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Triple proton coincidences following pion absorption in helium McAlister, John 1988

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T R I P L E P R O T O N COINCIDENCES F O L L O W I N G P I O N A B S O R P T I O N I N H E L I U M By John M°Alister B.Sc(Hons) Durham University 1985 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF M A S T E R OF S C I E N C E in T H E F A C U L T Y OF G R A D U A T E STUDIES Department of Physics We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y OF B R I T I S H C O L U M B I A September 1988 © John M c Alister , 1 988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of PHYSIC The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6(3/81) Abstract An experimental investigation of the absorption reaction 4He(7r+,ppp) has been undertaken on the M i l beamline at the TRIUMF cyclotron. Positive pions at an average kinetic energy of 165 MeV were directed onto a cylindrical liquid 4He target and the outgoing protons were measured by a combination of two time-of-flight arrays and two plastic scintillator telescopes. A description of the apparatus, experimental technique and calibration is presented. Results from triple proton coincidences at a single orientation of three of the detectors are discussed. Their angular settings with respect to the pion beam were 40°, 136° and —55°. Comparisons are made with Monte-Carlo simulations of three and four body phase spaces. Identification of a quasi-free three nucleon absorption mode is made for the first time at this energy. An integrated cross-section for this process is determined (<JQ3N = 4.4 ± 0.6m6). The quantitative agreement between these results and those of another recent experiment1 indicate that a small fraction(« 10%) of the coincidences could be due to a two step absorption mechanism. ^ackenstoss et al. Phys. Rev. Lett 61:923(1988) ii Table of Contents Abstract i i List of Tables vi List of Figures v i i Acknowledgements ix I Introduction 1 1.1 Experimental Physics and Time 1 1.2 The Pion as a Nuclear Probe 2 1.3 Aspects of Pion Absorption 2 1.4 Motivation for E328 6 II The Experiment 8 II. 1 The Cyclotron and the M i l Channel 10 11.2 The liquid targets 10 11.3 The in-beam Counters 13 11.4 The Wire Chambers 14 11.5 The Regina Detectors 15 11.6 The Tel-Aviv time-of-fiight arms 18 11.7 Overall Event Logic and L A M 18 11.8 Data Acquisition Structure 20 III Data Reduction and Offline Calibration 23 111.1 Beam Normalization 23 111.2 Wire Chamber Calibrations 24 iii 111.3 Calibration and Proton Identification in the Regina Arms 26 111.3.1 Pulse-Height calibration 26 111.3.2 Particle Identification 31 111.3.3 Measured characteristics of the Regina arms 32 111.4 Reaction Losses in the Regina Arms 33 111.5 Calibration and Proton identification in the Tel-Aviv arms 35 111.5.1 Position calibration 35 111.5.2 Time-of-flight calibration 36 111.5.3 Energy determination 38 111.5.4 Pulse-height calibration 39 111.5.5 Particle identification 39 111.5.6 The performance of the Tel-Aviv arms 41 111.6 Target traceback 42 111.7 Overall event definition 42 IV Results and Discussion 44 IV.l Results from R A R B T A coincidences for run 33 44 IV. 1.1 The missing mass check 44 IV.1.2 Monte-Carlo comparisons 45 IV. 1.3 The neutron momentum distribution 46 IV.2 The cross-section estimation 47 IV.3 Conclusions 50 Bibliography 53 A Energy Calibration in the Regina arms and Energy Loss treat-ment 56 A . l Energy Calibration in the Regina arms 56 iv A.2 Energy Loss Treatment 57 B The Monte-Carlo simulation 59 v List of Tables I The characteristics of the M i l tune used in E328 10 II The characteristics of the Regina telescopes 33 III The characteristics of the Tel-Aviv arms 41 IV Triple coincidence geometry and yield for run 33 44 V Efficiencies for the RA-RB-TA coincidences of run 33 49 VI Monte-Carlo acceptance value for run 33 50 VII Summary table of the uncertainties 51 VIII Constants and parameters for the Regina energy calibration. . . . 57 IX Parameters for the energy loss functions 58 vi List of Figures 1 Feynman diagrams for initial and final-state interactions 5 2 A typical set up showing the detector orientations 9 3 The M i l Beam Line Layout 11 4 The liquid 4He target cell and surroundings 12 5 Simplified electronics of the beam coincidence 13 6 A schematic diagram of a multi-wire-proportional chamber 15 7 The RA total Energy Telescope 16 8 The RB total Energy Telescope 16 9 Trigger electronics for RB 17 10 The TA time-of-flight arm 19 11 Trigger electronics for TA 21 12 The L A M logic and electronics 21 13 T C A P spectra for beam samples from the 165 MeV M i l tune. ... 24 14 A typical checksum spectrum 26 15 A prompt calibration peaks in the RA-ERU ADC spectra 27 16 Total Pulse-Height to energy calibration curve for RB 29 17 dE vs E scatterplot showing the particle separation in RA 31 18 Proton target energy measured by RA for a single arm run 32 19 Laboratory and centre-of-mass energies for ir+d —» pp protons .... 34 20 Vertical position calibration for TA-7 36 21 Mean-timed TDC spectrum for in-plane protons 37 22 Particle cuts in the Tel-Aviv arms 40 23 Vertex reconstruction for the empty 4He target in the X-Z plane. . . 43 24 Vertex reconstruction for the full 4He target in the X-Z plane 43 25 Missing mass spectrum for triple proton coincidences 45 vii 26 Neutron momentum spectrum for run 33 46 27 Neutron momentum spectrum for run 33 including Monte-Carlo com-parison 48 28 Neutron momentum distribution from 4He(7r+,ppp) from PSI .... 52 29 Pulse Height to Energy calibration curve for RA 58 Vlll Acknowledgements First and foremost I would like to thank Peter Weber for his work on the Monte-Carlo simulation and virtually every aspect of this project. Without his patience, supervision, vocabulary and whacky sense of humour this thesis would be some fifty pages thinner and my suntan ten times darker. Thanks also to all those people would participated in those hectic days of beam-time. In particular, I would like to acknowledge Rigo Olsweski for master-minding the whole thing; Martin for the cool software; Roman and George for the "spirited" discussions; Mark for an astonishing party performance and Sharon for the psychedelic wiring. (I am sure that diagram will turn up one day). Thanks to everyone would helped and survived. Next in line are the hordes of weary grad students who occupy TRIUMF and the Physics department in the small hours of rainy nights. Without their company and conversation things would be have been a lot less sane. Thanks to all of "Club Vax" Andrew, Chris, Jean, Geo, Hon, Marcello, Marty, Reena, Vesna and the plasma coffee guzzlers Angelo, Jim(what haircut?), Niall(what wall?) and Luiz. Finally I would like to thank my supervisor Dick Johnson for funding our trip to Lake Louise and the moose. This work was made possible through the sponsorship of the Commonwealth Scholarship. ix To my Gran. Nellie Roberts 1899-1987 C h a p t e r I I n t r o d u c t i o n 1.1 E x p e r i m e n t a l P h y s i c s a n d T i m e Herein lies the tale of one of the first triple coincidence experiments attempted by-members of the PISCAT group and collaborators. The experiment, E328, was performed to investigate the mechanism by which a positive pion is absorbed in the 4 He nucleus. A major part of the study involved the coincidence measurement of the three outgoing protons from the reaction 4He(7r+, ppp). By detecting three of the possible four nucleons our measurement was kinematically complete and allowed us to obtain the energy and momentum distributions of all four nucleons. In doing so we were able to make direct comparisons with simulations of three and four body phase-space and speculate on the number of nucleons actually involved in the absorption process. This comes at a time when there is growing interest in the search for multi-nucleon pion absorption channels [1]. In this essay I will describe the motivation for E328, the apparatus and methods employed, the analysis scheme and results from a limited set of the triple coincidence data. I make no apologies for the absence of detailed conclusions, given the extensive nature of the experiment and software. The future will, I have no doubt, reward the effort of the experimenters with worthy results. 1 1.2 The Pion as a Nuclear Probe Before describing the motivation for using 4He as the target for E328 it is only appropriate to say something about the nuclear probe used, i.e. the pion. First hypothesized by Yukawa [2] in 1935, the pion was introduced as the quantum exchanged in the strong nucleon-nucleon interaction. By attributing a rest mass of ~150 MeV/c2 to the new particle and invoking the Uncertainty Principle, the short range nature of the strong force could be readily introduced. It is now generally accepted that the exchange of pions and other mesons is a good description of the nucleon-nucleon interaction. The pion was "discovered" experimentally in cosmic ray data in 1947 [3] to confirm the original predictions of Yukawa. The usefulness of the charged pion as a nuclear probe stems from its properties as a light (m,± =139.6 MeV/c2), strongly interacting, long lived (r7r± = 2.6 x 10-8s) particle. It is therefore, possible to produce intense beams of 7r^" relatively economically. Although this is also true of electrons and positrons, these leptons are not strongly interacting and at intermediate energies "see" only the charged proton. The pion, on the other hand, interacts with both isospin projections of the nucleon. Consequently, by running experiments with alternatively 7r+ and 7r~ beams, it is possible to investigate different isospin channels of an interaction relatively simply. The construction of the meson factories in the 1970's is a testament to the worth of the pion as a nuclear probe. 1.3 Aspects of Pion Absorption Over recent years the study of pion absorption1 has become an exciting and controversial field. It is now apparent that existing theories do not account for the lm this case and throughout, pion absorption refers to a reaction in which there is no pion in the final state. See [1] for the convention used. 2 measured total pion absorption cross-sections and that new processes must be taken into consideration. In particular, there is growing evidence that absorption on more than two nucleons either directly or by a two-step mechanism, plays a significant role. In order to conserve both energy and momentum, at least two nucleons must participate in the pion absorption process. The simplest two nucleon system is the deuteron and the earliest work [1] in this field concentrated on the reaction Tr+d —> pp. When studies were extended to heavier nuclei [4] the angular distributions of the outgoing nucleons were well described by assuming the pion was absorbed on a quasi-free nucleon pair, Q2N within the nucleus. For a long time this was the hypothesis that dominated our picture of pion absorption. Firm evidence to contradict the Q2N assumption came first from bubble chamber work [5] and later from rapidity studies. The latter was performed by M cKeown et al. [6] on data from the single arm study of (7r±,p) on 1 2C and other heavier nuclei. They concluded that the average number of nucleons involved in the absorption process was ~ 3 and not the 2 of the Q2N model. A double coincident measurement by Altman et al. [7] of the reaction 12C(ir+,pp) concluded that Q2N absorption accounted for only 10% of the total pion absorption cross-section. A similar experiment and analysis on nickel [8] resulted in a figure of 9%. In both cases, the analysis involved decomposing the proton angular correlation into a narrow gaussian, attributed to Q2N absorption, and a broader background. Although this procedure has been challenged [9] this is just one example of the growing evidence suggesting that the two-nucleon absorption model does not account for a large fraction of the total pion absorption cross-section [1]. How can this discrepancy be accounted for ? Three processes have been put forward and studied experimentally:-3 • channels in which a composite particle is emitted. • sequential absorption processes in which the incoming pion undergoes an initial state interaction ISI, followed by Q2N absorption or, in which the pion undergoes Q2N absorption and an outgoing nucleon undergoes a Final State Interaction(FSI). Figure 1 illustrates these processes for a three nucleon system above the A resonance threshold. • genuine multi-nucleon absorption, in which the pion interacts directly with more than two nucleons. A recent example of the first of these processes is the measurement of the reaction 4He(-7r, Nd)N by Backenstoss et al. [10]. They demonstrated that an absorption channel existed in which the pion was absorbed on a quasi-free three nucleon, Q3N cluster. The fourth nucleon effectively acts as a spectator. ISI and FSI should be detectable by the characteristic kinematical signature of the two body processes involved. Such signals have been searched for in double and triple coincidence experiments. Yokota et al. [11] examined the angular distributions of the protons from 6Li, 1 2C(7r~,pp) at Tw+ = 165 MeV and reported enhancements at A 0 1 2 = 90° and 180°. They attributed this to FSI and ISI respectively. Tacik et al. [12] [13] have also recently observed FSI in a triple coincidence measurement of the reaction 12C(ir+,ppp). The most interesting of the three proposed mechanisms listed above, is the genuine multi-nucleon absorption. Such a process points to the possibility of new physics for which there are only a few relatively new models [14] [15] [16]. The first direct identification of such a process, 3N absorption, was made by Backenstoss et al. [17]. They performed kinematically complete, double coincidence measurements on the reactions 3He(7r+,pp)p and 3He(7r~,pn)n. In doing so they were able to show that a genuine 3N process contributed ~30% of the total 4 Figure 1: Feynman diagrams for Q2N, ISI and FSI on a three nucleon system, (a) Q2N absorption via a A resonance, (b) ISI resulting in a A formation followed by Q2N absorption, (c) FSI following Q2N absorption. 5 absorption cross-section. An experiment performed by Aniol et al. [18] produced similar results although there is a discrepancy2 of two standard deviations between the two experimental values of <73jv/cr2jv- The 12C(7r+,ppp) measurement mentioned in the last paragraph, identified a 3N absorption mode in which the pion interacts with a quasi-free 3He cluster. This channel was reported as accounting for only 11% of the total absorption cross-section at T„.+ = 180 MeV. Another recent preprint [19] has reported the existence of 3N and 4N modes in 4He in an experiment very similar to E328. 1.4 Motivation for E328 The experiments on 3He have demonstrated that it is possible to identify individual pion absorption channels using the kinematical completeness of their coincidences. The 3N mode was identified, in part, by comparing the measured momentum distribution of the undetected nucleon with that given by the nuclear wavefunction. Triple coincidence experiments on 1 2C have also reported 3N absorption. In this case, identification was made by examining the proton angular distributions. This work however, is limited by the number of nucleons left undetected and it is difficult to imagine higher absorption modes being extracted unambiguously from the data. 4 He is an ideal nucleus on which to perform a triple coincidence measurement. By detecting three of the outgoing protons in coincidence the missing neutron momentum is determined. With this kinematical completeness it should then be possible to compare the experimental distributions of missing momenta to Monte-Carlo predictions for 3N and 4N phase space. In doing so these multi-nucleon absorption modes can be quantified. Any FSI and ISI 2Here and throughout <TXN represents the integrated cross-section for a process in which the absorbed pion energy is distributed amongst x-nucleons. signatures should be seen as significant departures from the phase space. E328 set out to use the above method to investigate the absorption of ir+ on 4He at T„.+ =165 MeV . We not only intended to measure but also a^iii it existed) and <72jv in order to compare the relative contributions to the total absorption cross-section. At the time of the experiment there existed only a single published paper [12] of a triple coincidence measurement in this field. Our 4He experiment not only offers an independent examination of multi-nucleon pion absorption modes but also serves as a useful comparison to the recent results [19] from the Paul Scherrer Institute. 7 Chapter II The Experiment This experiment was performed at the Tri-University Meson Facility, T R I U M F , on the medium energy pion beam line M i l during two weeks of high intensity beam in October 1987. An earlier run in August was aborted due to R.F. failure. The incident 165 M e V 1 7r+ beam impinged upon liquid 2 H , liquid 4 He, and CD2 targets. Four detector arms were used to determine the reaction products . They were; two time-of-flight arrays from the University of Tel Aviv (TA, TB) and two plastic scintillator total energy telescopes from the University of Regina (RA, RB). A typical set up is shown in Figure 2. All the arms were timed into coincidence with respect to an in-beam scintillator SI. Data, in the form of Camac words, were written to magnetic tape by a PDP-11/34 computer at the prompt of a L A M ( look at me ) signal. This signal was triggered by a 7r+ event in SI and the in-beam hodoscope along with a given two or three-fold coincidence of the detectors. Protons from the reactions Tr+d —• pp and Tv+p —> n+p were used for timing and pulse-height calibration; the 2 H and CD2 were the targets for these runs. All four arms were then used to investigate the processes 4He(Tv+,pp) and 4He(7r+,ppp). In this thesis only the triple proton coincidences will be discussed. 1 T h i s is a nominal value. Including energy losses the pion kinetic energy at the target centre was calculated to be 163.46 M e V . 8 Figure 2: A typical set up showing the detector arm orientations with respect to the target cell. 9 II.l The Cyclotron and the M i l Channel The TRIUMF facility is based on a 6-sector isochronous cyclotron which accelerates H~ ions up to 520 MeV. Carbon strippers are used to remove the two bound e _ and the resulting protons are directed into two or more primary beam lines. The machine has a duty cycle of ~ 100 % and a time structure of one 3 ns beam bucket every 43 ns. The M i l channel is located off the beam line BL1A and downstream of the main pion production target 1AT1. Its layout is shown in Figure 3 and a detailed description of the components is given in reference [20]. By adjusting the settings of the various slits and magnets clean 7r+ and TC~ beams of between 60 and 300 MeV can be produced. The important characteristics of the M i l tune used in this experiment are given in table I. Table I: The characteristics of the M i l tune used in E328. Channel Momentum P 271.6 MeV/c Channel 7r+ Energy 166.1 MeV A P / P 1.1% 7r+ per second 4.5xl06 II.2 The liquid targets The composition of the liquid 4He target cell and surroundings is shown in Figure 4. The liquid 2 H cell was similar in construction2. Both cells were cylindrical in shape with diameters of 3 inches and 2 inches respectively; they were cryogenically cooled to operating temperatures of 1.8 K and 23 K. 2Full descriptions are given in the TRIUMF User's handbook [20] 10 Figure 3: The M i l Beam Line Layout. 11 12 B E A M C F D T S 1 s 1 J H C F D HODO H 1 D I S C H2 to H12 same as H1 Figure 5: Simplified electronics of the beam coincidence. II.3 The in-beam Counters The incoming pion beam was determined by two in-beam counters. A 12 strip 3 plastic scintillator hodoscope, H O D O , located 380 mm from the target centre and a single plastic scintillator, S i , 170 mm from the centre. The latter was fitted with a high rate photomultiplier tube (PMT). The simplified electronics for the in-beam counters is shown in Figure 5. Two different voltage thresholds were set on the Si discriminators; Six, below the observed pion signal and Slu above this signal but beneath an in-beam proton signal. The electronic logic was arrranged so that the output B E A M , was triggered by the coincidence of the Sl^, and H O D O signals with the anti-coincidence of the Sljj signal, i.e. B E A M = S 1 L S I H H O D O 3 Each strip has dimensions 1.6 x 2.0 x 20.0 m m 3 13 A B E A M trigger was taken as indicating that a pion was incident on the target cell. The coincidence was set up so that the signal from S 1 L carried the timing. The content of the beam was monitored by measuring the time-of-flight of particles through the channel. A capacitively coupled probe, TCAP, positioned before the 1AT1 target gave a time-to-digital converter(TDC) stop signal which was delayed so as to come after the start given by the B E A M coincidence. In order to get an event-independent measure of the beam constituents, samples of this TDC were written to tape at 1 s intervals regardless of detector arm signals. II.4 The Wire Chambers A l l six chambers were multi-wire proportional chambers(MWPC) and consisted of an anode wire plane sandwiched between X and Y cathode wire planes. The spacing of the cathode wires was 1mm and the anode wires were 2mm apart. TDC's sampled one end of the cathode wires via a delay line as illustrated in Figure 6. The chamber volume was filled with standard Magic Gas which is an 80:20 mixture of Argon and Isobutane4. The anodes are held at a high positive potential with respect to the cathodes(~ 4 kV) resulting in a large field around each wire. Incident charged particles ionize the chamber gas and the resulting electrons and ions are accelerated in the field of the nearest anode. An avalanche results as these particles ionize other gas molecules. The resulting electrons drift to the anode wire producing a pulse. The heavier positive ions drift more slowly to the cathodes. The prompt anode pulse capacitively induces signals in several of the neighbouring X and Y cathode wires and these are sampled by the TDC's. For each plane the difference in the TDC values from either end of the delay line is linearly related to the mean position of the cathode wires that produce signals. These positions are 4It also contains a small amount of Freon ( « 1%). 14 ANODE PLANE Y-TDC UP LiJ Z < _J Q_ UJ Q O < O Y-TDC DOWN 2 mm 1 mm 4000 V X-TDC LEFT X-CATHODE PLANE X-TDC RIGHT Figure 6: A schematic diagram of a multi-wire-proportional-chamber as used in E328. taken as the coordinates of the incident particle as it passed through the chamber. II.5 The Regina Detectors The Regina arms were the same absorption counters used in TRIUMF experiment E403 [21] and described in detail in [22]. I will limit this discussion to a schematic description. Each arm consisted of four large BC400 plastic scintillator E-blocks fronted by two 100 x 5 x 200 mm3 dE 5 counters and two 150 x 150 mm active area MWPC's. Figures 7 and 8 show the arrangements for RA and RB. Arm A had one PMT per 100 x 100 x 300 mm3 E-block and arm B had two PMT's per 100 x 200 x 150 mm3 block. The combined dimensions of the E-blocks for both 5 T h e term d E refers to a thin scintillator which is used to discriminate between particles of different energy by the light they produce as they pass through it. 15 RA-E Right Down ^RA-dE Right RA-WC Bock Target RA-WC Front DISTANCE TO ELEMENT TARGETmm WC-Front 3 0 0 WC-Back 390 RA-dE 4 5 5 RA-E 4 6 0 R A - E Scint i l lator block Light Guide Photomult ip l ier Tube Figure 7: The RA total Energy Telescope. Nomenclature and orientations are shown. R B - E Left Back - E Left Front ; RB R B - d E Left R B - d E Right R B - E Right B a c k R B - E Right F ron t Ta rge t Element Dis to target (mm) WC Front 300 WC Back 396 RB-dE 455 RB-E 460 Light Guides } Pho tomul t ip l i e r Tubes Figure 8: The RB total Energy Telescope. Nomenclature and orientations are shown. 16 RA and RB were 200 x 200* x 300 mm3 Energy measurement in these arms was achieved by stopping the incident charged particle in one of the E blocks and sampling the light produced with a calibrated analogue-to-digital converter(ADC). Particle identification was made by the dE vs E method and the two MWPC's allowed trajectory determination. A simplified diagram of the hardware trigger electronics for RB is shown in Figure 9. RA had a similar set up but was simpler due to the fewer number of PMT's. A hardware event in RB was given by the coincidence of one or more dE counters with one or more of the E-blocks. Using the notation of Figure 9 RB-EVENT = RB-dE(OR) RB-E(OR) Similarly for RA. Figure 9: Trigger electronics for RB. 17 II.6 The Tel-Aviv time-of-flight arms Each Tel-Aviv arm was made up of a standard TRIUMF two plane 150x150 mm2 MWPC, a thin dE scintillator and an array of eight 125x100x1000 mm3 long scintillator bars arranged as shown in Figure 10. Each bar was fitted with two PMT's, one at either end. The dE was connected to one PMT and was used in the hardware trigger to veto neutral particles. The energy of an incident charged particle was determined by measuring its time-of-flight and flight path length from the target to the scintillator array. Mean-timed TDC signals from either end of a bar with a start given by Si, were used for timing. The up-down TDC difference gave vertical position information and this combined with the bar position in the array and the MWPC allowed the trajectory to be determined. ADC's sampled the pulse from each PMT. By plotting time-of-flight vs pulse height particles of different masses could be distinguished by the characteristic areas they occupied on this graph. Figure 11 shows the simplified hardware trigger electronics for arm TA which were identical to TB. An event in this arm was given by the coincidence of the dE counter with one or more of the long bars. i.e. T A - E V E N T = T A - d E T A - ( O R ) II. 7 Overall Event Logic and L A M The electronics for the LAM generation and overall event definition is shown in Figure 12. The four event signals were timed into a MLU (majority logic unit). This unit could be set to give an output signal if there were one, two, three or four input signals. In other words, this unit set the lowest level of coincidence at which events were accepted i.e. two-fold and greater or three-fold and greater. 18 TA-WC TA-dE TA-1, 8 Target Photomultiplier Tube Light Guide Array centre o ' Element Distance to target (mm) TA-dE TA-WC o' 150 265 2000 Figure 10: The T A Time of Flight arm. Nomenclature and orientations are shown. 19 The L A M signal carried the timing of Si and so it was this signal that determined the TDC starts, opened the ADC gates and produced the J l l interrupts. An overall trigger for the double coincidence RA-TB was, for example, L A M = B E A M RA-EVENT TB-EVENT PDPBUSY Here the PDPBUSY is the computer busy flag. II.8 Data Acquisition Structure Data acquisition was made by the STAR system [23] fitted with the J l l preprocessor. The system responded to the prompt of the L A M described in the last section. A fraction of the taped events were analysed online to enable the performance of the apparatus to be monitored. One interesting feature of this experiment was the use of a variable length data sentence. Given that a three-fold coincidence, R B T A - T B had an event length of 117 Camac words and that a two-fold coincidence, RA-RB, had a length of only 63, it would have meant a considerable waste of magnetic tape to have written all events to tape with the same sentence length. Instead the J l l preprocessor was used to determine the combination of arms that had fired and read only the corresponding number of Camac words required for that event. The sentence was then written to the PDP11 buffer. In this way only the minimum number of words were written to tape. The J l l was also used to prescale certain combinations of coincidences during the 4He(7r+, pp) runs when the high event rate resulted in a significant computer dead-time. e.g. at certain geometries the event rate of the RA-TB coincidence far exceeded that of RB-TA; by accepting only a predetermined fraction of the former events more of the lower rate events could be recorded. The final numbers of coincidences were corrected offline for these prescaling factors. 20 A DC r Disc TA -dE CFD TDC TA -EVENT T A - d E ADC TA-1U CFD DISC r- AND TDC T A - O R ADC TA-1D CFD _ MT TA-TA-2 to TA-8 same as TA—1 TDC DISC Figure 11: Trigger electronics for TA. L A M EVENT J 11 —interrupt TDC Start ADC Gate PU Gate Figure 12: The L A M logic and electronics. 21 Visual and Camac hex-sealers were used to count the number of beam events, LAM's, beam-samples, Jll-interrupts etc.. In all there were 38 hex-scalers which were written to tape at 5 min. intervals. These values were summed in the offline analysis and compared to the recorded visual totals. 22 Chapter III Data Reduction and Offline Calibration The analysis of E328 was performed between January and August 1988 on the TRIUMF VAX cluster. In total 33 6250 bpi magnetic tapes of data were acquired of which approximately one sixth contained triple coincidences. In what follows I will describe how the apparatus was calibrated and the proton momentum determined in each arm. III.l Beam Normalization To be able to calculate cross-sections it is essential to know the number of incident pions that produce a given number of coincidences. In E328 a beam event was determined by Si and HODO as described in section II.3. The beam hex-sealer SBEAM w a s used to count all such events. To calculate the actual number of incident n+ from this value two corrections had to be made:-• The M i l beam was not free from contamination and beam triggers not caused by pions had to be accounted for. By histogramming the TDC of the TCAP probe for beam sample events only, an unbiased picture of the beam could be observed. At 165 MeV it was predominately 7r+ and the decay products, e + and /x+ were not separated in time from the main peak(see Figure 13). Therefore, previously measured [24] contamination fractions were used to correct SBEAM- These values yielded a pion fraction, fn+, of. 98.2%. • At fluxes of the order of MHz there is a significant number of multiple pions per beam bucket. The timing of the BEAM coincidence was such that only a 23 0 0 240 480 720 960 1200 TCAP TDC [channels] Figure 13: T C A P spectra for beam samples from the 165 MeV M i l tune. single pion could be counted per bucket. To take this into account the standard formula [25] giving the correcting factor, fd, was used i.e. m ( l - ^ ) •Id rate rf where rate was the measured number of 7r+ per second and rf was the T R I U M F R.F. frequency of 23 MHz. Thus the normalized number of incident 7r+ was Nw+ given by A^7r+ = fd • /tt+ • SBEAM III.2 Wire Chamber Calibrations The wire chambers in this experiment were used to find the trajectory of the charged particles incident on the detector arms. This enabled momenta to be 24 determined from energy. It also allowed background rejection of events whose trajectories did not intersect the target region. The position of hits in the chambers was obtained by converting the TDC-differences from either end of the cathode delay-lines to distances. The multiplicative factor, GAIN related these TDC-differences to spatial coordinates and was obtained by the picket-fence method [26]. A collimated electron source was directed at the centers of each chamber to find the corresponding X and Y TDC-differences. These values were used as offsets to enable the hit positions to be given with respect to the chamber centers.e.g. Xpos = GAIN[( TDC right - TDC left ) - offset] For each plane of cathode wires a checksum was calculated as the sum of the delay-lines TDC's. This quantity was required to establish whether the hit was good or not. If the electrons produced on ionization took no time to drift to the anode wires then the checksum would be a delta function. As it is, the width of this quantity(see Figure 14) is due to finite electron drift times. Shorter or excessively longer drift times are an indication of double hits or inefficiencies and such events were rejected. Good hits are taken as those within the cuts shown. An overall good hit for a chamber required both X and Y checksums to be good. For example, a good event in the RA front chamber would be RA-WCfront=Good X-checksum.AND.Good Y-checksum For each chamber a proton detection efficiency was determined. Particles were identified as protons (see 111.3,111.5) and the following fraction determined No. of protons hits ^ No. of incident protons Here the number of protons hits was the number of identified protons for which 25 500 | ' 1 1 1 1 1 1 r-r~i 1 1 ' 1 1 1 1 1 1 1 1 r 200 440 680 920 1160 1400 TA—Y checksum [channels] Figure 14: A typical checksum spectrum showing the good event cuts. the chamber registered good hits. These efficiencies were used to correct the final yield of three proton events when calculating cross-sections. III.3 Calibration and Proton Identification in the Regina Arms III.3.1 Pulse-Height calibration The segmented nature of these counters made it rather an involved process to obtain a consistent calibration. As with all detectors in this experiment, calibration was performed with the protons from the reactions n+d —* pp and ir+p —> TT+p. The liquid 2 H and solid C D 2 targets were used. Two incident pion energies were utilized, 65 and 165 MeV, to allow as wide a range of calibration energies as possible. RA and RB were placed on pairs of kinematically correct angles for the reactions and data were recorded. The angles were chosen so that 26 the outgoing protons were stopped in the Regina E-blocks. Figure 15 shows an example of a prompt peak in an E ADC spectrum. The peak position is proportional to the amount of light produced in the scintillator by a proton ionizing the medium. Suppose £' was the corresponding amount of energy deposited. £' was obtained from the known kinematics of the above reactions and corrected for ionization losses in the target and intervening materials before the scintillators. The principle of the calibration was to enable £' to be deduced from the sum of the light produced in all four E-blocks. Thus if a proton passes through one E-block and stops in another, the energy it deposits would be correctly computed from the total light it produces. 50 40 -30 c Z5 o °20 10 ~i—i—i—i—i—i—r- i 1 1 1 1 1 r-7T d > p £ OFFSET ii Jl n.nnO ill nnnln. nP, IVl W I K, A D C Peak -10 132 274 416 558 RA-ERU ADC [channels] 700 Figure 15: A prompt calibration peaks in the RA-ERU ADC spectra. To perform the light summation the different gains of each PMT had to be taken into account(each PMT had a slightly different voltage bias resulting in different light amplification for a given £') . In the case of RA this gain matching 27 was relatively simple as there was only one P M T per E-block. T h e to t a l light or pulse-height, produced by an incident p r o t o n was taken to be p r o p o r t i o n a l to CRA = gf(ADC{ - offseU) (4) i=i where i runs over the four R A E blocks. E a c h offset was obtain e d dire c t l y f r o m the raw A D C spectra as shown i n F i g u r e 15. T h e gains for each P M T , Qf were obtained using a known £' a n d the corresponding position of the prompt A D C peak. T h e gain is given numerically by A £' Gi = ADCfeak - offseU ( 5 ) T h e slightly different £'s for the left a n d right E-blocks, due to kine m a t i c a l va r i a t i o n of the prot o n energies w i t h angle, were taken into account. T h e two tubes, U p a n d D o w n per E-block of the R B a r m made matching more complicated. T w o gains Qfu a n d Qfd were obtained for each E-block by the same process described above. T h e overall light output was computed by summing over the mean A D C signals f r o m the U p a n d Down P M T s , i.e. CRB = £ G?U(ADC? - offset?) + G?d(ADC( - offset*) t=i ^ L i g h t to energy ca l i b r a t i o n was achieved by f i t t i n g CRA a n d CRB to the calculated values of £' over the f u l l range of ca l i b r a t i o n data. T h e following f u n c t i o n was f o u n d to provide a good fit E'= a1(FC) + B{l-exp{a2{FC)a*)) (7) Here the values of ai =i..3 are constants(see A p p e n d i x A ) a n d F a n d B were parameters obtained by minimization. T h i s was done for b o t h R A a n d RB. A none linear fit was used i n order to fit the lower energy d a t a c a l i b r a t i o n points. F i g u r e 16 shows the fit for R B a n d a comparison to a linear fit. 28 Calibration fit for R 0 500 1000 1500 2000 T o t a l P u 1 s e ~ H e i g h t Figure 16: Total Pulse-Height to energy calibration curve for RB. The plot shows a comparison of a linear fit to that of equation 7. Error bars represent the spread of proton energies over the solid angle subtended by the arm. 29 To obta in the energy, E of the proton at its point of product ion i n the target, the ionizat ion energy losses i n the target material , air , M W P C ' s etc. had to be included. T h i s was done by computing E and the corresponding value of £ ' over a range f rom 0 to 300 M e V using the F O R T R A N routine F L U G [27] which ut i l ized the Bethe-Bloch equation. A simple empirical funct ion 71 was fitted to this data, the form of which is given i n A p p e n d i x A . In principle the fu l l Bethe-Bloch equation could have been programmed into the analysis to calculate E f rom a measured value of £ ' . However, the much simpler funct ion, 1Z was found to be sufficient over the l imi ted energy range required. T h e proton target energy was thus determined by first calculating £ ' f rom the pulse-height and then calculating E using E = 7l(£') (8) Once E was known the three-momentum components were calculated using the trajectory information f rom the two wire chambers. A coordinate system was chosen so that the beam direction determined the positive Z axis, Y was vertically up and X completed the right-handed system. N o energy cal ibrat ion for the d E scintillators was required; they served only to enable particle identification. Instead a normalized total pulse-height or light output was obtained. The two tubes, U p and D o w n of each d E scintil lator were gain matched using the same calibrating proton signals and technique as previously described. The geometric mean of the two A D C signals was taken as the total pulse height. B y taking this mean the exponential attenuation of light w i t h distance i n the th in scintillator could be corrected for. T h i s gave a pulse-height which was almost independent of the posit ion of the hit . The total pulse-height i n an arm was then given by CiE = gfEJ(ADCr - offset?)(ADCf - offset?) (9) t=i 30 where i runs over left and right dE's. III.3.2 Particle Identification Particle identification in these arms was made using the dE vs E method. This involved plotting the calculated target energy E against CdE as shown in Figure 17. Particles of different masses fall on separate contours allowing a clean separation. A "box" was drawn around the area occupied by the protons and a test, R-BOX was made such that a proton was defined as a particle for which its (E, CdE) point lay within this polygon. 2 2 0 i i i •^1 76 JZ cn —i cu " f = 1 3 2 QJ cn •—i 3 O- QQ I CX CC 44 7Y d p 0RB=136 = -70^ 1—i >" 2 0 0 0 I I I I I i 5 0 0 1DD0 1 5 0 0 Rfl target energy [MeV*10 2 5 0 0 Figure 17: dE vs E scatterplot showing the particle separation in RA. The definition of a good proton in the Regina arms was taken as event for which both the chambers registered good hits and the R-BOX test was satisfied. For example, a proton in RB was given by RB-proton=RB-EVENT RB-WCfront RB-WCback RB-BOX 31 III.3.3 Measured characteristics of the Regina arms The following three characteristics were determined for Regina telescopes in order to assess their performance. • The energy threshold for the 4He target. • The energy resolution of the scintillators. • The solid angle of the detector. The first of these was determined from a single arm measurement with the 4He target. Figure 18 shows the measured spectrum of proton energies. Not being limited by coincidence kinematics this plot reveals the threshold of 36 MeV. Similar runs were made for all four arms. 100 • Threshold = 36 MeV 20 0 0 500 1000 1500 : RA p r o t o n e n e r g y [ MeV*10] 2000 2500 Figure 18: Proton target energy measured by RA for a single arm run. The energy resolution in each Regina counter was determined from the prompt proton energy peaks from the n+d —»• pp reaction. In the laboratory frame 32 of reference the proton energies vary over the solid angle subtended by the detectors. By making the Lorentz transformation from the laboratory system into the centre-of-mass system, this variation was eliminated, (the energies of the protons in the CM system are fixed for all lab angles). The FWHM of the resulting peak was taken as a measure of the energy resolution. Figure 19 shows the effect of the transformation and the resulting narrow peak in the centre-of-mass system. The solid angles of the Regina detectors were determined by the active area of the back wire chambers i.e. 150 x 150mm2 and their distances from the target centre. Table II summarizes the properties of the Regina arms. Table II: A Summary table of the characteristics of the Regina telescopes as used in E328 Characteristic Value for RA Value for RB AO 148 msr 143 msr AEFWHM/E at 80 MeV 6% 9% AEFWHM/E at 114 MeV 5% 6% AEFWHM/E at 150 MeV 5% 5% Proton threshold 4He target 36 MeV 36 MeV III.4 Reaction Losses in the Regina Arms It is well documented [28] [29] [30] that protons incident on scintillators may undergo nuclear reactions instead of ionizing the medium. Such processes result in a reduced light output and hence an energy miscalculation in telescopes such as the Regina arms. These losses were observed during E328 and can be seen as a tail in the ir+d —> pp proton peaks(e.^. Figure 19). A proton is defined1 as having undergone a reaction loss if it lies within this tail and outside of the gaussian-like peak. During the analysis of the Regina counters, the R-BOX cuts were made as lThe fraction of events selected as reaction losses is thus dependent upon the cut made separate the tail from the main peak. 33 110 88 8 66 44 22 '- Reacti ! l o s s e s \ _i i i jj I 1 1 1 1 r~ LAB 0 500 1000 1500 2000 RB target energy [MeV*10] 2500 110 88 - 66 -§ 44 o o 22 —1 1 1 1 1~ FWHM CENTRE • of MASS. 500 1000 1500 2000 RB target energy [MeV*10] 2500 Figure 19: The energy spectra of protons from Tt+d —• pp in the lab(upper Figure) and centre-of-mass(lower Figure.)systems. The FWHM of the latter peak was taken as the resolution at this laboratory energy. 34 tight as possible on the proton band specifically to exclude particles that had undergone nuclear reactions. When calculating cross-sections a term, er was introduced as the efficiency of the telescopes with respect to reaction losses. er was estimated by calculating the mean proton energy in each counter and looking up the corresponding reaction loss fraction. The data from reference [31] was used for this purpose. III.5 Calibration and Proton identification in the Tel-Aviv arms III.5.1 Position calibration The first part of the Tel-Aviv arm calibration involved obtaining the vertical position information about hits in each of the 16 scintillator bars. The difference in the TDC values from the Up and Down tubes were converted to distance with respect to the beam height. This was done in a manner similar to the wire chamber calibration(see Section III.2)z.e., Yposi = gT[(TDC? - TDC?) - offseU] (10) Where i runs over all 16 bars. The bars were physically centered about beam-height so the offset was obtained by centering the TDC-difference spectra around zero. The gain QT was obtained by timing a small (10 x 10 x 14 mm3) test scintillator, B l , into the event coincidence of TA and taking data with B l placed at six different vertical positions along TA-7. The LAM was given by L A M = B E A M TA-dE B l TA-7 Figure 20 shows the least squares fit to the plot of Up-Down TDC-difference vs vertical position of B l . QT was taken as the best slope (mm/TDC channel). The gains for the remaining 15 bars were assumed to be the same. Horizontal position 35 500 300 1 00 -'-IOO -300 -500 1 1 1 1 -n. Slope = —3.77 mm/channel «s Beam height s. 1 1 1 1 -150 -90 -30 30 90 150 TDC d i f f e r e n c e [ c h a n n e l s ] Figure 20: Vertical position calibration for TA-7. The plot shows a least-squares straight line fit. information was obtained from the location of the individual bars in the array. The centre of a bar face was taken as the horizontal position of the hit if that bar fired. For events in which adjacent bars fired the mean of the two positions was used. III.5.2 Time-of-flight calibration The Tel-Aviv arms were calibrated for time-of-flight by using the flight times of protons from the n+d —> pp reaction. All four arms were set at conjugate angles and the two-fold proton coincidences RA-TB, RB-TA were recorded. The software mean of the Up and Down TDC's of each long scintillator bar was used as a measure of the time-of-flight(Recall that the TDC start was given by Si). A vertical position cut was used to limit the possible time-of-flight's to those of in-plane protons. Only particles which hit ±20 mm of beam height were used. In doing so, the mean-time peaks were made as narrow as possible and a precise 36 10 8 -6 -CO -i-> % 4 O o _J I L_ FWHM= 14 channels = 0.7 ns J n I n I n i l ihrt fin I n fc. 240 480 720 TA —2 mt [channels] 960 1200 F i g u r e 21: A m e a n - t i m e T D C s p e c t r u m for i n - p l a n e p r o t o n s f r o m ir+d —> pp. T h e T D C ' s scale was set to 0.05 ns per c h a n n e l . c a l i b r a t i o n c o u l d be m a d e . F i g u r e 21 shows a n e x a m p l e of the m e a n - t i m e d p e a k i n T A - 2 c o r r e s p o n d i n g to a p r o t o n i n R B . T h i s figure also shows the t i m i n g r e s o l u t i o n ; t a k e n as the F W H M of the p e a k ~ 0.7 ns . F o r e a c h of the 16 bars a start value was o b t a i n e d s u c h that t ime-of - f l ight , TOFi was g i v e n b y TT)CU 4- TT)Cd TOFi = 0.05( ' 2 ) ~ starti (11) H e r e 0.05 is the convers ion factor f r o m T D C channels into n a n o s e c o n d s a n d was a h a r d w a r e set t ing . E a c h start was o b t a i n e d b y s u b s t i t u t i n g the centroids of the c a l i b r a t i o n m e a n - t i m e peaks a n d the c o m p u t e d flight t imes of the c o r r e s p o n d i n g p r o t o n s , in to the above e q u a t i o n . T h e s e flight t imes were c a l c u l a t e d u s i n g the F L U G r o u t i n e w h i c h took into account the i o n i z a t i o n losses f r o m the target to the array a n d the di f fer ing distances to i n d i v i d u a l bars . A c o r r e c t i o n was also m a d e 37 for the time-of-flight of the incoming 7r+ from Si to the 2 H target centre. III.5.3 Energy determination To obtain the energy of a proton from the measured time-of-flight to the Tel-Aviv array two factors had to be taken into account:-• The differing flight path lengths for a given time-of-flight • The ionization energy losses in the materials between the target and the array. A series of approximations were made to simplify the calculations. Firstly the energy losses were assumed to be independent of the flight path length to the array. This is a not unreasonable given the radial symmetry of the target and the relatively short distances involved. Secondly, for a given particle energy, the time-of-flight over a distance L, TOFL was taken to be related to the time-of-flight to the centre of the scintillator array TOF' by TOFL = TOF'-^— (12) Where Lmin was the distance from the target centre to the array centre, i.e. 2000 mm. This obviously relied on the fact that the particle's velocity did not vary significantly from the target to the array so that time-of-flight was proportional to distance. This relationship was found to hold very well above 80 MeV and resulted in discrepancies of ~ 1-2 MeV at lower energies. This "reduced time-of-flight" TOF' was used in the energy calculation for all events. To calculate a target proton energy E from a given TOF', a simplified empirical functional fit was made similar to that used for the Regina arms. E and the corresponding value of TOF' were calculated over an energy range of 0 to 300 MeV and an empirical function T was then fitted to the resulting data. The 38 form of this function is given in Appendix A. Thus for a given TOF' of a proton, the energy measured in the Tel-Aviv arms was E = T(TOF') (13) Initially the distance L was determined assuming a point target and using the horizontal and vertical position information from the array only. Once the reaction vertex had been found (see Section III.6) a corrected value of L was used. 111.5.4 Pulse-height calibration Pulse height calibration in the long scintillator bars were made in an identical way to the dE's of the Regina arms as described in Section III.3.1. To obtain a position-independent signal the geometric mean of the Up and Down ADC's was taken(see for example [32]). Prompt A D C calibration peaks from the ir+d —• pp reaction were used2. Gains and Offsets were obtained and normalized pulse-heights CTA and CTB calculated. If two adjacent bars registered hits the corresponding pulse-heights were summed. This was done to take into account particles that passing through more than one bar. Events were rejected if more than two bars fired or if the hits were none adjacent. 111.5.5 Particle identification Particle identification in the Tel-Aviv arms was achieved by the time-of-flight vs pulse-height method. Figure 22(upper) shows a plot of time-of-flight vs CTA. The three main reaction products, protons, pions and deuterons, lie on different contours as shown. The box T-B0X1 was used to make an initial separation of the protons. The major drawback with using only 100 mm thick scintillators was that protons over 120 MeV were not stopped. This results in a turn over point on 2 T h e protons were stopped in the scintillator bars 39 D 1000 2 0 0 0 3000 4000 Tfl time-of-flight [ns*1001 1 0 I i i , i I i i i i I i , . K d • W \ ' 0R B=136° l&V^v P 0 T A=-7O° + \ • \ •' - • TA-BOX2 0 700 1 400 2100 2800 3500 Tfl target energy [ rieV*1 03 Figure 22: Particle cuts in the Tel-Aviv arms. The upper plot shows the time-of-flight vs pulse-height cut. The lower shows the additional cut used to elim-inate the pions that pass TA-BOX1 cut. 40 the time-of-flight vs pulse-height plot at which the pulse-height falls as the higher energy protons begin to punch through the scintillator. The proton band then dips towards the pion band. To avoid any possible misidentification of high energy or reaction loss protons with pions, a second box, T-B0X2 was made on the dE vs E plots as shown Figure 22(lower)(Recall the TA-dE and TB-dE veto counters). The first box T-B0X1, separated all of the protons and a small number of pions from the deuterons. The second box T-B0X2, separated the protons and deuterons from the pions. By requiring that both these box tests be passed, the protons could be completely separated. A proton was defined as a particle for which a good chamber hit was recorded and for which both box tests were satisfied, e.g. a proton in TA was defined by TA-proton=TA-EVENT TA-WC TA-BOX1 TA-BOX2 III.5.6 The performance of the Tel-Aviv arms Energy resolutions and thresholds of the Tel-Aviv arms were determined in the same way as for the Regina detectors. Protons were not required to stop in the the scintillator bars so the solid angle was determined purely from geometry of the array. Table III summarizes the measured characteristics of these detectors. Table III: A Summary table of the characteristics of the TA arm as used in E328. The figures are the identical for TB. Characteristic Value for TA Aft 250 msr AtpwffM 0.7 ns AEFWHM/E at 115 MeV 8% &EFWHM/E at 190 MeV 14% Proton threshold 4He target 38 MeV 41 111.6 Target traceback The large number of components used in this experiment meant that the there was a possibility of random hits and or background sources. Online coincident timing and offline proton cuts got rid of most of these events. However the possibility existed for three proton events originating from outside the target. The carbon in Si and other in-beam materials may have provided such a background. In order to eliminate these events the reaction vertex for each event was reconstructed. A CERN routine, VERTEX was used for this purpose. It calculated the closest point of approach of three measured proton trajectories and the beam direction3 and returned this as the vertex. All trajectories were modified to pass through this point and the corresponding angles, momenta and flight path lengths were similarly corrected. Figures 23,24 show the X-Z plane vertex reconstruction for the empty and full 4He target. Both graphs were produced with the same set of cuts. The box shown, termed T G T C U T , was made to limit good events to those originating in the target. 111.7 Overall event definition A good triple proton coincidence was defined as an event for which all wire chambers involved registered good events, the four particle identification box tests were passed and the T G T C U T was satisfied. A triple proton coincidence in RARB-TA was, for example, given by RA-proton RB-proton TA-proton T G T C U T 3Ideally H O D O could have been used to provide x information about the 7r+ for each event. However the inefficiencies of this device required that in some (~20%) cases, the z axis be used as the beam direction. 42 10 events/ 10 ix I i i i i I i i i i I i i1 i i | 'i* i i i I i i i i | -2000 -300 -180 -60 60 180 300 Target-XO [n*10] Figure 23: Vertex reconstruction for the empty 4He target in the X-Z plane. 10+4 events. 10 7T Figure 24: Vertex reconstruction for the full 4He target in the X-Z plane. 43 Chapter IV Results and Discussion In this section I w i l l describe the prel iminary results f rom the analysis of E328. In part icular I w i l l concentrate on the triple coincidences R A - R B - T A i n the single configuration given i n table I V . IV.1 Results from R A - R B - T A coincidences for run 3 3 I V . 1 . 1 The missing mass check Triple-proton events were filtered f rom the raw data by requiring that good events conformed to the definition given i n Section III.7, i.e a l l five chambers registered good hits , a l l proton box tests were passed and the target cut was satisfied. One further check was made to confirm that these events really were f rom the absorption reaction 4 H e ( / T + , p p p ) . The so-called missing mass M , was calculated for each event satisfying the above conditions. M is defined as the magnitude of the difference between the i n i t i a l and final 4-momenta. For the coincidence i n question it was given by M2 = (PZ + P&e-P&A-P£B-P$A)2 (14) Table I V : Tr iple coincidence geometry and yie ld for r u n 33 R u n Number Detector angles N o . of incident ir+ Triple proton yie ld 33 BRA = 40° ORB = 136° eTA = - 5 5 ° 950.88 x 10+8 7489 44 180 144 ? 108 i 72 o o 36 ~I 1 1 | 1 1 1 1 1 1 1 1 r~ Jl eRA=40 e R B =i36° e T A=-55 _J I I I I L_ FWHM=20 MeV/c MK _J I L. 9 11 13 Missing m a s s [ M e V / c *10 ] 15 Figure 25: Missing mass spectrum for triple proton coincidences. Here are the 4-momenta. The kinematical completeness of the measurement predicts a value of M equal to the mass of the undetected neutron. Figure 25 shows the missing mass spectrum obtained for the geometry of run 33. The distribution is a peak centered around 938 MeV/c 2 which is consistent with the neutron mass(mn=939.6 MeV). Thus the origin of the events was confirmed. IV.1.2 Monte-Carlo comparisons One of the principle aims of E328 was to investigate the number of nucleons involved in the pion absorption process. To this end, the experimental results were compared to results obtained from simulations of 4N and Quasi-3N absorption . These processes were approximated by the corresponding phase-space predictions and were generated by the Monte-Carlo method as described in Appendix B. 45 600 480 360 240 -1 20 -" i 1 1 1 r 100 200 300 400 500 N e u t r o n m o m e n t u m [ M e V / c ] Figure 26: Neutron momentum spectrum from 4 H e ( / T + , ppp) for run 33. IV.1.3 The neutron momentum distribution The most direct way of identifying the number of nucleons involved in the absorption process is to examine the momentum distribution of the undetected neutron. Experimentally, this quantity is readily calculated from the known energy of the pion beam and the measured energies and trajectories of the three protons. Unlike the proton momenta however, the neutron's is not limited directly by the detector thresholds and so the full range of momentum is present. The low momentum region is of particular interest because this allows a comparison to the neutron momentum within the 4He nucleus. Figure 26 shows the neutron momentum spectrum obtained for run 33. The measured distribution is dominated by a sharp peak around 110 MeV/c which tails off more slowly at higher momentum. Figure 27 shows the attempts made to fit this spectrum with the neutron momentum predictions obtained from the 46 Monte-Carlo simulations. In the Figure 27(upper) a linear combination of Q3N and the 4N phase space predictions has been fitted to the data. The coefficients of the sum were varied and the best fit obtained by the least squares method. This fitting reveals two facts: in the momentum region below 230 MeV/c the data is very well described by the Q3N phase space prediction; at higher momentum the data deviates from the phase space predictions particularly around 300 MeV/c. In an attempt to fit this latter region a second fit was made. This time a linear combination of the Q3N distribution and an arbitrary gaussian was fitted. The width and centroid of the gaussian were varied along with the coefficients of the sum. Figure 27(lower) shows the result of the fit. The full momentum range is well described by a combination of Q3N phase space and a gaussian enhancement around 300 MeV/c. An estimate of the number of events fitting the Quasi-3N prediction was made and a fraction <7Q3JV(« 90%) was calculated as the ratio of these events to all triple-proton events. IV.2 The cross-section estimation The first step in calculating cross-sections involved correcting the triple-proton yield for the inefficiencies of the apparatus. Events missed due to wire-chamber inefficiencies, computer dead-time and reaction losses in the Regina telescopes had to be accounted for. The corrected number of triple-proton events N3p was calculated from the measured yield using the following equation YIELD (llL,4)-v e. ( 5 ) Where elwc are the wire-chamber efficiencies as defined in section III.2. er is the Regina arm reaction loss efficiency and ec is the computer efficiency. The latter is simply the ratio of the number of events taped to the number of LAM's (beam-samples were excluded). Table V contains the evaluated efficiencies for 47 D 100 2 0 0 300 400 5 0 0 6 0 0 N e u t r o n momentum [ M e V / c ) 4 He(n + ,ppp) 0 100 2 0 0 3 0 0 400 5 0 0 6 0 0 N e u t r o n momentum 1 M e V / c l Figure 27: Neutron momentum spectrum from 4 H e ( < T + , p p p ) for r u n 33. The upper Figure shows the Q 3 N + 4 N phase space fit. The lower Figure shows the Q 3 N + G A U S S fit. G A U S S is an arbitrary gaussian. 48 run 33. Table V: Efficiencies for the R A - R B - T A coincidences of run 33 R A - W C Front 0.974 R A - W C Back 0.926 £wc R B - W C Front 0.869 £wc R B - W C Back 0.930 €wc T A - W C 0.943 £c 1.00 er 0.86 The six-fold differential cross-section in energies and solid angles is defined by the following expression; *° = N(AE) 1 1 f 1 6, dn1dSl2dSl3dE1dE2dE3 N^NTarget A J ^ A ^ A f k AE1AE2AE3 ' \ ' Here N(AE) is the corrected number of triple-proton events within energy intervals AE'(i = 1..3). Nrarget is the total number of nuclei per unit area of the target. This was obtained directly from the target thickness(76.2 mm) and density of liquid 4He(0.146 g/cm 3 [31]). To obtain an estimate of the three-fold differential cross-section the energy dependence was eliminated by summing1 over all events within the detected energy intervals and using the detector solid angles i.e, d3a _ ^ N(AE) 1 1 dn^dils ~ AEI,^,AE3 N«NTarget ' Aft 1 Aft 2 Aft 3 ' AE1AE2AE3 N3P 1 = — (17) N„NTarget AQ 1 Aft 2 Aft 3 V ; = 150 ± 13 fib/sr3 The differential cross-sections for the Quasi-3N absorption process was obtained by multiplying this figure by the percentage obtained in Section IV. 1.3. Thus 1 Formally the integration should cover the regions from the threshold to zero energy, although it is unclear if this is done in many publications. 49 d3aQ3N/dQ3 = 135 ± 14 fib/sr3. The contributions to the error are given at the end of this section in Table VII. To obtain the integrated cross-section for Q3N absorption the angular integration had to be performed. This was done by using the results from the Monte-Carlo simulation of the Quasi-3N process. The Q3N acceptance AQ3N, W A S calculated as the ratio of the number of events which fell within the detector solid angles to the total number of generated events. Table VI gives the results of the acceptance calculations for the geometry of run 33. This ratio was used to estimate the number of triple-proton events over the full 47r solid angle given the number of events detected by the apparatus. Including the previous corrections the integrated cross-section was given by d3a A f i i A f l 2 A f i 3 Q3N 9Q3N dCl^Q^dSlz «4Q3JV 1 (1S) Substituting the values for run 33 into this equation yielded <7Q3N = 4.4 ± 0.6mb. Table VI: Monte-Carlo acceptance value for run 33. Process Acceptance No. of Monte-Carlo trials Quasi-3N 1.62 x 1(T4 50 x 10+6 IV.3 Conclusions Triple-proton coincidences following pion absorption in 4 He have been observed at a pion energy of 165 MeV. Preliminary analysis of the data have been completed for the single detector geometry detailed in Table IV. In this configuration a dominating three nucleon absorption mode has been identified which accounts for approximately 90% of the triple-proton coincidences. The integrated cross-section 50 Table VII: Summary table of the non-negligible uncertainties that contribute to the cross-section error. Quantity Uncertainty SBEAM 1% 9Q3N 5% -A.Q3N 12% (AO) 3 7% er 5% Liquid 4 He density 1% Target thickness 2% for this process has been evaluated ((TQ3N = 4.4 ± 0.6mfe). The remaining 10% of the coincidences appear as an enhancement of the neutron momentum distribution around 300 M e V / c and are not described by either three or four body energy spaces. These results can be directly compared to the recent PSI results from a measurement [19] of the same reaction. In this experiment a pion energy of 120 MeV was used and the three detectors were placed at 55°, 120° and —70°. Both the three nucleon absorption and the enhancement in the neutron momentum spectrum were reported. The latter was attributed to four nucleon absorption coupled to a neutron-proton final state interaction channel. This feature is more prominent(see Figure 28) than at our geometry although it occurs in the same region of the neutron momentum distribution. This suggests two things: the enhancement observed in E328 is due to the same processes; the relative strengths of these processes with respect to the three nucleon absorption is far greater at the PSI geometry. The three nucleon cross-section measured in this experiment {<JQ3N — 2.1 ± 0.5 mb) is approximately 50% lower than obtained in E328. Given that the experiments were both performed at different energies and that these cross-sections are but a small fraction of the total pion absorption 51 cross-section [33] i n 4 H e , it is difficult to make quantitative comparisons. However it should be noted that the cross-section for the free three nucleon process 3 H e(7r + , p p ) p at a pion energy of 120 M e V is higher [17] (a3^ = 3.9 ± 0.5 mb) than the Quasi-free process measured at P S I . T h i s suggests that the three nucleon To conclude, it should be noted that the results presented here were obtained from a t iny fraction of the data set. The major i ty of the tapes have yet to be analysed. W h e n this is done we shall have a detailed picture of the 4 H e ( 7 r + , ppp) reaction over several different geometries. It is not unreasonable to suggest that these results w i l l be as interesting as those described w i t h i n . F igure 28: Neutron momentum pn, d is tr ibut ion f rom 4 He (7r + ,ppp) f rom PSI [19]. The dashed line is the Q 3 N simulation; the dash-dotted line is the 4 N simulation; dotted line is the coupled 4 N and neutron proton f inal state interaction simulation; the solid line is the fit obtained from Q 3 N plus the coupled channel. process is somehow suppressed i n He which is somewhat surprising. 20. 17.5 52 Bibliography [1] D. Ashery and J.P. Schiffer. Ann. Rev. Nucl. Part. Sci., 36:207, 1986. [2] H.Yukawa. Physico-Mathematical Society of Japan, 17:48, 1935. [3] C.M.G.Lattes, H.Muirhead, C.F.Powell, and G.P.Occhialini. Nature, 159:694, 1947. [4] E.D.Arthur, W.C.Lam, JAmato, D.Axen, R.L.Burman, P.Fessenden, R.Macek, J.Oostens, W.Shlaer, S.Sobottka, M.Salomon, and W.Swenson. Physical Review, Cll:332, 1975. [5] E.Bellotti, D.Cavalli, and C.Matteuzzi. Nuovo Cimento, 18A:75, 1973. [6] R.D.McKeown, S.J.Sanders, J.RSchiffer, H.E.Jackson, M.Paul, J.R.Specht, E.J.Stephenson, R.P.Redwine, and R.E.Segel. Physical Review Letters, 44:1033, 1980. [7] A.Altman, E.Piasetzky, J.Lichtenstadt, A.I.Yavin, D.Ashery, R.J.Powers, W.Bertl, L.Felawka, H.K.Walter, R.G.Winter, and J.v.d.Pluym. Physical Review Letters, 50:1187, 1983. [8] W.J.Burger, E.Beise, S.Giland, R.P.Redwine, P.G.Roos, N.S.Chant, H.Breuer, G.Cianguru, J.D.Silk, G.S.Blanpied, B.M.Preedom, B.G.Ritchie, M.Blecher, K.Gotow, and H.Ziock. Physical Review Letters, 57:58, 1986. [9] B.G.Ritchie, N.S.Chant, and P.G.Roos. Physical Review, C20:969, 1984. [10] G.Backenstoss, M.Izycki, P.Salvisberg, M.Steinacher, P.Weber, H.J.Weyer, S.Cierjacks, B.Rzehorz, H.Ullrich, M.Furic, T.Petkovic, and N.Simicevic. Physical Review Letters, 59:767, 1987. [11] H.Yokota, T.Mori, T.Katsumi, S.Igarashi, K.Hama R.Chiba, K.Nalai, J.Chiba, H.En'yo, S.Sasaki, T.Nagae, and M Sekimoto. Physical Review Letters, 56:191, 1987. [12] R.Tacik, E.T.Boschitz, W.Gyles, W.List, and C.R.Otterman. Physical Review, C32:1335, 1985. [13] R.Tacik, E.T.Boschitz, W.Gyles, W.List, C.R.Otterman, M.Wefiler, U Wiedner, and R.R.Johnson. (Submitted to Phys.Rev C). [14] E.Oset, Y.Futami, and H.Toki. Nuclear Physics, A448:597, 1986. 53 G.E.Brown, H.Toki, W.Weise, and A.Wirzba. Physics Letters, B118:39, 1982. D.Ashery. Physical Review, C36:460, 1987. G.Backenstoss, M.Izycki, P.Salvisberg, M.Steinacher, P.Weber, H.J.Weyer, S.Cierjacks, S.Ljungfelt, H.Ullrich, M.Furic, and T.Petkovic. Physical Review Letters, 55:2782, 1985. K.A. Aniol, A. Altman, R.R. Johnson, H.W. Roser, R. Tacik, U. Wienands, D. Ashery, J. Alster, M.A. Moinester, E. Piasetzky, D.R. Gill, and J. Vincent. Physical Review, C33:1714, 1986. G. Backenstoss, D.Brodbeck, M.Izycki, P.Salvisberg, M.Steinacher, P.Weber, H. J.Weyer, A.Hoffart, B.Rzehorz, H.Ullrich, D.Bosnar, M.Furic, and T.Petkovic. Physical Review Letters, 59:767, 1987. TRIUMF User's Handbook. Second edition, 1987. TRIUMF experiment E403, spokesperson G.J.Lolos. Z.Papandreou, G.J.Lolos, G.M.Huber, and X.Aslanoglou. Nuclear Instruments and Methods, A268:179, 1988. G.Smith. The STAR Online Data Acquisition System. Technical documentation, TRIUMF, 1987. G.R.Smith, D.R.Gill, D.Ottewell, P.Walden, R.R.Johnson, R.Olszewski, R.Rui, M.E.Sevior, R.P.Trelle, E.L.Mathie, V.Panlis, R.B.Schubank, N.R.Stevenson, A.Rinat, and Y.Alexander. Physical Review, C38:240, 1988. F.M.Rozon. Pion induced Pion production in Oxygen at 280 MeV. PhD thesis, University of British Columbia, 1988. C. P.Ponting. Pion induced verbosity at UBC. Master's thesis, University of British Columbia, 1988. P.Weber. Unpublished FORTRAN routine. D. F.Measday and C.Richard-Serre. Nuclear Instruments and Methods, 76:45, 1969. J.F.Janni. Atomic Data and Nuclear Data Tables, 27:150-529, 1982. Z.Papandreou, G.J.Lolos, G.M.Huber, J.C.Cormier, S.I.H.Naqvi, E.L.Mathie, D.F.Ottewell, P.L.Walden, G.Jones, R.P.Trelle, X.Aslanoglou, and S.Orfanakos. Submitted to Nuclear Instrumentation and Methods. [31] TRIUMF Kinematics Handbook. Second edition, 1987. 54 [32] S.Cierjacks, T.Petkovic, H.Ullrich, D.Gotta, S.Ljungfelt, N.Simicevic, M.Izycki, P.Wobbler, and H.J.Weyer. Nuclear Instruments and Methods, A238:354, 1985. [33] M.Baumgartner, H.P.Gubler, G.R.Plattner, W.D.Ramsay, H.W.Roser, I.Sick, P.Zupranski, J.P.Egger, and M.Thies. Nuclear Physics, A399:451, 1984. [34] P.Weber, private communication. [35] P.Bennett and C.Kost. OPDATA: A command driven program that Operates on Data. Technical documentation, TRIUMF, 1987. [36] F.James. Monte-Carlo Phase Space. Yellow Report 68-15, CERN, 1968. [37] J.F.J.van der Brand, H.P.Blok, R.Ent, G.J.Kramer, J.B.J.M.Lanen, L.Lapikas, E.N.Quint, G.van der Steenhoven, and P.K.A.de Witt Huberts. Physical Review Letters, 60:2006, 1988. 55 Appendix A Energy Calibration in the Regina arms and Energy Loss treatment A . l Energy Calibration in the Regina arms Nearly monoenergetic protons from the reactions n+d —> pp and n+p —> ir+p were used for the pulse-height calibration. The pulse-height or light £ produced by a proton stopping in the E scintillator blocks was fitted to the calculated energy deposited. The functional form of the fit is given by £' = ai • (F • C) + B • (1 - exp(a2 • (F • C)a3) (19) This function has been used in previous experiments in a slightly modified form [34] and for different plastics. The exponential term is an attempt to model the well documented non linearity of scintillator response at low pulse-heights [31]. Table VIII shows the values of the constants ai=i..3 and the fitted parameters F and B. Fitting was made using the TRIUMF programme OPDATA [35]. Each data point was weighted by 1/(A.E,)2 were AEi is the kinematical energy spread of the proton energy over the counter solid angle. Figure 29 shows a comparison of a linear fit to that of our function for the RA telescope. The fit for RB is shown in the main text. It should be noted that in our experiment the number of data points in the non linear region was minimal. Any future work should consider using different calibration energies to determine the low pulse-height characteristics of the BC400 plastic. Using low energy protons directly from the M i l channel could be tried. 56 Table VIII: Constants and parameters for the Regina energy calibration. Constant/Parameter Value ai 1.077 a2 -0.20 MeV" 1 a 3 0.62 FRA 9.883xl0"2 MeV BRA 21.179 MeV FRB 6.540 xlO" 2 MeV BRB 36.837 MeV A.2 Energy Loss Treatment To calculate the kinetic energy E of a proton at its production vertex in the liquid 4He target the ionization energy losses along its flight path had to be taken into account. The losses from the target centre to the detector arms were computed using a FORTRAN routine FLUG [27] which utilized the Bethe-Bloch equation. The energy deposited in the Regina E-blocks £' and the corrected time-of-flight T O F ' (see Section III.5.2 to the Tel-Aviv bars were tabulated over a range of E. Empirical functions 1Z(£') and T(TOF') were fitted to the data allowing E to be determined from a given £' or TOF' respectively. In the case of the Regina arms, the following arbitrary function was found to give the best fit for the fewest parameters E = %{£') = 6i + b2£' + b3exp(l + b4£' + bb£'2) (20) A power series was sufficient for the Tel-Aviv arms E = n(TOF') = ± ^ - 1 (21) Table IX shows the values of b; = 1...5 and c,=i...6 obtained from an OPDATA least squares fitting. 57 Table IX: Parameters for the energy loss functions Parameter Value from OPDATA b i 8.3562 MeV b 2 0.97717 b 3 9.8003 MeV" 1 b 4 -3.5019xl0"2 b 5 1.00585xlO"4MeV-1 C l 36.090 MeV c2 495.62 MeV-ns c3 -41735 MeV-ns2 c4 1.4679 xlO 6 MeV-ns3 c5 -1.43061 xlO 7 MeV-ns4 C6 6.1979 xlO 7 MeV-ns5 R A c a l i b r a t i o n c u r v e 0 450 900 1 350 1 800 T O T A L P U L S E H E I G H T Figure 29: Total Pulse Height to energy calibration curve for RA. A comparison of a linear fit to that of equation 19 in the low energy region. Error bars represent the spread of proton energies over the angle subtended by the counter 58 Appendix B The Monte-Carlo simulation 4N and Quasi-3N phase-spaces were simulated for E328 using Monte-Carlo [36] events from the CERN routine GENBOD. 4-momenta for three(indistinguishable) protons and one neutron were generated in their centre-of-mass system. Each event was given the appropriate phase-space weighting. The Quasi-3N phase-space was calculated by weighting the 4N phase space with the 4 He proton wavefunction1 gotten from 4He(e, e'p)3H studies [37]. The experimental environment was simulated by lorentz transforming the 4-momenta into the laboratory coordinate system. Geometrical and energy cuts were imposed on the proton 4-momenta to simulate the finite solid-angle and thresholds of the detectors. Events for which three protons fell within the detector geometries with energies above the thresholds were taken as representing good coincidences.The acceptances of the apparatus A, for the 4N and Quasi-3N phase-spaces were calculated as the ratio of weighted good coincidences to the total number of weighted events generated, i.e. ^ ^2 Weighted good coincidences £ 3 Weighted events 1 T h e neutron wavefunction was assumed to be identical. 59 


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