium [139,151], but have not been previously discussed specificallywith respect to EMS studies. The present measurements may provide important insight intothe two-step scattering mechanism, and a theoretical evaluation of the EMS cross section at alevel of theory sufficient to account for the TS- 1 and TS-2 processes is eagerly anticipated.Chapter SixEMS of Two Electron Systems: Molecular Hydrogen and Deuterium6.1 BackgroundThe investigation of the electron impact ionization of two electron systems to excitedfinal ion states is extended in this chapter, with the study of molecular hydrogen anddeuterium. In parallel with the theoretical cross sections of helium, discussed in the previouschapter, the EMS PWJA cross sections for the transitions to the excited H2 ion states may beexpected to be particularly sensitive to the description of electron correlation in the groundstate molecular wavefunction. Accordingly, the experimental measurement of the momentumprofiles for these transitions may provide insight into the role of electron correlation, as well asthe accuracy of theoretical wavefunctions for the ground state molecular species. As thesimplest two-electron neutral molecular system, the theoretical description of the H2 groundstate, and the influence of electron correlation, have received much attention. An earlyexample of this is given in the “long and illustrious list of calculations...” [156] performedprior to 1960, summarized by McLean et al. [156].The experimental measurement of the transitions to the excited ion states is complicatedby the relatively low (e,2e) cross sections associated with the transitions. In the study of171Chapter Six EMS of Two Electron Systems: H2 and D2 172hydrogen, further difficulties arise from the broad, overlapping binding energy line profiles,which result from the vibrational motion of the ground state molecule and the dissociativenature of the (unbound) excited ion states (see figure 6.2). In spite of these difficulties,Weigold et at. [157] have reported single channel measurements of binding energy spectra ofH2 (up to —45.5 eV) at two relative azimuthal angles, and experimental momentum profilesobtained at a few binding energies. The experimental profiles were compared to thetheoretical profiles bases on the ground state molecular wavefunction of McLean et a!. [156].Significant discrepancies between theory and experiment were exhibited, particularly in theintensities of the 250g profiles at low momentum. Similar discrepancies between the singlechannel measurements [157] and theoretical momentum profiles calculated using moreaccurate correlated ground state wavefunctions, were subsequently reported by Liu and Smith[66]. However, the low cross sections of the excited ion transitions, coupled with thelimitations of the single channel EMS architecture, resulted in relatively large uncertainties inthe experimental profiles reported by Weigold et at. [157]. This prompted Liu and Smith tostate, somewhat emphatically, that “experimental data for the transitions to all the n=2 andn=3 excited states are urgently needed” [66]. The single channel results of Weigold et at.[157] represent the only published measurement of the 112 EMS cross sections for thetransitions to excited ion states that is published in the literature, although unpublishedmeasurements using an energy dispersive multichannel spectrometer have been obtained byBharathi et al. [158]. The original aim of the present study of molecular hydrogen, was toexploit the greatly enhanced collection efficiency of the momentum dispersive multichannelChapter Six EMS of Two Electron Systems: H2 and D2 173spectrometer to obtain improved measurements of the momentum profiles for the (e,2e)transitions to excited ion states and thus a more precise test of theory. However, in light ofthe multichannel measurements of helium presented in chapter 5, the present study alsoprovides an additional opportunity to investigate the possible influence of second order (i.e.two-step) collision processes in the transitions to excited ion states.6.2 Theoretical Momentum Profiles of Molecular HydrogenTheoretical momentum profiles for the EMS transitions from the ground state of H2 tothe lsag ion state, and n=2 (2pa, 2Ptu, and25Gg) excited ion states have been tabulated byLiu and Smith [66], and are presented in figure 6.1. The TMPs using the SCF and correlatedwavefunctions of Davidson and Jones (DJ) [159], and the correlated wavefunction ofHagstrom and Shull (HS) [160] are shown. The DJ and HS wavefunctions are of similaraccuracy, accounting for 96.5% and 96.7% of the total correlation energy respectively. Thecalculation of the EMS cross sections involved the overlap of these wavefunctions with thefinal ion wavefunctions, which, within the Born-Oppenheimer approximation, are expressedexactly [66]. All of the TMPs in figure 6.1 have been folded with the present instrumentalresolution (see chapter 4) using the GWPG method [49]. Additionally, the excited ion profilesinclude a term representing the small change in kinematic factors at the various impactenergies of the transitions [28].The variation amongst the profiles for the transition to the ground state ion is small; onthe order of a few percent at low momentum. The shapes of the TMPs for the25Gg ion stateChapter Six EMS of Two Electron Systems: H2 and D2 1741.00.80.60.40.20.00.8bO.6I0.20.10.00.020.010.000.0 0.5 1.0 1.5Momentum (a.u.)Figure 6.1: The TMPs for the transition from the ground state of H2 to theground and excited final ion states, obtained from Liu and Smith [66]. Theprofiles have been folded by the present instrumental resolution, and include thevariation in the kinematic (i.e. Mott) scattering factors with impact energy. Notethe scale of the 2pa and 2pit profiles.2.0 2.5Chapter Six EMS of Two Electron Systems: H2 and D2 175are very similar to those for the 1 5Gg transition, in contrast with the large change of shapebetween the helium n=2 and n=1 TMPs. Only a small difference is observed between the 2SGgprofile using the uncorrelated SCF wavefunction and the profiles using highly correlatedwavefunctions. Initial state electron correlation has a greater influence on the theoretical crosssections for the transition to the 2POU ion state. While no theoretical cross section is predictedif an (uncorrelated) SCF wavefunction is used, relatively low cross section TMPs for thisionization process are given using the correlated wavefunctions. Additionally, the TMPs usingthe two correlated wavefunctions, DJ and HS, are in fair agreement with each other, andfurther improvements to the H2 wavefunction may be expected to exhibit little change fromthese TMPs. Finally, the cross sections of the theoretical profiles for the transition to the 2PJtustate, based on the correlated wavefunctions, are extremely small. In the analysis of theexperimental BES measurement presented below, the intensity for the transition to the 2pItUstate is assumed to be negligible (i.e. <0.5% 2po).6.3 Multichannel BES Spectra and Momentum Profiles of H2As PES measurements of the ionization of H2 to the excited final ion states have notbeen reported, except for a relatively crude retarding potential measurement by Samson [1611,theoretical estimates of the BES lineshapes were required. The potential energy curves of theH2 ground state and H2 ion states were obtained from the tabulated data of Bates et at. [162],and of Sharp [163], and are presented in figure 6.2.Chapter Six EMS of Two Electron Systems: H2 and D2 176605040‘1)20100BES transition profiles Internuclear distance (A)60504030C2010Figure 6.2: The potential energy curves of the H2 ground state and the H2ionstates, obtained from Bates et al. [1621 and Sharp [1631. To the left are calculatedbinding energy line profiles for the transitions to the excited ion states, and thePES spectrum [1641 for the transitions to the ground state ion. For clarity, manyion states have been ignored. This figure is similar to figure 3 of Gardner andSamson [161].0 1 2 30Chapter Six EMS of Two Electron Systems: H2 and D2 177The probability distribution of the internuclear separation in the hydrogen molecule(shown in figure 6.2) was obtained from the ground state H2 vibrational wavefunction,calculated using a Morse potential [166]. Applying the probability for a given internuclearseparation to the appropriate transitions energy given by the energy of the excited ion potentialcurves, produced an estimate of the (asymmetric) binding energy spectrum line profiles.However, these line profiles were found to be in very poor agreement with experimentalmeasurements, and additionally, were 1 eV higher in energy than the BES line profilesreported by Gardner and Samson [165]. The high values of the transition energies, calculatedin this manner, result from the neglect of the continuum wavefunctions of the excited ionstates. A more realistic estimate of the line profiles was obtained by evaluating the FrankCondon overlap of the ground state vibrational wavefunction, with the radial continuumwavefunction of an excited state at a specific energy. These overlaps were calculated using acomputer program [167] written and provided by R. Le Roy of the University of Waterloo[168]. The resultant BES transition lineshapes are shown on the left hand side of figure 6.2,and are in good agreement with the curves of Gardner and Samson, evaluated in a similarmanner [165].The angle integrated (0 - ±26°) binding energy spectrum of H2 over the range from 10-65 eV is shown in figure 6.3. The spectrum is clearly dominated by the transition to the isa5ion state. The energy scale of the spectrum was determined by positioning the 1 sa5 peak withrespect to the vibrationally resolved photoelectron spectrum of H2, reported by Samson [164].Chapter Six EMS of Two Electron Systems: H2 and D2 178Figure 6.3: The angle integrated (0 - ±26°) binding energy spectrum ofmolecular hydrogen. The solid line through the 1 peak represents the PESspectrum of Samson [1641, convoluted by the present instrumental energyresolution.10080Cl)Cc-)40-40‘-4CL)2000 10 20 30 40 50Binding Energy (eV)60Chapter Six EMS of Two Electron Systems: H2 and D2 17916001200Cl)Cc-)1)C.)a)• —C.)CC-)400045 50 55 6CBinding Energy (eV)Figure 6.4: An expanded view of the H2 binding energy spectrum about theregion of the transitions to excited ion states. The solid points represent higherpressure (8.8x106torr) measurements, while the open circles represent lowpressure (3.0x106toff). The dotted lines are the line profiles obtained from theoverlap of the ground state H2 and continuum H2 vibrational wavefunctions. Thelong dash lines labeled HP and LP represent the modified (see text) opticaloscillator strength measurements of Chan et al. [169], added to estimate doublescattering events at higher pressure (HP) and lower pressure (LP). The higherdashed curve is the sum of the BES components including HP, while the solid lineis the sum including LP.25 30 35 40Chapter Six EMS of Two Electron Systems: H2 and D2 180The PES measurement, presented on the lower left hand side of figure 6.2, was corrected for asmall background intensity and was convoluted by the present experimental energy resolution.The resultant slightly asymmetric peak is presented is figure 6.3 (solid line), and is in verygood agreement with the experimental data.The region of the binding energy spectrum about the excited state transitions has beenexpanded in figure 6.4. Prior to the modification of the collision chamber outlined in section3.1.3, BES measurements exhibited a considerable intensity in the region just below theposition of the 2pau transition. The additional intensity in this region was found to originatefrom multiple (two molecule) scattering effects, also seen in the BES measurements of helium,and discussed in section 5.2.2. In the present measurements of hydrogen, the multiplescattering process involves a forward scattering energy loss interaction of an incident electronwith one hydrogen molecule, followed by an (e,2e) ionization collision with a second hydrogenmolecule in the collision region. Shortening the length of the gas cell prior to the collisionregion and improving pumping efficiency in the vicinity of the incident electron beam,significantly reduced the intensity from the double scattering process, although some smallintensity from this source remains.The solid circles in figure 6.4 represent measurements obtained following the collisionchamber modification at a sample gas pressure of approximately 8.8 x 1O torr. The opencircles represent measurements obtained at a reduced gas pressure of 3.0x106torr. TheChapter Six EMS of Two Electron Systems: H2 and D2 181pressure dependence of the BES spectra, in the region between 25-35 eV, is a good indicationof the influence of the multiple scattering process. The lineshape of the contribution from thismultiple scattering process was estimated from the optical oscillator strength measurement ofChan et al. [1691. The optical oscillator strength cross section was scaled by B0, where E0 isthe electron impact energy, to yield the differential (forward) electron scattering cross section.Convolution by the experimental width of the 1 sa5 transition produced the lower dashed curvein figure 6.4, representing the influence of double scattering in the lower pressure (LP)measurement. The summed intensity of this curve and the BES line profiles is shown by thesolid line, and is in good agreement with the low pressure measurement in the 25-35 eVregion. Scaling the intensity of the double scattering process to account for the change in gaspressure produces the higher dashed curve (HP) shown in figure 6.4. The summed intensityusing the higher double collision estimate is also represented by a dashed curve, and is inreasonable agreement with the higher pressure BES measurements.The binding energy spectrum shown in figure 6.4 has been fit with the calculated lineprofiles and positions for the transition to the 2pa, 2sag, 3SGg, 4pa, and doubly ionized states(see figure 6.2), in addition to the double collision estimates. The 2pic state is not included asthe theoretical cross section calculation of Liu and Smith [66] indicates that the (e,2e)transition probability to this state is very low (see figure 6.1). Other n=3,4 and higher excitedion states have also been neglected as the intensities for these transitions should be small [66],and would overlap considerably with the transitions to the 3sag and 4pa states. TheChapter Six EMS of Two Electron Systems: H2 and D2 182agreement of the summed intensity to the experimental measurements is generally very goodover the full binding energy range. At higher energies (48-60 eV), the fit would likely beimproved by accounting for the (e,2e) intensity above the double ionization threshold. Theareas of the BES peaks for the 2pa and250g transitions are particularly important for thenormalization of the experimental momentum profiles for these ion states to the 1 sa XMP.From the binding energy spectrum in figure 6.4, the areas of the peaks have been determinedto an estimated accuracy of ±5%.The experimental momentum profiles for the transitions to the ground and excited finalion states were obtained by measuring the angular distribution of (e,2e) coincidence events fora number of binding energies, at a target gas pressure of 3.0x106 The XMP for the transitionto the lSOg state is presented in figure 6.5a, and is in good agreement with the shape of the DJtheoretical profile. The sum of measurements obtained in a narrow range of binding energiesabout an average value of 32.5 eV is shown in figure 6.5b, while the XMP acquired at anaverage binding energy of 40.2 eV is presented in figure 6.5c. Although small contributionsfrom the double collision process and from transitions to the 2sa state are expected in theXMP measurement at 32.5 eV, greater than 90% of the intensity at this energy arises from the2pa transition, and the additional transition process at this energy should have only a smallinfluence on the shape of the XMP. Similarly, greater than 90% of the intensity at 40.2 eV isdue to the 2SOg transition, with small contributions arising from the 2pa and 3SGg transitions.As the shapes of the2sag, and 3SOg theoretical cross sections are very similar [66], theinfluence of the 3SGg transition on the XMP should be especially small. Hence, the XMPs inChapter Six EMS of Two Electron Systems: H2 and D2 183figures 6.5b and 6.5c are labeled by the primary components, 2pa afld2SGg. The profiles forthese two transitions have been normalized to the intensity of the 1 SGg XMP, by the areas ofthe transitions in the BES, shown in figures 6.3 and 6.4. The theoretical momentum profilesobtained using the correlated wavefunction of Davidson and Jones [159] are also shown infigure 6.5. The agreement between the experimental and theoretical profiles is clearly verypoor.The measurement at 32.5 eV was corrected for the overlap of the double scatteringevents, and for the small intensity from the 2sag transition, by removing the appropriatecontribution of the lSGg and 2SGg XMPs. The corrected and renormalized 2pc XMP isshown in figure 6.6b. The effect of the correction is small, and acts to slightly lower theintensity in the low momentum region. A similar correction procedure to remove thecontributions from the2PYU transitions from the measurements at 40.2 eV has a negligibleeffect on the XMP. The corrected2SGg XMP is presented in figure 6.6c. As in the previousfigure, the discrepancy in the shapes and intensities of the theoretical and experimental profilesis quite dramatic.The theoretical profile of the 25Gg transition significantly overestimates the experimentalintensity at low momentum, and underestimates the intensity at higher (>—O.7 a.u.) momenta.The theoretical profile of the 2pa transition greatly underestimates the experimental intensity,Chapter Six EMS of Two Electron Systems: H2 and D2 1841.00.80.60.40.20.00.00600L)1)a)0.0000.0250.0200.0150.0100.0050.0000.0 0.5 1.0 1.5 2.0Figure 6.5: The XMPs (solid circles) for the transition to the isa5, 2pcy, and2SGg H2 ion states. The XMPs have been normalized to the areas of the lineprofiles in the BES of figure 6.4. The solid lines are theoretical profiles calculatedby Liu and Smith [661 using the correlated wavefunction of Davidson and Jones[159], as shown in figure 6.1.Momentum (a.u.)Chapter Six EMS of Two Electron Systems: 112 and D2 185(a) Ii.o\ H20.8 lSGg0.60.4 -0.2-0.0 I I(b)0.006- 2pa• I ii (corrected)‘ f’i0.0O4- I0.002-§ I0.000(c)0.025- \ 2SGg\ (corrected)0.020-0.0150.010 +40.005•. C..0.000 I I0.0 0.5 1.0 1.5 2.0Momentum (a.u.)Figure 6.6: The lsa, 2pa , and 2ScT XMPs (solid circles) corrected for thesmall contributions from overlapping transitions. The open circles are the energydispersive measurements of Bharathi et al. [158].Chapter Six EMS of Two Electron Systems: H2 and D2 186and while the TMPs drop close to zero at low momentum (due to the symmetry of the 2Paustate), very little decrease is exhibited by the XMP.The unpublished multichannel energy dispersive measurements of Bharathi et al. [158]are represented as open circles in figure 6.6, for comparison with the present measurements.The two multichannel measurements of the 2SGg XMPs are in excellent agreement. The 2POUXMP reported by Bharathi et aL [158] is slightly lower, and exhibits a greater decrease in thecross section at low momentum than the present momentum dispersive XMP. Importantly,the large discrepancies with the theoretical profiles for the excited ion transitions arereproduced, providing strong independent support for the accuracy of the presentmeasurements.6.4 Multichannel BES Spectra and Momentum Profiles of D2In the evaluation of the H2 theoretical momentum profiles, it was assumed that the rangeof internuclear separations resulting from the vibrational motion of the ground state moleculemay be approximated by using the electronic wavefunctions at the equilibrium bond distance.This approximation is generally employed in EMS studies on molecular systems. The viabilityof the approximation has been investigated by Dey et al. [170], through the measurement ofthe XMPs of H2 and D2. No variation in the profiles for the transition to the isa5 ground stateion were observed, indicating that the EMS cross section is not strongly influenced by thevibrational motion of the target. Similarly, isotopic substitution measurements ofH20 andChapter Six EMS of Two Electron Systems: H2 and D2 187D20 were performed by Bawagan et al. [37] to investigate the possible contribution ofmolecular vibration to the discrepancies observed between XMPs and high quality theoreticalprofiles (see section 1.3). Again, no variation with isotopic substitution was observed.Additionally, explicit calculation of the TMPs ofH20 at a range of nuclear coordinates wasevaluated by Leung et al. [171]. While the XMPs were shown to vary with nuclear geometry,the vibrationally averaged profiles were found to be quite well described by the XMP at theequilibrium bond distance. These studies suggest that vibrational effects should be small in thepresent measurements on H2 and D2 for the transition to the 1 sa final ion state. However therole of molecular vibration in the cross section for the transitions to the repulsive excited ionstates is unclear. To investigate the possible contributions from molecular vibration, themeasurements for H2 were repeated using D2 as the target gas species.The angle integrated (0- ±26°) BES of D2 is shown in figure 6.7. The energy scale ofthis spectrum was set by positioning the lSGg peak to the curve obtained from the energycalibrated [172] vibrationally resolved PES measurement of D2 reported by Cornford et al.[173]. In figure 6.7b, the BES in the energy region of the excited state transitions isexpanded. The solid and open circles in this figure represent measurements at target gaspressures of 5.8x106ton and 2.4x10 ton, respectively. As in the hydrogen binding energyspectrum, the influence of the double scattering process (from two D2 molecules) is apparentin the region below the 2Ou transition peak. The theoretical line profiles displayed in thisfigure were evaluated from the overlap of the ground state D2 vibrational wavefunction andexcited ion continuum wavefunctions, using the computer code of R. Le Roy [167]. RelativeChapter Six EMS of Two Electron Systems: H2 and D2 188to the area of the 1 SGg peak, the areas of the BES peaks for the excited ion state transitionshave been fixed to the relative areas of the H2 BES transitions (figures 6.3 and 6.4). The BESline profiles, constrained in this manner, are in reasonable agreement with the experimentaldata. The restriction on the areas of the D2 line profiles was imposed to emphasize anyvariation in the shapes of the D2 2PGu and 2SGg XMPs relative to the shapes of the H2 XMPs,independent of any (small) variation in the BES areas, which are used to normalize theexperimental profiles to the isa5 XMP.The momentum profiles for the transition from the ground state of D2 to the 1 sa stateand the 2pau and 25Gg excited ion states (obtained at average energies of 32.9 eV and 40.4 eVrespectively), are shown in figure 6.8. The (uncorrected - i.e. fig 6.5) momentum profiles forH2 are also presented (open circles). In the case of the 2Pau transition (figure 6.8b), the D2experimental profile is marginally higher than the H2 measurement at low momentum. This islikely due to a slightly greater contribution of the double scattering process at the transitionenergy of the D2 2PGU XMP. Except for this small discrepancy, the agreement between the H2and D2 experimental momentum profiles is generally excellent. This strongly suggests that theevaluation of the theoretical profiles at the equilibrium bond distance is a reasonableapproximation, and eliminates vibrational effects as a source of the discrepancy betweenexperimental and theoretical momentum profiles.Chapter Six EMS of Two Electron Systems: H2 and D2 189I I I I I(a)60 2lSGg BES50C.,CC)a)C)a)20-10 2SGg2pa /_____0 ••••••________ ____ __ ____0 10 20 30 40 50 60Binding Energy (eV)I I I I I I1000 - (b) 2Sag D2BES800- ......./600-2pa .400 - ...3SGg200- / I..... DD0 - ...-LPI I I I I I I25 30 35 40 45 50 55 60Binding Energy (eV)Figure 6.7: a) The angle integrated (0 - ±26°) binding energy spectrum of D2.b) An expanded view of the BES about the transitions to the excited ion states.The solid and open circles represent measurements at gas pressures of 5.8x106and 2.4x106torr respectively.Chapter Six EMS of Two Electron Systems: H2 and D2 190CC)ci)Cl)C,)C’.)C-)ci)1.00.80.60.40.20.00.0060.0040.0020.0000.0250.0200.0150.0100.0050.0000.0 0.5Momentum (a.u.)1.0 1.5 2.0Figure 6.8: The lSGg, 2pa, and 2Sa XtvIPs of H2 (open circles) and D2 (filledcircles). The profiles have been normalized to the areas of the line profiles in theBES of figure 6.4 (and figure 6.7), and have not been corrected for the smallcontribution of neighbouring transitions at the binding energy of each XMPmeasurement.Chapter Six EMS of Two Electron Systems: H2 and D2 1916.5 DiscussionThe momentum dispersive multichannel measurements of the EMS cross section for the(e,2e) ionization to excited ion states of molecular hydrogen are significantly different, both inshape and magnitude, from the theoretical profiles calculated with highly correlatedwavefunctions and based on the plane wave impulse approximation. The possible influence ofthe vibrational motion of the molecule on the experimental cross sections has been addressedthrough the measurement of the XMPs of D2. These profiles were found to be in goodagreement with the XMPs for H2, and hence also exhibit large differences from the theoreticalprofiles. Bharathi et al. [1581 have suggested that the poor agreement with theory resultsfrom deficiencies in the Davidson and Jones (DJ) [159] molecular ground state wavefunction.However, the TMPs based on the DJ wavefunction are in good agreement with the TMPscalculated with the correlated wavefunction of Hagstrom and Shull [160] (figure 6.1). Inaddition, the TMPs for the 2sag transition using the correlated wavefunctions (HS and DJ),are very well matched by the TMP using an SCF wavefunction (figure 6.1). Hence, the use ofa more accurate ground state wavefunction (in terms of its energy) in the calculation of theTMPs would likely exhibit little change from the profiles displayed in figure 6.1, particularlyfor the 2SGg transition.The possibility for the observed discrepancies to result from an instrumental effect is alsoremote. As discussed in chapter 3, the response of the multichannel instrument has been wellcharacterized and has been shown to be linear over a very wide range of operating conditions.Chapter Six EMS of Two Electron Systems: H2 and D2 192The series of measurements presented in chapter 4 confirms the quantitative accuracy of themultichannel measurements. Additionally, the deviations observed between the theoretical andexperimental profiles are quite different for the transitions to the 2paU and 2Sag final ionstates. While the 2pa XtvIP is significantly higher in intensity than the TMP, particularly atlow momentum values, the 2SGg XMP underestimates the TMP in the low momentum region,and overestimates the TMP in the higher momentum region. If an unknown instrumentaleffect were manifested in the experimental profiles, the discrepancy with the theoreticalprofiles would be expected to be similar for the two final ion state transitions. Finally, theagreement observed between the unpublished measurements of Bharathi et al. [158] and thepresent experimental results provides independent support for the present work.The differences observed between the TMPs and XMPs for H2 (and D2) are even morestriking than those exhibited by the n=2 and n=3 cross sections of helium, presented in thechapter 5. The influence of second order collision processes’, not considered in a PWIAanalysis, was demonstrated in chapter 5 to be a likely cause of the enhanced experimentalcross sections for the ionizing transitions to the excited helium ion states. The possible secondorder processes include the two-step TS- 1 mechanism, in which the projectile interacts withboth target electrons, and the TS-2 mechanism, in which, following a collision with theprojectile, the outgoing target electron interacts with the second target electron. In the‘As in chapter five, it must be noted that the double (second order) collision processes should not be confusedwith the double scattering processes. The double scattering mechanism involves two separate first ordercollisions with two target atoms or molecules, while the double collision mechanism involves a second orderinteraction with a single target species.Chapter Six EMS of Two Electron Systems: H2 and D2 193present measurements of the (e,2e) cross sections for H2 and D2, these two-step mechanismsare a likely source of the discrepancy with the (PWIA) theoretical cross sections.Scattering experiments involving the transition of two electrons are much morenumerous for helium target species than for molecular hydrogen. However, Edwards, Ezell,Wood and colleagues have recently reported a series of measurements of the doubleexcitation, ionization plus excitation, and double ionization cross sections for electron andproton impact of hydrogen [174 - 178]. The final ion states of the collision events wereidentified by the analysis of the kinetic energy of the H fragments. Initial measurementsinvestigated the dissociation of H2 into angles perpendicular to the direction of the incidentprojectile beam [174,175]. As observed in helium [140], the double ionization cross section ofhydrogen was shown to be significantly higher for electron impact than for proton impact atequal projectile velocities [174,175]. A similar projectile charge dependence (proton Ielectron) was observed in the cross sections for the ionization to the H2 excited ion states(2PGu, 2Ptu,2sag) [175]. These findings are believed to be the result of an interferencebetween the two-step TS-2 term and both the first Born shake-up or shake-off and the TS- 1terms [175]. The influence of the two-step terms in these measurements offers strong supportfor the suggested role of these scattering processes in the present EMS cross sectionmeasurements.In the EMS scattering kinematics, the two-step TS-1 and TS-2 terms involve theinteraction of either the incident or scattered electron with the remaining H2 target electron,Chapter Six EMS of Two Electron Systems: H2 and D2 194following a binary (e,2e) collision. If the second collision event involved a reasonablemomentum transfer, the azimuthal angular relationship of the two outgoing electrons may bemodified. This process would likely result in a more homogeneous angular distribution ofelectrons over the azimuthal range detected by the MCPIRAE detector. In accord with thisanalysis, the present measurements of the experimental profiles for the excited ion transitionsare much more uniform across the momentum (angular) range than the theoretical profiles.The 2SGg experimental profile presented in figure 6.6 is much flatter than the TMP, while the2Pau, XMP does not exhibit the clear maximum at —.7 a.u. or the deep minimum at lowmomentum, displayed by the theoretical profile. While this picture of the two-step scatteringprocess in EMS is rather simple, a qualitative description of the experimental measurements isprovided.6.6 ConclusionsThe EMS experimental momentum profiles for the (e,2e) ionization of molecularhydrogen to the 1 so, 2pa, and 2SGg final ion states have been measured using themomentum dispersive multichannel spectrometer. While the momentum profile of l5Ggtransition is very well described by theoretical profiles, the experimental profiles for theexcited ion transitions are in poor agreement with TMPs based on highly correlated H2wavefunctions. The discrepancies between the experimental profiles and the theoreticalprofiles calculated in the PWIA are likely caused by two-step second order collision processes.These processes were also proposed to give an enhanced cross section in EMS transitions toChapter Six EMS of Two Electron Systems: H2 and D2 195the excited ion states of helium (chapter 5). The present (e,2e) measurements of hydrogencomplement the measurements on helium (chapter 5), and it is hoped that they will initiate atheoretical reinvestigation of the (e,2e) scattering process. The well defmed final state and thelarge incident and outgoing electron energies of the EMS measurements should be a favorablekinematical arrangement for the theoretical description of the second order processes. Thecalculation of the H2 cross sections will likely be complicated by the multicenter character ofthe molecule. However, for the transition to the 2sa5 ion state the calculation may besimplified by the use of an (uncorrelated) SCF molecular wavefunction, which has been shownto give an accurate prediction of the 2SGg theoretical profile in the PWIA compared to TMPscalculated with correlated wavefunctions. The differences between the experimental crosssections and the (first order) theoretical profiles are quite dramatic, and the EMSmeasurements should provide a sensitive test for the theoretical description of the secondorder two-step processes.Chapter SevenClosing RemarksA brief review of historical developments in chemistry, or for thatmatter in natural science as a whole, will convincingly show thatmethodological developments .. .that is, the emergence of newtheoretical or experimental tools or substantial improvement of oldones.. .often have had an enormous and sometimes quite dramaticimpact on the progress of science.Professor Sture Forsén [1791The development, characterization, and application of a new multichannel spectrometerfor the electron scattering coincidence technique of electron momentum spectroscopy has beenpresented in this thesis. Incorporating some aspects of previous single-channel andmultichannel designs, together with many original approaches, the new instrument has beenshown to provide a significant improvement in the detection efficiency over conventionalsingle channel spectrometers. A channel electron multiplier and a microchannel plate/resistiveanode position sensitive detector are situated on opposite sides of the exit circle of acylindrical mirror analyzer to permit detection of coincident pairs of (e,2e) electrons over anazimuthal range of ±26 degrees. Departing from a conventional TAC based system, thecoincident arrival of electrons at the two detectors is recognized by the pile-up of pulses fromeach detector. The implementation of the PPU technique using ECL circuitry and rf-power196Chapter Seven Closing Remarks 197combiners has provided the ability for very fast detection of coincidence events, which in turnhas permitted the gating of the RAE position computer. Of the many electrons striking thedetector, only the positions of electrons coincident with an electron at the CEM aredetermined and recorded, significantly reducing the dead time of the detection system andoptimizing the performance of the new spectrometer.The new instrument has been fully characterized through measurements of a number ofsystems including: Ne, Ar, Kr, Xe, CH4 and SiH4. A comparison of a 15-minute multichannelmeasurement and a 46.5-hour single channel measurement of the XMP of the Ar 3p electronhas provided a dramatic example of the capabilities of the momentum dispersive spectrometer.A more precise multichannel measurement of the Ar 3p XMP exhibited very good agreementwith a theoretical profile calculated with a very high quality CI wavefunction. Similarly goodagreement was exhibited in the XMPs of the outer valence orbitals of Kr and Xe withtheoretical profiles bases on near-Hartree-Fock limit wavefunctions. Less influenced bydistorted wave effects, the measurements on the molecular species CH4 and SiH4 havepermitted an evaluation of the spectrometer over a range of binding energies. Very goodagreement of the XMPs and high quality TMPs for both the outer and inner valence electronsof these systems, and consistency with earlier single channel measurements, have confirmedthe quantitative response of the instrument.Chapter Seven Closing Remarks 198The enhanced capabilities of the multichannel spectrometer have been exploited in theapplication to the measurement of the (e,2e) transitions from the ground states of helium andmolecular hydrogen (and D2) to excited, singly charged, final ion states. On the basis of earlierpublished studies with much less sensitive instrumentation, it was anticipated that the presentmeasurements would permit a very detailed investigation of the influence of electroncorrelation in the ground state of each target species. However, the experimental crosssections for the (e,2e) transitions of helium to the n=2 and n=3 fmal He ion states, as well asthe transitions of hydrogen (and deuterium) to the2PGu, and 25Gg ion H2 (D2) states, havedisplayed significant differences in both shape and intensity relative to the theoretical profilescalculated using high quality correlated wavefunctions. Citing studies involving doublephotoionization, as well as double ionization and ionization plus excitations by electron andproton impact, the findings of the present measurements have been rationalized in terms ofsecond order two-step collision processes, which are not accounted for in the two-body PWIAdescription of (e,2e) scattering typically used in EMS studies. Such processes involving two-electron transitions have been of much interest and debate in recent years. The well defined,high energy scattering kinematics of the present measurements should prove to be a valuableaid in the theoretical analysis of the two-step mechanism, and it is hoped that the results willprecipitate an in-depth theoretical investigation of the second order (e,2e) cross sections forthese transitions. Confirmation of the present hypothesis may, in turn, instigate furtherexperimental studies of these systems at different impact energies, and involving transitions tohigher final ion states.Chapter Seven Closing Remarks 199With the improvements in sensitivity provided by the present instrument, as well as therecently reported instrument of Storer et al. [60] for the study of EMS of solids, the field ofEMS is entering a new era. Over the past twenty-two years, EMS studies of small atomic andmolecular gas phase systems have identified the general experimental and theoreticalrequirements for an accurate description of the momentum profiles of target electrons. Manyof these studies have led directly to the development of improved electronic wavefunctions forthe target species. The present measurements for hydrogen and helium notwithstanding, it hasbeen established that for typical EMS scattering kinematics (impact energies 1200 eV), theapplication of the binary encounter plane wave impulse approximation is sound. Hence, thepast investigations have laid the groundwork for the future application of the EMS scatteringtechnique to explore the electronic structure of larger and more complex systems. Futuredirections in gas phase systems will likely be towards the study of large biomolecules, van derWaals complexes, and oriented molecules, as well as excited molecules, radicals and ions.Additional gains in sensitivity will be required to investigate these systems, although thedevelopments and design of the present instrument offer great hope and insight for theachievement of such sensitivity. It is important to note that, even with the presentmultichannel detection, only a fraction of the total number of valid (e,2e) scattering events aremeasured. However, the extension of the momentum dispersive architecture of the presentinstrument, leads to an instrumental design in which coincidence events may be detectedaround the full 2it azimuth with all possible angular correlations. Such an instrument willincorporate a cylindrically symmetric energy analyzer, with microchannel plate electronChapter Seven Closing Remarks 200multipliers located at the exit plane. For full 2it detection, the convenience of large-areaposition sensitive resistive anodes will have to be sacrificed, and discrete anodes (on one- ortwo-degree centers) are likely to be employed. In light of this, the application of a TAC-basedsystem for coincidence detection, requiring start and stop signals from the detectors, will beproblematic. However, the PPU system, employed to great effect in the present spectrometer,may be readily extended to detect coincidences between any two of a number of discretedetectors. Developments along these lines promise additional gains of approximately twoorders of magnitude. The ability to extend the range of EMS measurements to more exoticand challenging species looms on the not-too-distant horizon.Bibliography[1] J.W.M. DuMond and H.A. Kirkpatrick, Phys. Rev. 37 (1931) 136.[21 J.W.M. DuMond and H.A. Kirkpatrick, Phys. Rev. 38 (1931) 1094.[3] R.H. Stuewer and M.J. Cooper, in: Compton Scattering, ed. B. Williams (McGrawHill, Toronto, 1977) pp. 1.[4] J.W.M. DuMond and H.A. Kirkpatrick, Rev. Sci. Instrum. 1 (1930) 88.[5] I.E. McCarthy and E. Weigold, Phys. Rep. 27C (1976) 275.[6] C.E. Brion, mt. J. Quantum Chem. 29 (1986) 1397.[7] I.E. McCarthy and E. Weigolci, Rep. Prog. Phys. 54 (1991) 789.[8] H. Ehrhardt, M. Schulz, T. Tekaat and K. Willmann, Phys. Rev. Lett. 22 (1969) 89.[9] U. 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