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A study of X and gamma rays following muon capture in 28Si Moftah, Belal Ali 1991

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A STUDY OF X AND G A M M A RAYS FOLLOWING M U O N C A P T U R E IN 2 8 Si By B E L A L ALI M O F T A H B.Sc, University of Winnipeg, 1988 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Physics We accept this thesis as conforming to the required standard T H E UNIVERSITY OF BRITISH COLUMBIA April 1991 © Belal Ali Moftah, 1991 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 ' pAj/S I C -C The University of Britisn Columbia Vancouver, Canada Date DE-6 (2/88) Abstract Negative muons produced via the backward decay of pions in the M9b beam channel at TRIUMF were stopped in a 2 8Si target. The energies of the muonic X-rays and nuclear 7-rays following the muon capture were measured in order to identify a Doppler broadened 7 ray line in 28A1 which is suitable for analysis in terms of a 7 — v angular correlation to determine a value for the induced-pseudoscalar coupling constant (gp )• The muon beam was also stopped in 6 other background targets ( polythene, Al, stainless steel, Cu, Pb and BGO ) and their X- and 7-ray energies have been studied so as to fully understand the backgrounds associated with such a transition. 11 Contents Abstract i i List of Tables v List of Figures v i Acknowledgements v i i i 1 Introduction 1 1.1 The Muon 1 1.2 Weak Interactions 2 1.2.1 The Weak-Interaction Hamiltonian 4 1.3 Free Muon Decay 7 1.4 Mesic Atoms 9 1.4.1 Formation of Muonic Atoms 11 1.4.2 Bound Muon Decay 12 1.5 Nuclear Muon Capture and the Induced Pseudoscalar Coupling . . . 16 1.5.1 The 7 — z/ Angular Correlation 20 2 Description of the Experiment 23 2.1 Channel Description 23 2.2 Experimental Arrangement 25 2.3 Detection System 28 2.4 Electronics and Data Acquisition 31 2.4.1 Telescope Logic 31 2.4.2 Germanium Logic 32 2.4.3 The BGO Logic 34 iii 2.4.4 Computer Logic 34 3 Data Analysis and Experimental Results 39 3.1 Introduction 39 3.2 Detection System Response 40 3.2.1 Line Shape 40 3.2.2 Resolution 41 3.2.3 Energy Calibration 41 3.2.4 Cuts 42 3.3 Analysis of Background Spectra 47 3.3.1 Room Background Run 47 3.3.2 Empty Target run 52 3.3.3 Polythene target 54 3.3.4 Al Target 56 3.3.5 Stainless Steel Target 61 3.3.6 Cu Target 65 3.3.7 Pb Target 68 3.3.8 BGO Target 72 3.4 Analysis of the Si Target Runs 74 3.4.1 Summation of Individual Data Runs 74 3.4.2 Beam Related Backgrounds 74 ( 3.4.3 Line Identification 75 3.4.4 Contribution to 1229 keV 87 4 Conclusion 92 Bibliography 93 iv List of Tables 1.1 Properties of the muon 2 1.2 Theoretical and experimental weak coupling constants 7 1.3 Summary of values of gp/gA a s determined from recent measurements of RMC 20 3.1 Peaks observed in the room background spectrum 52 3.2 Peaks observed in the empty-target spectrum 55 3.3 Peaks observed in the aluminum-target spectrum (a) 58 3.4 Peaks observed in the aluminum-target spectrum (b) 59 3.5 Peaks observed in the steel-target spectrum (a) 63 3.6 Peaks observed in the steel-target spectrum (b) 64 3.7 Peaks observed in the copper-target spectrum 67 3.8 Peaks observed in the lead-target spectrum 69 3.9 Peaks observed in the BGO-target spectrum 73 3.10 Peaks observed in the silicon-target spectrum (a) 84 3.11 Peaks observed in the silicon-target spectrum (b) 85 3.12 Peaks observed in the silicon-target spectrum (c) 86 v List of Figures 1.1 Decay energy spectrum of the free muon 9 1.2 Muonic cascades 13 1.3 Decay energy spectra of the bound muon 15 1.4 The single pion exchange diagram (the source of the weak pseu-doscalar coupling). . ., 18 1.5 Si kinematics 22 2.1 TRIUMF beamlines 24 2.2 M9 channel 26 2.3 Experimental setup 27 2.4 Schematic of Victoria BGO 30 2.5 Telescope logic 32 2.6 Germanium logic 33 2.7 BGO logic 35 2.8 Computer logic 36 2.9 Complete electronic logic 38 3.1 Calibration curve for Gel for a typical Si run 42 3.2 Timing spectrum typical for Si target 43 3.3 Suppressed and unsuppressed spectra typical for Si target 45 3.4 Data removed by the BGO suppressor 45 3.5 Suppressed 6 0Co spectrum 46 3.6 Room background spectra 49 3.7 Least-squares fit to the 840 keV-line 50 3.8 Room background spectra taken for the first and last 50 k events. . . 51 3.9 Empty-target spectrum 53 3.10 Polythene spectrum 56 3.11 Aluminum spectrum 57 vi 3.12 The aluminum prompt and delayed spectra 60 3.13 The stainless steel spectrum 62 3.14 The delayed stainless steel spectrum 62 3.15 The copper spectrum 65 3.16 The copper delayed and prompt spectra 66 3.17 Time curves for the Cu lines 1173 and 1514 keV 68 3.18 The lead spectrum 70 3.19 Prompt and delayed spectra for the lead lines 570 keV and 803 keV. 71 3.20 BGO-target spectrum 72 3.21 Silicon spectrum resulted after tuning for pions 75 3.22 Energy spectrum after u.+ stopping in 2 8Si 76 3.23 /x~Si summed spectra for Gel 77 3.24 /i~Si summed spectra for Ge2 78 3.25 Time spectrum for an (n,n') line in Ge 79 3.26 Nuclear levels diagram of 2 8 A l 81 3.27 Part of the Si spectrum showing the muonic X-ray lines 83 3.28 Time distribution for the three lines seen in Si spectra at 400.1, 1014.4 and 1293.4 keV 87 3.29 The 1229 keV energy spectra 89 3.30 The vicinity of 1229 keV in the steel spectrum 90 vn Acknowledgements I would like to extend my sincere gratitude and appreciation to my supervisor Professor David F. Measday for his guidance, advice and encouragement throughout this work. I am greatly indebted to Dr. David S. Armstrong who acted as the spokesman of the experiment as well as my unofficial second supervisor. His suggestions and discussions during the entire course of this work were well appreciated. I would like also to thank Drs. T.P. Gorringe, A.J. Noble, P. Weber and S. Stanislaus for their contribution to the progress of the experiment. I am grateful for the honour of the receipt of the Secretariat of Scientific Research (Libya) scholarship through the Canadian Bureau for International Edu-cation (C.B.I.E.). Finally, I would like to thank my family for their continuous help and encour-agement. viii Chapter 1 Introduction 1.1 The Muon Muons were first discovered in studies of cosmic rays with cloud-chambers and Geiger counters by Street and Stevenson (1937) [1] and Anderson and Nedder-meyer (1938) [2,3]. Two years earlier, particles of approximately the muon mass had been postulated by Yukawa [4] as quanta of the nuclear field. However, it turned out that the observed cosmic-ray particles were not the Yukawa ones; for, although they have about the right mass, they do not interact strongly with nu-clei [5]. Shortly thereafter, the pion was discovered [6] in photographic emulsions. Subsequent experiments demonstrated that it was the pion, not the muon which is the Yukawa particle. The muon, it turned out, was the decay product of this particle. The properties of the muon can be summarized by describing it as a "heavy electron", for the only fundamental attribute that distinguishes a muon from elec-tron is its mass ( about 207 times the electronic mass). The muons are point-like leptons, which experience the electromagnetic and the weak interactions but not the strong interaction. Table 1.1 gives some properties of the muon. The muon has been an important test particle not only in the various physics branches, but further in several other science fields, see the review article of Scheck [8] and references therein. 1 Table 1.1: Properties of the muon(after [7]). Mass m„ = 105.658387 ± 0.000034 MeV/c2 Charge Spin 1 2 Mean lifetime T = (2.19703 ± 0.00004) xl0~6 s Magnetic moment H = 1.001165923 ± 0.000000008 eh/2m^ Electric dipole moment d < l.OxlO"18 e-cm 1.2 Weak Interactions By now the distinction -at low energy- among the four known interactions is established by both the large differences in their relative strengths as well as by their distinct properties. Two of these interactions whose effects are evident in everyday life are the electromagnetic and the gravitational ones in contrast to the other two, namely the strong and the weak interactions. The interaction strengths are usually characterized by the so-called coupling constants. Roughly speaking, the weak interaction is 109 and 1012 times weaker than the electromagnetic and the strong interactions respectively (the fourth interaction, gravity, is negligible at the level of particle physics since it is some thirty orders of magnitude weaker than any other interaction). The apparent weakness of the weak interaction is ascribed to the very short range associated with its massive propagators. Although these (three) processes appear to be different, their mathematical formulation is very similar. They are all described by gauge theories; i.e. theories in which fermions interact by the exchange of spin 1 gauge bosons. In fact, advances toward the "ultimate" unification of these interactions are underway. 2 Unlike strong interactions, weak interactions involve both hadrons as well as leptons. Furthermore, the weak interaction operates at approximately the same strength among these particles; a phenomenological observation known as the uni-versality of the weak interaction [9,10]. In view of the above, it seem unreasonable to develop theories of the weak interaction neglecting the induced effects of the other two non-weak processes. Other properties that distinguish the weak interaction include its range and behaviour under symmetry principles. Within the Yukawa picture, the range of an interaction, R, is associated with the reciprocal of the mass of its propaga-tor. Thus R^eaA: ~ M\\) ~ 10~18m and R s t r 0 „ a ~ M~x ~ 1.4 x 10~15m while the range of the electromagnetic interaction, with M7=0, is infinite. In contrast to the electromagnetic and strong interactions, the weak interaction violates some of the symmetry principles and conservation rules such as the discrete operations P (par-ity), C (charge conjugation) and T (time reversal), as well as the hypercharge (Y) gauge transformation and I3 (isospin). For further discussions of these principles and their experimental status, see references [11] and [12]. The weak interactions were observed about a century ago through the discov-ery of radioactivity by Becquerel. However, the establishment of the weak interac-tion as a separate and independent process was rather gradual. In 1934 E. Fermi [13] formulated the first theory of the weak interaction based on a four-fermion point interaction to describe the beta decay of nuclei, n p + e~ + ue. It took about 14 years after the original formulation of Fermi on nuclear 8 decay before the "fj,-e uni-versality" sprang forth through the work of Pontecorvo [14] and Puppi [15] leading to the hypothesis of the Universal Fermi Interaction. During the following two decades, theoretical effort was directed toward find-ing out the structure of the weak interaction. Fermi's first theory was based on direct four-fermion coupling of vector type only. This interaction was later gener-3 alized (Gamow and Teller, 1936 [16]) to a linear combination of the five bilinear quantities: vector as well as scalar, pseudoscalar, axial vector and tensor. In con-trast to the original V form which allow transitions between nuclear states of equal angular momentum (Fermi transitions), this general interaction could couple nu-clear states differing by one unit of angular momentum (Gamow-Teller transitions). The turning point in the construction of the weak interaction came about with the questioning of parity conservation in the weak interaction by Lee and Yang [17] and later by its verification by Wu et al. [18]. Subsequent experiments established the so-called universal V-A (vector-axial vector) character of the weak interactions. In this framework, the odd and even parity amplitudes have roughly the same magnitudes and give what is called the principle of maximal parity violation. The V-A theory is not the whole truth, rather its success lies in explaining a large class of weak phenomena. It is now generally regarded as a particular case of the extremely successful Weinberg-Salam-Glashow electroweak theory [19,20,21] in the limit of low energy. The electroweak theory is a renormalizable gauge theory unifying weak and electromagnetic interactions in one mathematical framework. Its success was highlighted by the prediction of the neutral weak current discovered at CERN in 1973 [22], and by the prediction of the W and Z heavy gauge bosons discovered 10 years later, also at CERN [23]. 1.2.1 The Weak-Interaction Hamiltonian As noted above, weak processes, such as muon capture, at low momentum transfer q (q2 ~ m2 <C Myy), are adequately described by the V-A theory and hence will be used in this section. Within this picture, the weak interaction Hamiltonian, at a given space-time point(x), has the form 4 H(x) = -^{Jt(x),j\x)} (1.1) where G = 1.16637(2) x 10"5 GeV - 2 [24] is the universal Fermi coupling constant and J x is the weak four-current composed of hadronic and leptonic terms Jx{x) = J hx + J[. (1.2) Accordingly, weak processes are usually classified as • pure leptonic, where only leptons are involved, • semileptonic, where both leptons as well as hadrons are involved, • hadronic, in which only hadrons are involved. T h e leptonic current The leptonic current has the V-A structure J{= £ ^ 7 A ( 1 - 7 SM - (1-3) i=e,fi,T with 75 = «7o7i7273 a n d ipj and 7^  are the lepton fields and the Dirac 7-matrices respectively. The (1 — 75) in J[ automatically selects left-handed leptons consistent with the fact that weak interaction couples only to left-handed particles (and right-handed anti-particles). T h e hadronic current The details of the hadronic weak current, is not as clearly established as that of the leptonic one. This is due to the presence of the strong interaction which induces extra structure in the hadronic weak currents. In fact, it is for the 5 unravelment of this induced structure that most muon capture experiments are concerned with. In terms of the V-A structure and the Gell-Mann-Cabibbo universality hy-pothesis [25,26], the hadronic current for the semi-leptonic weak process of muon capture ( see / 1.5 ) can be written as j£ = cos6e(Vx-Ax) (1.4) with ^A = » ? „ Ax = -?p and aXu = \(jX7^ - 7*7A) where M and m are the nucleon and lepton masses respectively. The angle 8C is the Cabbibo angle, introduced to account for the different rates in the strangeness conserving and non-conserving weak decay processes. The ga are coupling "con-stants" which are functions of q2 (q\ = n\ — p\, where n\ and p\ are the neutron and the proton 4-momenta respectively). The terms gy and gA are the conven-tional vector and axial vector coupling constants. These two are the only ones that contribute in the q2=0 limit. The other four coupling constants gM-,9s,9P and gr are the induced ones. They measure the strength of the induced weak magnetic (^Ai/), the scalar, the pseudoscalar (75) and the tensor(crAj/75) currents respectively. The determination of these couplings are based upon several general theoretical constraints. These include T-invariance(TI), G-invariance(GI), conserved current hypothesis(CVC) and partially -conserved axial- vector current hypothesis(PCAC), see Mukhopadyay [9] and references therein. Table 1.2 below gives the calculated and measured weak coupling along with the theoretical constraints used. . 9M . .gs 9vl\ + 7TT7°~\vav + %—9\ 2M m (1.5) 19P 19T x 9 AWs + 7s?A + 7T77<7A1/^75) m AM 4>n (1.6) 6 Table 1.2: Theoretical and experimental weak coupling constants a . "We define <7y=l but gy = \Vud\ </> where \Vud\ is the up-down quark-mixing element of the Kobayashi-Maskawa matrix with value [27] |V^d|2=0.9507(8) and g^ is the muon coupling. Coupling Theoretical Hypothesis Experimental constant prediction used measurement 9v TI,CVC 1 [28] 9M TI,CVC 3.706 [28] 3.78 ± 0.22 [29] gs TI,CVC(GI) 0 0.0005 ± 0.0031 [30] 9A TI,PCAC 1.32 ± 0.02 [31] 1.262 ± 0.0010 [32,27] 9P TI,PCAC 8.56 ± 0.13 [33] 8.7 ± 1.9 [34] 9T TI,GI 0 0.06 ± 0.49 [30] As can be seen in this table, the coupling constants gvidA a n d 9M A R E W E U determined by experiment and in rather good agreement with the theory (< 5% discrepancies), while the pseudoscalar coupling gp is only measured to a 22% pre-cision. 1.3 Free Muon Decay Free muons normally decay into electrons and two neutrinos as follows H+ e+ + ve + 17^  (1.7) [i~ -> e~ + ve + (1.8) This three-particle decay scheme is consistent with the observational fact that the resulting electron spectrum is a continuum. Furthermore, the masses of the neutral particles, neutrinos, must be small (when compared to their charged coun-terparts) as a direct consequence of momentum-energy conservation. In the rest frame of the decaying muon, the maximum energy of the electron - when the two neutrinos escape in the same direction, opposite to that of the electron - is given 7 by E = ' v " ' ^ - = 52.83 MeV (1.9) 2m, v ' and hence is consistent with the previous sentence, i.e. mVe-\-mv ~ 0. Today, upper limits on these masses are m„e < 17 eV [7] and mVil < 0.27 MeV [35] as obtained from the tritium experiments and the ir —> p,v^ decay experiments respectively. The identification of the particles in equations 1.7 and 1.8 is further justified by other considerations such as the universality of weak interaction and the conservation of lepton number, (see reference [11] for further discussion). Muon decay is a pure leptonic decay and hence it constitutes a clean case for testing weak-interaction theory. The V-A Hamiltonian for muon decay, eq. 1.8, leads to the energy spectrum of the emitted electrons(positrons) N(x) = 4x 2 T 3(1 -x) + |p(4s - 3) (1.10) where x=E/E, r is the lifetime of the muon and N(x) is the number of e~'s emitted per second. The parameter p is predicted [36] to be | in the V-A interaction which leads to the energy spectrum of figure 1.1. Experimentally, p is measured to be 0.7518±0.0026 [37] in good agreement with the theoretical prediction and in favor of the V-A interaction. Other p, de-cay parameters of interest include the decay asymmetry (£) and energy dependent asymmetry(^ ) and again their experimental values are consistent with the V-A the-ory [38] of the weak interaction. Other fj, decay modes, including forbidden lepton family number violating modes are listed, along with their branching ratios [7], below H~ —* e~ + ue + + 7 0.014 ±0.004 (1.11) e~ + ve + v„ + e+ + e~ (3.4 ± 0.4) x IO - 5 (1.12) e- + ve + Vp <0.05 (1.13) x = E / E Figure 1.1: Decay energy spectrum of the free muon. e - + 7 < 4 . 9 x l 0 - 1 1 (1.14) e- + e+ + e- < 1.0 x IO - 1 2 (1.15) e"+27 <7 .2x lO _ n (1.16) 1.4 Mesic Atoms In a mesic -or more generally exotic- atom, a negatively charged particle replaces one of the orbital electrons of an ordinary electronic counterpart. Until now five such atoms have been successfully observed. These are pionic, kaonic, muonic, hyperonic and antiprotonic atoms. Mesic atoms have been known for more than four decades. The first experimental indication of such atoms could be traced beck to the work of Conversi et al. in 1947 [5] who measured the ratio of nuclear absorption of negative muons in light elements. At the same time, Wheeler [39] 9 and Fermi and Teller [40] theoretically argued that mesic atoms should exist since the atomic cascading time (~ 10_13s) is short compared with the lifetime of the involved particles. The first demonstration of the existence of mesic atoms was made by using muons in cosmic radiation [41]. Mesic atom physics has become an important tool for understanding nuclear properties. It can, in principle, provide information about the elementary parti-cles themselves and their interactions. Indeed the field of mesic atoms involves molecular, atomic and particle physics; See refs. [42,43,44] for.applications of mesic atoms. Two technological advances of recent years have activated the interest in this field. These are the establishment of high-flux meson factories (e.g. TRIUMF, LAMPF, SIN) and the development of high-resolution solid state detectors. The properties of the exotic atoms are not only similar to each other, but are rather closely related to those of the hydrogen atom. This is due to the dominant role of the electromagnetic interaction1. However, exotic atoms have two important characteristics considerably different from those of their electronic counterparts. These are consequences of the great difference in mass between the involved particles and the electron. For example, the lightest of these particles, the muon, is 207 times as heavy as an electron. These characteristics follow from the fact that -for the same quantum numbers- the energy levels(radii) of the orbits are (inversely) proportional to the mass of the orbital particles. For example, the diameter(energy) of muonic atom is l/207th (207times) that of the hydrogen atom. Therefore, these particles spend more time inside the nucleus and hence are much better suited for probing nuclear properties than the electrons. Although the discussion below is specific for muonic atoms -for which this 1This is true even for hadrons, since the strong field has a much shorter range than that of the electromagnetic field and hence there is a wide range in which the electromagnetic interaction dominates. 10 work is related-, most of the general processes - apart from strong interaction phenomena- are essentially the same for all exotic atoms. 1.4.1 Formation of Muonic Atoms The history of a negative fi undergoing atomic capture may be conveniently divided into three stages [45]. Initial slowing down: In this stage muons enter the target with energies of the order of tens of MeV (~70 MeV/c in our case), and possess velocities (vM) greater than those of the valence electrons (ve ~ ac, where a is the fine structure constant). They lose most of their energies in two phases. First, for the high velocity region (vM >^ve) the energy loss is determined by the normal Bethe formula [46] for charged particles(of charge z=l), cLE_ _ 4ne4NZ dx mev2 l n ( ^ - l n ( l - / ? 2 ) - / ? 2 (1.17) where v and E are the velocity and kinetic energy of the /x, N is the number density of the stopping medium with Z protons and I (~174.5 eV in Si [47]) is the adjusted ionization potential. The slowing-down time for the \i to low (a few keV) energy on the basis of equation 1.17 is ~ 10 - 9 to 10_10s in condensed matter. Once the n reaches the thermal e velocities, the Bethe formula begins to fail and nuclear stopping, elastic nuclear scattering and energy exchange processes become important. In the second phase, the energy loss increases roughly as y/E as compared to the 1/E dependence predicted by equation 1.17. In this phase, muons rapidly come to stop with stopping times of ~ 10~13s in metals and ~ 10"9s in gases. 11 Atomic capture: Once the /x comes to a stop, it will be captured by the host atom into high orbital angular momentum states, forming a muonic atom. Not much is known about the distribution of the initial states in this process. The atomic capture is roughly explained by the so-called "Z-law" [40] in which the capture rate is taken to be proportional to the nuclear charge, Z. Following its capture, the fi (within ~ 10_14s) will be inside the K-shell electron orbit at a principal quantum number, n given approximately by nM ~ (m^/m,,)1/2 ~ 14. Electromagnetic cascade: Since all of the low-lying "muonic" states are unoccupied, the /x cascades down (within ~ 10-13) from n~14 to the Is quantum state. In this cascade, the ft will interact with outer electrons and will lose energy through Auger processes. However, as the transition energy increases rapidly (~ 1/n3), this interaction is no longer important and radiative electric-dipole transitions (muonic x-rays) dominate, see figure 1.2 Most of the negative muons captured in the atomic orbits are expected to reach the Is orbit. This is consistent with the previously stated time-scales needed for the formation of muonic atoms. Once the n~ reaches the lowest Is state, it either decays (/4.2) or gets captured by the nucleus(/5). 1.4.2 Bound M u o n Decay Decay of muons bound in the Is orbitals has two fundamental differences from that of free muons (§3). The difference between the two decays has been realized, four decades ago, by Porter and Primakoff [48] who pointed out the first difference, the decay probability. The second fundamental difference is in the resulting electron 12 energy spectra. Both differences are caused by three effects which all depend on the Z value of the hosting nuclei, viz., 1. reduction in energy available in the decay due to the muon binding to the nucleus, 2. motion of the muon in the Is orbit, 3. nuclear Coulomb field. The first and second effects reduce the decay probability of bound muons through the resultant reduced phase space accessible to the decay products and the relativistic dilation of the muon's lifetime respectively. On the other hand, the third effect would increase the decay probability by increasing the overlap of the muon and the electron wavefunctions. As to the second difference the decay-electron energy spectrum is also changed by all the effects. The orbital motion of the fx produces a Doppler-shift which in turn stretches the high-energy side of the spectrum beyond the cut-off energy given in equation 1.9 but modified by the binding energy. In addition the nuclear Coulomb field shifts the peak of the spectrum to the lower energy side as the atomic number of the nucleus increases. Figure 1.3 demonstrates these changes to the electron spectrum as compared to the free decay. The total disappearance rate (A< = z~) of a bound muon is given by A t = A c + QAd (1.18) where Ad = and Q is the Huff factor to take into account the first effect discussed above, and A c is the total nuclear capture rate. The measurement of the total nuclear capture rate (Ac) amounts simply to the determination of the bound muon lifetime (Tm-) in the relevant material. This 14 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 A 1 . 0 1 . 2 1 . 4 1 . 6 x = E / E Figure 1.3: Decay energy spectra of the bound muon as compared to the free decay (after [49] and [50]). 15 had been demonstrated at TRIUMF by Suzuki et al. [51,52] who measured the lifetime of p.~ in 50 elements plus 8 isotopes and deduced the associated capture rates. For example, the mean lifetimes of C, Si and Pb are 2026.3, 756.0 and 72.3 ns respectively. 1.5 Nuclear Muon Capture and the Induced Pseudoscalar Coupling Besides decay, the basic process contributing to the disappearance of a negative muon in the Is orbit is nuclear capture, proceeding through the elementary reaction [i~+p-+n + Vp (1-19) which in the nuclear environment becomes p~ + (A, Z) —* (A, Z — 1)* + Vp (1.20) The daughter nucleus,(A,Z-l), is normally left in one of its excited states (usually a giant resonance state). A distinct feature of the rate of reaction 1.20 is its strong Z-dependence. This was observed by the Conversi et al. experiment [5] and its form was later unraveled by Wheeler [53]. Wheeler, in a simple model, assumed that all protons, Z, in the nucleus can interact independently with the /J, and that the interaction is proportional to the probability of finding the p in the nucleus |^V*/x(0)|2 .^ Now since the fi is observed from the Is state which has, for hydrogenic atom, the wave function [54] M*) = y/Z3/nalexp [-Zr/aJ (1.21) where aM is the first muonic Bohr radius, the capture rate is A c cx Ztf} (1.22) 16 where the effective charge was used to account for the finite nucleus size. Although this Z 4 law is a good approximation for the light nuclei, theoretical muon capture rates are usually obtained from the Primakoff formula [55] or its extension, the Goulard-Primakoff formula [56], viz., A „ A-2Z „ (A-Z A-2ZY MA,Z) = ztffXl [1 + G 4 - G 2 ^ - G 3 ( ^ + (1.23) 8AZ J} where X\ represents the muon capture rate in hydrogen, reduced by the neutrino phase space and G, take into account the (higher) order Pauli corrections for the nuclear environment. The study of muon capture has been established as a powerful tool to pro-vide valuable information on both the weak interaction and nuclear structure [9]. Most importantly is the sensitivity of some observables in muon capture to the ill-determined pseudoscalar coupling, gp . The sensitivity comes about due to the large characteristic momentum transfer, q, in muon capture as compared to, say, /3-decay or e-capture. This can clearly be seen in the axial vector matrix element, equation 1.6, where the whole pseudoscalar coupling is multiplied by q. Since fur-thermore the dominant contribution to the pseudoscalar coupling comes from the single pion exchange diagram2 (see fig. 1.4), gp is given (the Goldberger-Treiman relation [31]) as 2Mmii 9P= 2 ^ \ 9A = 8.6 ±0 .2 (1.24) where M is the nucleon mass, and hence gp is a strong function of q2. While several gp -sensitive observables exist [57], one is faced with two difficul-ties in measuring them. Firstly, the outgoing particles (n,i/) in the capture process are hard to detect. Secondly, these observables are, to some degree, dependent on the nuclear structure, i.e. the initial and final wavefunctions. The only observable avoiding the second difficulty -although adversely affected by the Z 4 law- is the 2The pion being the lightest available pseudoscalar particle. 17 Figure 1.4: The single pion exchange diagram (the source of the weak pseu-doscalar coupling). 18 rate of muon capture on hydrogen which has provided the average value of gp [34] flfP = 8.7±1.9 (1.25) in good agreement with the theoretical value of equation 1.24. In the context of muon capture (MC), the process 1.20 is referred to as the ordinary muon capture (OMC) as opposed to its much less probable version H~ + (A,Z)-+(a,Z -1)* + Vp + j (1.26) known as the radiative muon capture(RMC). Apart from its rarity (branching ratio ~ 10 - 4 for heavy nuclei), RMC has sev-eral advantages over OMC in determining gp . While the four-momentum transfer (q2) is fixed at q2 ~0.88 m2 in OMC, it could approach —m2 for RMC. This in turn enhances the pseudoscalar contribution in eq. 1.24 by up to a factor of 3.52 over that of OMC. One other advantage of RMC is the relatively straightforward -as compared to n and v— detection of the 7 ray involved. Due to the extremely low radiative capture rate (~ 6 x 10~8/x-1) in hydrogen 3 , efforts -both experimentally and theoretically- have concentrated on heaver nuclei. The experimental results to date on the value of gp (as gp/gA) in nuclei from RMC are summarized in table 1.3. Two conclusions are in order, one is that the values of gp are not consistent and do not agree with the Goldberger-Treiman expectation 4 . The other is the fact that the same experiment, when compared to different theoretical models, can produce different extracted values of gp . 3Despite this, E452 at TRIUMF has already started data-taking to measure RMC on hydro-gen [58] 4This might be interpreted in terms of a modification(renormalization) of gp inside nuclei, a topic that has continued to fuel interests in low-energy weak interaction fields in general and muon capture in particular. For further discussion see the review articles of Gmitro and Truol [66] and Mukhopadhyay [67] for different views on this subject. 19 Table 1.3: Summary of values of gp/gA a s determined from recent measurements of RMC, taken from Armstrong et al. [59] and Dobeli et al. [60]. Nucleus Theory 9P/9A 1 2 C 16Q V [61] [62] ' [63] 16.2 10;7 7.3 ±0.9 13.6 t\i 4 0 Ca [64] 5.7 ±0.8 [64] 4.6 ±0 .9 [63] 4.6 ± 1.8 natpe [65] 3.0 ± 1.3 1 6 5Ho [65] -0.5 ±1 .4 2 0 9 B i [65] 0.2 ± 1.1 1.5.1 The 7 — u Angular Correlation The last paragraph in the previous section outlined the demand for more reliable observables for the determination of the pseudoscalar coupling (gp ), i.e. observables which offer both sensitivity to gp and a lesser dependence upon nuclear structure uncertainties. One such observable is the angular correlation between the v and a nuclear de-excitation gamma-ray in the reaction H~+(A,Z)-* (A, Z - 1)* + i/M *-*(A,Z-iy + 7 - (1-27) Unlike most OMC and RMC observables, v — 7 correlation has the advantage of being an exclusive process. The muon capture sequence (eq. 1.27) has been studied extensively by Popov et al. [68] and Parathasarathy and Sridhar [69,70] with the motivation of deter-mining gp . Their theoretical analysis showed that the correlation coefficient can, in certain cases, be sensitive to gp and largely independent of nuclear structure uncertainties. This is the case for the muon capture sequence ^-+ 2 8 Si(0 + )^ 28A/(l+,2.2MeV)* + i/M (1.28) 20 -+28 A1(0+, l.OMeV)** + 7 (1.29) for which the correlation function can be written as [70] I{B1U) = 1(0) [1 + aP 2(cos0 7„) + A(£ • 7)(7 • *>)P2(cos07„) + 32(fi • • v)]. (1.30) where /i,7, v and 07„ are defined in figure 1.5. The correlation coefficients a,3i and 82 involve nuclear matrix-elements and weak coupling constants. In fact, within the Fujii-Primakoff approximation (i.e. neglecting relativistic terms and higher partial wave neutrinos), these coefficients are given by [69,70] n ZgpQA - 92P N „ N a — 7T^ o 7. (1-^ 1) 3<7A + 92P- 29P9A V ' 3^  - a2 + g2P - 2gPgA Zg2A-g2p 3g2A + g2p + 2gPgA' which involve only the coupling constants. Furthermore, these coefficients are found to be connected through A+/?2 = 1 + « . (1-34) An experimental method to measure such u — j correlation has been suggested by Grenacs et al. [71]. They pointed out that this correlation is equivalent -within a factor of 7r- to the angular correlation between the nuclear recoil and the 7 ray. Now since the observed energy of the emitted 7 ray is related to the energy E 0 in the emitting nucleus by the Doppler equation 5 E = E0(l — Vcos0) (1.35) where V is the velocity of the recoiling nucleus, (fig. 1.5), the correlation function, eq. 1.30, can be written as an energy distribution of the emitted 7 rays. Conse-5This is valid provided there is no appreciable slowing-down effects, which is the case for eq. 1.29 where the lifetime of the (l +,2.2MeV) line is 65 fs. 21 Figure 1.5: Kinematics of reaction 1.29 quently, the measurement of this distribution constitutes a measurement of the j — u angular correlation. The only experiment to our knowledge of this kind was performed by the William and Mary group [72,73,74] at SREL in the late 1960's. Unfortunately, the extracted results were primarily limited by statistics and the signal/noise ratio, as well as by the energy resolution of the detectors. Several authors [9,70] pointed out the need for more precise measurement of the 7 — v correlation in 2 8Si. One such improved experiment with which this work is associated is underway at TRIUMF [75]. It is not the aim of this work to extract such correlation, but rather to try to understand the contribution from backgrounds to the specific transition as such understanding is essential for a precise measurement of this nature. 22 Chapter 2 Description of the Experiment The experimental setup was primarily designed for the first phase of experiment 570 at TRIUMF whose aim is to measure the Doppler broadening of a de-excitation gamma ray in 2 8 Al following muon capture on 2 8Si [75]. A precise measurement of this nature requires complete understanding of the background and any peaks underlying the gamma ray of interest. 2.1 Channel Description The experiment was performed during the course of a 2-week cyclotron run on December, 1989 at the TRIUMF meson facility in Vancouver, Canada. The TRIUMF accelerator is a sector-focusing cyclotron with a special feature being the acceleration of negative H~ ions which, in turn, permits a convenient extraction of the beam. This is done by passing the beam through a thin carbon foil to strip the two electrons and hence the resulting beam of positive ions curves in the opposite direction in the magnetic field and exits the cyclotron. As shown in Figure 2.1, two stripping foils, located 180° apart, are used to feed the two main beam lines BL4(P) and BL1(P) with proton beams of current up to 140 u.A and energy range of 183 to 520 MeV. The first beam line is dedicated to proton-induced reactions while the other is used for pi meson production. The secondary \i beam used in this experiment was produced when the primary proton beam in the meson beamline impinges on the meson production 1AT2 target, typi-cally a water cooled strip of beryllium 10 cm thick in the beam direction and 5 mm 23 to **3 t—» • cm c to pa I—I cr* CD & 3 r—» S3 (B C O PROTON HALL EXTENSION (p,n)(n,p) • FACILITY BL4B (PL | MRS / T O P - — \ . SPECTROMETER SASP 1 t SERVICE ANNEX \ SERVICE EXTENSION ION SOURCE 3&4 42M.V ISOTOPE PRODUCTION CYCLOTRON BATHO BIOMEDICAL LABORATORY THERMAL NEUTRON FACILITY MESON HALL SERVICE ANNEX x 15 mm in cross sectional area. The primary proton beam is normally delivered in 3 nsec pulses every 43 nsec and with a 99% duty factor. See TRIUMF users handbook [76] for more information on the TRIUMF cyclotron and other primary and secondary beamlines. The muon beam used was obtained from the new M9B channel which incor-porates a superconducting solenoid which collects low-momentum polarized muons from the decay of pions. About 2 x 105fi~/sec at medium momentum (~ 70 MeV/c) were required to stop in our targets. Figure 2.2 shows the layout of M9 channel, with its two legs M9A and M9B. 2.2 Experimental Arrangement The experimental setup is shown in Figure 2.3. Si, S2 and S3 are plastic scintillators with active regions of 25 cm x 25 cm x 0.32 cm, 15.2 cm x 15.2 cm x 0.32 cm, and 50 cm x 50 cm X 0.64 cm respectively. SI and S2 with S3 in anti-coincidence defined a muon stop in the target. A lead collimator 7.5 cm in both length and diameter was used to collimate the beam spot and lead and borated concrete shields were placed upstream of the germanium detectors to absorb low-energy X-rays and as a shield from neutrons and background radiations. In fact, the shielding was different for different targets. A variety of targets were used (C, Al, Co, Fe, Cu, Pb and BGO) to study backgrounds. They were set at 45° to the beam and to the detectors axis so that more gammas escape the target towards the detectors. This orientation also reduces the bremsstrahlung from muon-decay electrons. The two detectors were at 90° with respect to the muon direction 1The reason for this specific angle was to drop out the terms involving (ft • y) in eq. 1.30 and so that the 7 — v correlation would essentially be characterized only by one coefficient, a. 25 26 Figure 2.3: Experimental setup. 27 2.3 Detection System The 7—ray detectors used were two high purity germanium crystals (HPGe). Gel was the smaller one with 21% efficiency and a system resolution of 2.5 keV full width at half maximum (FWHM) for 1 MeV 7 rays under experimental conditions. The other detector, Ge2, was a better one with 33% efficiency and a resolution of 2.2 keV. In order for a detector to serve as a good gamma-ray spectrometer, it must carry out two distinct functions. First, it must act as a conversion medium in which incident gamma rays have a reasonable probability of interacting to yield one electron via the photoelectric effect or two electrons via pair production; second, it must function as a conventional detector for these secondary electrons. Thus, the detector should possesses several characteristics. For semi-conductor detectors like Ge, the number of charge carriers (electron-hole pairs) should be linearly proportional to the energy of the photoelectron or pair of electrons and be as large as possible for a given incident radiation to minimize the statistical contribution to the energy resolution. In addition, they should be highly mobile with a low probability of trapping or recombination, so that, a large fraction (preferably 100% ) of all the charge carriers created by the passage of the incident radiation should be collected. This condition will hold provided the collection time for the carriers is short compared with their mean lifetime. In order to meet this condition, a large electric field ( 105 V/m) must be applied to impart velocity to the charge carriers, and thus to minimize the collection time and the detrimental effects due to recombination and trapping. Gamma rays interact in a detector through three processes: 1. photoelectric absorption, which predominates for low-energy gamma rays, 2. pair production predominating for high energy gamma rays, and 28 3. Compton scattering being the dominant process over the range of energies between the first two processes. One other related premium on choosing detectors for gamma-ray spectroscopy is their atomic number. Since the cross section for the preferred mode of interac-tion, the photoelectric absorption, varies approximately as Z 4 , 5 , the trend is to incorporate elements with high atomic numbers. The best material which satisfies the above requirements is the semiconductor germanium. Due to their excellent energy resolution, virtually all gamma-ray spec-troscopy that involves complex energy spectra is now carried out with germanium detectors. The Ge detectors must be operated at liquid nitrogen temperatures so as to reduce the rise in noise level and hence to reduce thermally generated leakage current (due to thermal excitation of electron-hole pairs over the 0.74 eV forbidden energy gap). Each of the 7-ray detectors was surrounded by a Compton suppression device. These suppressors are made up of bismuth germanate (Bi4Ge30i2) crystals, com-monly abbreviated as BGO, arranged in segmented configurations and constructed for use in experiments with intense beam environments. The basic aim of the BGO suppressors is to detect the gamma rays that are Compton scattered out of the surrounded detector -before depositing all their energies- and reject the related events by operating the BGO and the detector in anticoincidence mode. The choice of BGO over Nal as a Compton suppressor is due both to its higher density and atomic number which allow a more compact configuration and much lower (n,n') cross section. BGOl was developed at TRIUMF by the University of Victoria group [77]. It is constructed out of sixteen 5.5 x 5.5 x 8.0 cm3 BGO crystals viewing 10 phototubes (see Figure 2.4). 29 INCIDENT PHOTONS RM.T.'S Ge DETECTOR ENTRANCE BGO CRYSTALS Figure 2.4: Schematic of Victoria BGO. 30 BG02 was borrowed from the University of Kentucky. It has six BGO crystals arranged in coaxial geometry around the detector entrance hole. Each crystal is optically separate and viewed by a phototube. 2.4 Electronics and Data Acquisition The DAQ system can be divided into 4 distinct parts. These are : the telescope logic, the germanium logic, the BGO logic and the computer logic. For both detection systems, the germanium energy and time and the BGO time follow-ing a muon stop were processed in CAMAC (Computer Automated Measurement and Control) logic units which were read by the computer program MULTI on a PDP11/34 computer. In addition to reading the CAMAC crate for each event, MULTI logged all the read-data onto magnetic tape, updated various histograms of the raw data for on-line analysis and also performed several basic monitoring and control processes. Each time the trigger logic received an event detected in either germanium detectors, the corresponding BGO suppressor and the scintillation telescope were examined. If the event was not vetoed by the BGO and it satisfied the stop definition, a valid trigger was generated by which relevant information from the detection system was digitized and recorded on magnetic tape and part of the data was analyzed immediately for on-line monitoring of the experiment. 2.4.1 Telescope Logic A schematic of the telescope logic is shown in Figure 2.5. In this diagram the triangles represent logical fan-in/fan-out units, which are essentially OR gates with many outputs. Signals from scintillators 1, 2 and 3, used for stop definition, were taken from the M9B experimental area to the counting room through 50 ohm cables. These linear signals were input to quad discriminators (LRS 821) which 31 S1 D S2 S3 D D i n h i b i t — 5 C 1.2 r C - ^ • t o Route r input PU (2M=) - > t o TRIG, - > t o TRIG, - > t o TDC Figure 2.5: Telescope logic. in turn produced an output logic pulse for every input signal that crossed a fixed threshold level. Incident particles were determined by a (1.2) coincidence while stopped muons in the target were defined by a (1.2.3 = "//")coincidence, where 3 means an anticoincidence of counter 3. Provided an event was not already in progress, a signal from the "//" coinci-dence unit was used to initiate a 2 //sec gate for the two main coincidence units, TRIG1 and TRIG1. Another "//" signal was used to define stop signals for the Time-to-Digital Converters (TDCs). 2.4.2 Germanium Logic The signals from the two germanium detectors were sent to charge sen-sitive preamplifiers in order to maximize their signal-to-noise ratios and match impedances. The preamplifiers provided 2 output signals: energy and time sig-nals. The energy signals were shaped and amplified in linear amplifiers and fed into high-speed, high-resolution CAMAC Analog-to-Digital Converters (LeCroy model 32 to TDC Ge, BGO. CFD to ADC D PU inhibit -PU fl -to TDC - a - to STROBE Ge, CFD PU J BGO, to ADC to TDC inhibit SCA fl — -ss - t o TDC to STROBE C,=Ge,.BGO, C2=Ge2.BGOj Figure 2.6: Germanium logic. 3512 buffered ADC) where their energy dependent amplitudes were digitized and recorded. The timing signals, obtained from the other two preamplifiers outputs, were fed to timing filter amplifiers (ORTEC model 474 TFA) where they were shaped and amplified before being applied to constant fraction discriminators (TENNELEC TC455 CFD) for fast-time pickoff. CFDs are used to produce fast signals with a baseline crossover independent of the input signal amplitude. One CFD output signal amplitude was checked for pileup and then passed to the corresponding main 33 coincidence unit (TRIG1 or TRIG2). For Gel, it was found desirable to include pulse height rejection. This was employed by passing the TFA signal into a high threshold discriminator and then into a pileup gate (PU) of which the busy com-plementary logical signal is used to veto the TRIG1 trigger for overload rejection. The other two CFD output signals were sent to coincidence units Gel • BG01 and Ge2 • BG02 The germanium signals were also sent to TDCs to measure their rise times in order to correct for charge collection time variations known as ballistic deficit. 2.4.3 The BGO Logic For each of the 10 phototubes of BGO 1, two output signals, corresponding to the anode and dynode amplifiers, were fed into discriminators and then formed a coincidence defining a valid event in a particular crystal. For each of the six segments of BG02, the analog output was fed through photomultiplier amplifiers (LeCroy NIM model 612M) before being fed into a LeCroy 623BLZ discriminator to define a valid event in the crystal. The BGO signals are then fanned-in through OR gates and then used as TDC stops and event vetos. 2.4.4 Computer Logic The two trigger signals, TRIGl and TRIG2, were input into a quad logic fan-in/fan-out unit (LaCroy 429). Several strobe outputs were used from this unit. One output was used as a C212 strobe. Two outputs were stretched to 16 //sec by a dual gate generator(LRS 222) and used to gate two ADCs starting the digital conversion of the slow Ge signal. Other outputs were used to start two TDCs. A least-delayed strobe output was sent to a fan-in unit known as the "INHIBIT" unit; where a computer busy signal was also fed to form system-busy inhibits. Since it took a few 34 to C to TDC CM CD c c o CD co — D D — — Figure 2.7: BGO logic. D=Discr iminator F=Fan —In C=Coinc idence to a to TDC hundred nanoseconds for the data acquisition system to produce the busy signal, a 330 ns protection gate was created at the end of the strobe gate to account for the in-between events. The inhibit signal was fanned-out to TRIG1, TRIG2, and 1.2 coincidence units in order to have deadtime-corrected scaler values. Once the crate was read by the computer, the NIM drivers released the inhibit and opened the electronics for the next event. Another strobe output was sent to a LeCroy 222 Dual Gate Generator from which a 2 fxsec NIM output and a delayed signal were respectively used as muon gate and reset signal into UBC Router box [78] where the input was provided by the muon stop coincidence This router, also called pulse separator, accepts a train of up to 4 logic pulses within a time window, splits them and routes the individual pulses into 4 separate outputs: Al , A2, A3 and A4. Hence it, along with a TDC permits recording of multiple time spectra; so that it will give times of up 35 to C212 to A D C , s t a r t to A D C 2 s t a r t to T D C s s t a r t s Figure 2.8: Computer logic. 36 to 4 muons within the 2 /Ltsec gate, ie: if there is only 1 muon in the 2 fisec gate, its time relative to the TDC start, 7, will be in channel A=l, if there are 2 muons, their times will be in A=l and A=2 etc. For each strobe event, the following information were digitized and written to tape: • C212 : event bit patterns for Si, S2, S3, Gel, Ge2, BGOl and BG02, • EGE1 and EGE2 : Gel and Ge2 energies respectively, • TS3 : S3 time relative to strobe, • TBGOl and TBG02 : BGOl and BG02 times relative to strobe, • TGE1 and TGE2 : Gel and Ge2 risetimes, • R1,R2,R3 and R4 : time of strobe relative to the 4 preceding muons, • PU1 and PU2 : time of pile-up events. In addition to the above information, 7 CAMAC scaler values were kept at the end of each run. These were: 1.2, 1.2.3, BGOl, BG02, TRIG1, TRIG2, and STROBE. A complete electronic diagram is shown in Figure 2.9. 37 to C212 V.S. Ge, SCA to TDC I— TF»^> D P U • V.S. C.S. E C , o TDC S 1 -S2H D S3-H 0 Ge, -to ADC -to TDC ' CFD -m E -— A D — Busy siqnol G.G NIM-OUT "INHIBITS •to 1.2 G.G (16/xs)| _to TDCs starts G.G UBC! R 0 U T E R A=1 r-t-A=2 o A=3 TDi <. J A=4 to C2!2 Tl V.S. C.S. -to TDC V.S. C.S. Figure 2.9: Complete electronic logic. 38 Chapter 3 Data Analysis and Experimental Results 3.1 Introduction The measurement was first performed in May 1989, then repeated in December 1989. The May data were not analysed due to poor detector resolutions (~6 keV FWHM at 1.17 MeV). As noted before, the primary aim of the data taken was to measure the Doppler broadening of a de-excitation gamma ray in 2 8 A l following muon capture on 2 8Si [75]. A precise measurement of this nature requires complete understanding of the background and any peaks underlying the gamma ray of inter-est (see § 3.4.4). Hence, the principle goal of the data analysis in this work was the identification of X- and 7-ray lines seen in background targets ( /3.3) and in the Si target (/3.4). This identification is often needed in other experiments that run in the same area as well. The general characteristics of the detection system response including different conditions imposed on the data to select events are discussed in section § 3.2. The off-line analysis of the data was carried out using the TRIUMF Data Analysis Centre VAX cluster of computers (two VAX 8650's and a VAX 780). Var-ious computer programs were used for different aspects of the data analysis. In the first step in the data analysis, the TRIUMF software package MOLLI [79] with user written subroutines reads the data written on magnetic tapes and sets up various histograms and scatterplots. These histograms and scatterplots were further exam-ined and analysed using the program REPLAY. Besides REPLAY, several TRIUMF general-purpose routines such as PLOTDATA, OPDATA and EDGR were very use-39 ful for manipulation, fitting and plotting of data. 3.2 Detection System Response 3.2.1 Line Shape The response function of a germanium detector is nearly Gaussian, reflecting the statistical character of the ionization processes produced by the electron-hole pair multiplication in the crystal. The statistical fluctuation of the ionization process is due to the random energy loss division between this process and competing energy losses. A small additive component to the Gaussian shape caused by incomplete charge collection, due to trapping impurities or defects in the crystal lattice, within the detector is characterized in the output signal by an excess of pulses in the spectrum on the low energy side of the peak, referred to as the low energy tail. Since the primary interest of this analysis is the centroid of the 7-ray peaks, the complicating effect of these tails is not significant. For this reason, the spectral lines were analysed by a least squares fitting procedure incorporating a simple Gaussian function plus a constant to represent the background : Y(X) = a exp 1 -xx - x0y + b (3.1) 2a2 where a, XQ and a are the amplitude, the position and the width of the Gaus-sian respectively. A modification to the fitting procedure was introduced to test the effect of a linear background. The effect proved to be negligible in the line positions even though a considerable reduction in \ 2 P e r degree of freedom and a decrease in the line widths were noticed for some peaks. The fitting program is run from an input file that contains all the information on the initial values of position and amplitude of the peaks, the detector resolution and the background level. These parameters can either be fixed or allowed to float to minimize the least-squares 40 residual between the Gaussian function and the data points. The fitting procedure yielded an amplitude, centre, width and background level for each peak together with their associated errors, and a normalized \ 2 representing the goodness of fit. 3.2.2 Resolution From the properties of the Gaussian curve, the full width at half maximum can be calculated from: FWHM = 2\/21n2 a = 2.355cr. The energy resolution of the detectors can be determined by fitting the FWHM of as many clean (resolved) peaks as possible to the expression (FWHM(keV))2 = a + b * E(keV) [ note: FWHM = yJ(FWHM)2noise + (2.35)2FeE , F is the Fano factor, e is the energy necessary to create one electron-hole pair], where a and b are respectively the peak widths that would be observed due only to effects of charge carrier collection and electronic noise and of carrier statistics. It is clear that the in-beam resolution is usually worse than that obtained out-of-beam, as would be expected due to high-rate beam environments. The energy resolution of Ge2 was considerably better than that of Gel. Although histograms were stored on tape every 1-3 hours, broadening of the lines by electronic and temperature drifts of the detection system were unavoidable. Typical resolutions for the Si target runs varied from 2.5 to 3.0 and from 2.2 to 2.8 keV FWHM for Gel and Ge2 respectively. 3.2.3 Energy Calibration In order to compute their energies, the channel numbers corresponding to the X- and 7-ray peak centroids were converted into energies. This was done by fitting the peak positions of well-determined X- and 7-rays from the stopping target to a linear function using a least-squares fit. A quadratic function was used to check for possible non-linearities of the detecting systems; however, the quadratic term always turned out to be small ( of the order of 10-8) and hence the linear function 41 1800- • i • • I ' I I I 1 I I I I 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1600- ->1400->_ 1200 -^ 1000-Ld 800-600-400- — i 1 — r ^ T — 1 1 — i — i — i 1 1 — i — i — i — ] — i 1—i 1 — | — i — i — i — i 1—i—i—i 1 — | 1 — i 1 — i — 1000 2000 3000 4000 5000 6000 7000 8000 CHANNEL NUMBER Figure 3.1: Calibration curve for Gel for a typical Si run. was adopted. A calibration curve for a typical Si run ( run # 64) is shown in figure 3.1. 3.2.4 Cuts This section outlines the different conditions imposed on the data to select events. Timing Cut Signals from the Ge detectors can be divided into one of three categories de-pending upon their time relative to muons stopping in the targets, the (1.2.3) signal. The first of these contains the Ge signals which are in prompt coincidence with a stopped muon and constitute essentially only X-rays from the muonic cascade. The corresponding energy spectra are called the "prompt" spectra. "Delayed" spectra, recorded within the muon lifetime in the relevant target and preferentially contain delayed 7 events, resulting from nuclear muon capture in the target. The third 42 10 6 H 00 o o _ l I I I I I I l _ _ l I I 1_ I I I _ l I I l _ - I I I L . — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — r 0 100 200 3 0 0 4 0 0 500 CHANNEL NUMBER ~ \ — i — i — r I — r — i — r 600 700 8 0 0 Figure 3.2: Timing spectrum typical for Si target. The dispersion is 2.67 ns/ch (time goes in the "backwards" direction). category constitutes the "background" spectra. It contains the Ge signals which are not related in time to a muon stop. A typical plot of MUSTOP timing distribution is shown in figure 3.2. It is characterized by the above three categories: a large spike due to prompt muonic X rays, a long decaying exponential tail with a slope characteristic of the muon disappearance lifetime in the relevant target ( in this case Si ) and a flat random background. By choosing different time windows on the MUSTOP spectrum, energy spectra were reconstructed offline to reduce background and increase the signal to noise ratio. 43 Energy Cut In addition to being used as energy fitting windows in the least squares fitting for energy calibration, energy cuts were most useful in the identification of unknown lines. Looking at the time structure of a peak with a preselected energy window reveals good hints on the origin of the peak. B G O Cut The data recorded on the tape during this experiment included the time information for each event detected in the two BGO suppressors. In order to see the effect of this cut, the BGO vetos were not hardwired for some runs. Instead, all the data were written to tape and then different BGO cuts could be established offline to reject the Compton scattered events. The suppression factor of BGO is usually defined as the ratio of unsuppressed to suppressed data. The average factor obtained was about 5. Figure 3.3 shows a part of a Si spectrum with/without BGO cut. One notes that the BGO cut preferentially rejects events that only add to the continuum, without affecting the full-energy events except for accidental coincidences. This is demonstrated in figure 3.4, which shows the data that was actually removed from the unsuppressed spectrum of figure 3.3 by the BGO suppressor. Note however that the 511 keV peak due to 8+ annihilation is prominent because it comes in pairs. Another remark here is the relative broadening of Compton edges in the suppressed spectra, see figure 3.5. This is most likely due to 7's scattered back out of the Ge entrance holes in the suppressors, and hence not detected in the respective BGO ( Compton edge events correspond to incident 7 rays being backscattered toward their direction of origin, i.e. head-on Compton scattering with 8 = n ). 44 600 900 1200 1500 1800 ENERGY (keV) Figure 3.3: Suppressed and unsuppressed spectra typical for Si target. 300 600 900 1200 1500 1800 ENERGY (keV) Figure 3.4: Data removed from figure 3.3 by the BGO suppressor. 45 oo 10 o o 10% 10% I ' I I I I I I I I I I I I I I I I I I I I I I I I I I • 0 I 1 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 200 4 0 0 600 800 1000 1200 1400 ENERGY (keV) Figure 3.5: Suppressed Co spectrum, note the compton edges. Michel Veto One major background in this type of experiment is the flat background underneath the photopeaks. This is either due to the Compton continuum from higher energy transitions or from bremsstrahlung of electrons from muon decay. The former is greatly reduced by the BGO cut as demonstrated in the previous section. The second is more serious. In 2 8Si only 65.7 % of muons that stop in the target will undergo nuclear capture; the remainder will decay, with a Michel spectrum of up to 53 MeV in energy. The fraction of these decay electrons converted into bremsstrahlung with the emission of low-energy gammas can be quite large. To reduce this background, decay electrons were detected in the plastic scintillators and 7-rays in coincidence with these electrons were rejected. 46 3.3 Analysis of Background Spectra This section is concerned with the identification of lines seen in the background target runs. These lines, especially the prominent ones, might show up in the Si target spectra and hence comparisons between these spectra and the Si ones would unravel their identities in the Si spectra. The measured energy spectra start from about 200 keV and extend up to about 2000 keV. Identification of lines observed was generally based on the available information on energy levels of relevant nuclei. Agreement with known associated cascades and consistency of branching ratios were considered. 3.3.1 Room Background R u n Although this run was underestimated ( lasted for less than 100 min ), it proved to be very essential. Some persisting unknown lines in Si spectra sprang forth to be room background ones. Several comments applying to all runs should be made about the two detectors' spectra. The first one is the use of different amplifier gains and thresholds for the two detectors, and hence slightly different energy windows. Another one is that Ge2 spectra contain more than twice the total counts of Gel. This is due mainly to the relatively larger size of Ge2 ( active volume 133 cm3 ). Moreover, the energy resolution for Ge2 is considerably better than that of Gel. Lastly, Ge2 proved to be much more stable against gain and temperature drifts than Gel. Least-squares fitting to 4 well-known peaks in the two spectra: 511.00 keV annihilation line x , 1173.238 keV and 1332.502 keV 60Co lines and 1460.830 keV 1This line was used as to cover the whole energy range even though it might be shifted by several eV's, see [80,81] for more discussions. 47 'K line provided the energy calibration functions for the two detectors. These are: where (E\,C\) and (E^C^) are the energy and channel number of Gel and Ge2 respectively. The resultant (calibrated) spectra are shown in figures 3.6a and 3.6b. Some of the background lines in these spectra were induced or at least en-hanced by inelastic neutron scattering and possibly Coulomb excitation of low-lying excited states in both detectors and nearby materials. Of these, iron and aluminum represent the greatest bulk of material. The prominent complex peak around 840 keV is presumably due to several unrelated effects. As seen in figure 3.7, it comprises three distinct peaks at, as given by least squares fit, : 834.8 keV, 843.8 keV and 846.7 keV. The first of these is mostly from the decay of 7 2Ga(t1/2 = 14.1 hrs) formed by the 72Ge(fi, v) reaction in the previous runs with a possible contribution from the decay of 54Mn(ti/2 = 312 d). The middle peak at 843.8 keV along with the 1014 keV line appear to be the result of neutron inelastic scattering of the first and second excited states of 2 7 Al during the early stage of the data ( see figure 3.8 and below ). The third of these at 846.7 keV is most likely from the decay of the manganese isotope,56Mn(ii/2 = 2.6 hr), formed by muon capture on the respective iron isotope,56Fe during earlier runs, eg. nearby steel, and the line at 1811 keV appears to come from the same source. Also occurring as feature in the background spectra is the relatively strong line at 1293.6 keV. It is presumably due to 41Ar(t1/2 = 1.8 hr). It is produced on-site by the cyclotron and may make its way into the air to the two detectors. [It has been seen in other background studies [82] ] The line at 1274.4 keV is a doublet from two unrelated sources. One source, the dominant here, is the famous 22Na(<i/2 = 2.6 yr) line at 1274.542(7) keV [83]. 48 Et = (0.24443(3))ifceV/c/i * Cx - 11.73(8)JbeV (3.2) E2 = (0.22703(2))A;eV/ch * C2 + 8.82(7)keV (3.3) J 1 I I ' I I I I I I I I 1 1 1 L a) Ge1 ENERGY (keV) Figure 3.6: Room background spectra. 49 180 1 4 4 - 834.8 keV 843.8 keV / 846.7 keV o + -3 4 4 0 3460 3 4 8 0 ; CHANNEL NUMBER 3 5 0 0 3520 3540 Figure 3.7: Least-squares fit to the 840 keV-line. The other source is the 1273.34(4) keV [84] transition in 29Si. It could be produced via the decay of 29Al(ti/2 = 6.6 min) formed by the 29Si(p, u)29Al reaction in the previous run. ( notes: natural Si is 4.7% 2 9Si, the target in previous run was Si and was left in position.) This conclusion is further checked by histogramming the first and last 50 k events of the total data in figures 3.8. This doublet is both reduced and narrowed in the last part of the run. Figures 3.8a and 3.8b also unravel the production method for the 2 8Si line at 1779.1 keV to be the decay of the short lived 2 8A/(ii/ 2 = 2.3 min) formed in the previous run by either 28Si(fj,, u) or 27Al(n,j). The line at 1368.8 keV is from the decay 24iVa(<1/2 = 15 hr) formed by either 285i(/x, a) or 27Al(n, a). Although the exact production method is not clear, the line at 1434 keV is probably due to the first excited state in 5 2Cr. Table 3.1 lists the primary peaks observed in figure 3.6. 50 250 200 oo o o 150 H 100 50 H , i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i_ a) F i r s t 50 k events. l^y^ A^JV^ .l^ 'r^ ^l'^ ^^ 'y''T''"rv^ f^ I'T"V | A• •• •• • r 0 —I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1-"-!-1 800 910 1020 1130 1240 1350 1460 1570 1680 1790 1900 ENERGY (keV) 250 200 H oo 150 H ZD 8 100 H 50 H 0 i . . . . i . . . . i . . . . i . . . . i . . i . . . . i b) Last 50 k events. si - i — i — i — i — i — i — r ~ l — i — | — i — i — i — i — | — I ' I I i | i i l l M>,. I. _ l I I I I L_ I ''I" 'I ' IlhI , ll* 'T i y r-f < w |~T ,i 'T lV' JL. 800 910 1020 1130 1240 1350 1460 1570 1680 1790 1900 ENERGY (keV) Figure 3.8: Room background spectra taken for the first and last 50 k events. 51 Table 3.1: Peaks observed in the room background spectrum. Measured energy Identification (keV) 478. 511.0 annihilation 834.8 7 2Ga, 5 4Mn 843.8 27Al(n,n') 846.7 56Mn(2.58hr)-^56Fe*, 56Fe(n,n') 1014.6 27Al(n,n') 1173.2 6 0Co 1274.4 22Na(t1/2=2.6 yr), 29Al(6.6min)-^ 29Si* 1293.6 41Ar(t1/2=1.8 hrs) 1332.5 6 0Co 1368.9 24Na(t1/2=15 hr) 1408.1 1434.1 52Cr(1434.1^ 0) 1460.8 4 0 K 1779.1 28Al(t1/2=2.24 min) 1811.0 56Fe(n,n') , 56Mn(t1/2=2.58 hr) 3.3.2 Empty Target run For this run, no target was used and hence no "MUSTOP" (1.2.3) requirement was present in the logic. It consisted of letting all 7 rays incident upon the detectors be analyzed. The 7-ray spectrum induced in this run is shown in figure 3.9. The dispersion of this spectrum is 0.244 keV/ch and its resolution is about 2.4 keV at 1 MeV. Approximately 7.8 x 108 muons were incident with a rate of about 140 k/s. In addition to the lines seen in the room background spectra, muonic X rays and inelastic neutron scattering induced 7 rays from the nearby materials such as Al and stainless steel, were evident. The intense line at 346.8 keV and the less intense line at 412.9 keV are the nKa and u-Kp X-rays in Al. Similarly, the lines at 1252.8 and 1257.2 keV are the muonic 2p-ls X-ray doublet of Fe. 52 I I I ' I I I I I I I I I I I I I I I I I I I I I I I I I I I I 11 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 0 200 400 600 800 1000 1200 1400 1600 1800 2000 ENERGY (keV) Figure 3.9: Empty-target spectrum*. "The funny binning seen in this spectrum and the subsequent energy spectra is a roundoff problem occurring within the histogramming program FIOWA [85] when binning integer channel numbers. 53 Occurring as a feature in this spectrum ( and all subsequent in-beam runs) is a number of prominent peaks at about 600 and 700 keV. These peaks appear as a consequence of excitation of the first excited states of the nuclei of several isotopes of germanium atoms in the detectors by inelastic neutron scattering followed by emission of conversion electrons and X-rays which are totally observed within the Ge crystals. The skewness toward higher energies of these peaks happen because some of the nuclear recoil energy is converted into electron-hole pairs [86] that add to the associated transition energy. These background peaks are usually seen in most in-beam gamma-ray measurements that follow reactions involving neutrons as outgoing particles. They were extensively investigated early by Chasman et al. [87] and others [86,88] . In addition to these Ge(n,n') peaks, lines were observed from inelastic neutron excitation of the nearby material. These include the 843.8 and 1014 keV lines from the 28Al(n,n') reaction. The room background lines at 846.7 and 1811.2 keV are enhanced by both fi capture and inelastic neutron scattering in 56Fe. The peak at 1238.1 keV appears to come from the same source and will be discussed more thoroughly in § 3.4.4. Unlike the situation in the background spectrum, the line at 1274 keV is mainly from the excitation of the first state in 22Ne formed by 27Al(/z,na) ( and 27Al(n,da) ). A summary of the energies of the major peaks occurring in figure 3.9, along with their identification, is shown in table 3.2. 3.3.3 Polythene target This target was used mainly as a dummy target in order to understand backgrounds since carbon has very low capture cross sections for both /J, and n. 54 Table 3.2: Peaks observed in the empty-target spectrum. Measured energy Identification (keV) 346.8 fJ,Ka Al 412.9 fiK0 Al 511.0 annihilation 563. 76Ge(n,n') 584.8 596. 74Ge(n,n') 693. 72Ge(n,n') 834.8 7 2Ge 843.8 27Al(n,n') 846.7 5 6 F e 1014.6 27Al(n,n') 1173.2 6 0Co 1274.4 22Ne 1293.6 41Ar(t1/2=1.8 hrs) 1332.5 6 0Co 1368.9 24Na(t1/2=15 hr) 1408.1 1434.1 52Cr(1434.1-+ 0) 1460.8 4 0 K 1779.1 28Al(t1/2=2.24 min) 1811.0 56Fe(n,n') , 56Mn(t1/2=2.58 hr) 55 Figure 3.10: Polythene spectrum Furthermore, its muonic X ray energies are low (Ka ~ 75 keV) and hence would not have shown up in our ADCs. Another use for this target was to look for lines that might be caused by the carbon in scintillators and nearby materials. Figure 3.10 shows the energy spectrum for this target. Hardly any new lines appear beyond those in the empty target spectrum. 3.3.4 Al Target The 7-ray spectrum for this target is shown in figure 3.11. The strong lines appearing below the annihilation peak are identified as the muonic X-rays induced in the target, Al, as their energies agree with literature values [10]. This is further confirmed by comparing the prompt and delayed energy spectra; see figure 3.12; whereby these lines are greatly suppressed in the later spectrum. Similarly, the doublet at 1257 keV is consistent with its previous identification as the [iKa in 56 I I I I I I I I I I I I I I I I I I I I I I I I I I 11 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 11 I I I I 1 I I I I I I I I I I I I I I I I'l I 0 200 400 600 800 1000 1200 1400 1600 1800 2000 ENERGY (keV) Figure 3.11: Aluminum spectrum iron. The main production mechanism of the background doublet at 1274 keV in this run is 27A1(//, na)22Ne*. At least 4 different magnesium isotopes are excited in this run. These nuclei are 2 7Mg, 2 6Mg, 2 5Mg and 2 4Mg corresponding to the escape of 0, 1, 2 and 3 neutrons after /z capture on 27A1. Gamma rays resulting from these reactions along with other lines observed in this run are identified in tables 3.3 and 3.4. In addition to the (n,n') reaction, the Al transitions, 843.8 and 1014.4 keV, are enhanced by the 9-min decay of 2 7Mg formed by the 27Al(fj,, u) reaction. Although the main source of the complex peak around 1172 keV could not be identified, two possible contributing sources are the 1169.2 keV 2 6Mg and the 1173 keV 6 0Co lines. Comparing their branching ratios other associated transitions, eg. 1698 keV 2 7Mg and 1332.5 keV 6 0Co respectively, these two lines cannot be the 57 Table 3.3: Peaks observed in the aluminum-target spectrum (a). Measured energy Identification (keV) 346.8 fiKa Al 412.9 fiK0A\ 436.1 pK1 Al 440.0 2 3Na 446.7 fiKs Al 452.6 \i Al(6p-ls) 456.1 H Al(7p-ls) 472.2 2 4Na 511.0 annihilation 563. 76Ge(n,n') 585.2 27A\(fi,2nu) 25Mg(585.1 —> 0) 596. 74Ge(n,n') 693. 72Ge(n,n') 713. (?) 834.8 72Ge, 25Mg(?) 843.8 27A\(n,v) 27Mg*(9mm) ^ 2 7 A / * , 27Al(n,n') 846.7 5 6 F e 955.6 2 7Mg 975.0 2 5Mg 985.0 2 7Mg 58 Table 3.4: Peaks observed in the Aluminum-target spectrum (b). Measured energy Identification 1003.7 2 6Mg 1014.4 27A1 1129.7 2 6Mg 1169.2 2 7Mg 1172.9 \iKa in Mn, 6 0Co 1238.2 5 6 F e 1257.2 fiKa Fe 1274.4 22Na(t1/2=2.6 yr), 29Al(6.6min)^295z* 1293.6 41Ar(ti/2=1.8 hrs) 1332.5 6 0Co 1368.8 2 4Mg 1410.8 2 7Mg 1434.1 52Cr(?) 1460.8 4 0 K 1611.7 2 5Mg 1698.5 2 7Mg 1779.1 28Al(t1/2=2.24 min) 1808.1 2 6Mg 1811.0 56Fe(n,n') , 56Mn(t1/2=2.58 hr) 1896. 1940.0 2 7Mg 59 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I _ , a) Delayed spec t rum : 0 200 400 600 800 1000 1200 1400 1600 1800 2000 ENERGY (keV) I | t i i i i i i I I I I i I i i i i i, |, I.K 1.1 „| | i I i I i i r i i i i i i 1 i i i 1 i i i i i i i i i I i i i i i i i i i ENERGY (keV) Figure 3.12: The aluminum prompt and delayed spectra. 60 only sources. As seen in figure 3.12, the 1172 keV line appears more strongly in the prompt spectrum than the delayed one. This suggests, along with its shape, that it might be a fiKa doublet line. The only fxKa X ray in this energy vicinity is that of manganese ( 1171.2 keV [89] ). The only single-run that has such a doublet is stainless steel which does have some manganese in its composition. However the ratio of the fj,Ka lines of Fe and Mn in the steel doesn't agree with that in the Al run. The only explanation for the enhancement of this doublet in this spectrum is from Mn contamination in the Al target used. This could be as a contaminant added to Al to harden it ( a few tenths of a percent). Finally, the sodium background line, at 1274 keV, is relatively stronger in this run. This is likely to be due to another contribution from the same transition in 22Ne though through (fi, a) on 2 7 Al . 3.3.5 Stainless Steel Target The calibrated muonic X- and 7-ray spectrum obtained for this target is shown in 3.13. The target was just a standard piece of steel used in the meson area. The existence of Fe, Cr, Ni and Mn is evident by the presence of their muonic K a lines. Furthermore, several lines due to muonic excitation of nuclear states in 56Fe,57Fe and 5 2 Cr are observed. The line at 989 keV is due to a transition in 5 4 Cr through the Mn(fi,nu) reaction and henceforth the background line at 834.8 keV would have a contribution from this source as well. The most likely candidate for the source of the 898 keV line is 57Fe. It could result from thermal neutron capture on 56Fe. This last process is also responsible for the enhancement of the Ge(n,n') peak at 693 keV. The observed transitions along with their identification where possible are listed in tables 3.5 and 3.6. The identification of the muonic X-rays was based 61 0 200 400 600 800 1000 1200 1400 1600 1800 2000 ENERGY (keV) Figure 3.13: The stainless steel spectrum. • i i i i i i i i i i i i i i i t i i i i i i i i i i i i i— i — i — | — r — i — i — i—|— i — i — i — i — | — i — i — i — i — | — i — i — i — i—|— i — i — i — i —|— i — i — i — i — | — i — i — i — i —|— i — i — i — i —|— i — i 1 i 0 200 400 600 800 1000 1200 1400 1600 1800 2000 ENERGY (keV) Figure 3.14: The delayed stainless steel spectrum. 62 Table 3.5: Peaks observed in the steel-target spect Measured energy Identification (keV) 307.0 ^Cr(4d5/2 -» 2p3/2) 312.7 X-ray 319.0 S l y 357.4 ^Fe(4d5/2 -> 2p3/2) 361.3 /iFe(4d3/2 -> 2pi/2) 376.8 5 3Mn (?) 400.7 //Fe(5d5/2 -> 2p3/2) 404.6 /uFe(5d3/2 -> 2pi/2) 424.6 //Fe(6d5/2 -> 2p3/2) 428.5 //Fe(6d3/2 2pi/2) 438.6 ^Fe(7d5/2 -> 2p3/2) 511.0 annihilation 563. 76Ge(n,n') 596. 74Ge(n,n') 693. 72Ge(n,n') 834.8 5 4 Cr 843.8 27A1 846.7 5 6 p e 858.7 5 5Mn 898.2 57Fe 929.5 S l y 63 Table 3.6: Peaks observed in the steel-target spectrum (b). Measured energy Identification (keV) 989.2 5 4 Cr 1014.4 27A1 1089.7 ^Cr(2pi/2 -> ls1/2) 1092.2 //Cr(2p3/2 -+ ls 1 / 2) 1171.2 (j,Ka in Mn 1238.2 5 6 F e 1252.2 //Fe(2p1/2 -* ls 1 / 2) 1257.1 ^Fe(2p3/2 -» ls 1 / 2) 1423. l*Ka Ni (?) 1433.9 5 2 Cr, [5 2 mMn (?)] 1522.0 pFe(3p -* Is) 1528.5 5 5 Mn 1614.7 /xFe(4p Is) 1657.4 //Fe(5p —> Is) 1681.2 /iFe(6p —> Is) 1695.0 //Fe(7p -> Is) 1704. /xFe(8p -> Is) 1710.6 /xFe(9p -» la) 1714.7 ^Fe(10p -» Is) 1811.0 56Fe(n,n') , 56Mn(t1/2=2.58 hr) 1896. 64 i — i — i — r n — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — r T 0 200 400 600 800 1000 1200 1400 1600 1800 2000 ENERGY (keV) Figure 3.15: The copper spectrum. on both their prompt nature, ( compare figure 3.14 with figure 3.13 ), and the calculated set of muonic X-rays in Fe [90]. 3.3.6 C u Target The target used for this run was just natural copper with an isotopic composition of about 69 and 31 % for 6 3 Cu and 6 5 Cu respectively. Figure 3.15 shows a calibrated spectrum obtained while figure 3.16 shows prompt versus delayed spectra. As a way of illustration, the time structure of the two peaks at 1173 keV and 1514 keV are plotted in figures 3.17a and 3.17b showing the respective delayed and prompt time characteristic of these two peaks. Table 3.7 lists most of the important lines appearing in these spectra along with their identification when possible. 65 I I I I I 1 I I l_J 1_ I I I I I I I I I I I I I I I I I I I I I _ l I I 1_ a) P rompt s pec t r um i — i — i — i — | — r n — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — I T " i 0 2 0 0 400 600 800 1000 1200 1400 1600 1800 2000 ENERGY (keV) • . i 1 • i i i I i _ _i_L J I I I I I I I I 1 I 1_ J I I I I I 1_ b) Delayed spec t rum - i — i — i — i — | —rn— i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i i i 0 2 00 400 600 800 1000 1200 1400 1600 1800 2000 ENERGY (keV) Figure 3.16: The copper delayed and prompt spectra. 66 Table 3.7: Peaks observed in the copper-target spectrum. Measured energy Identification (keV) 329.1 //Cu(3d5/2 -> 2p3/2) (?) 335.3 /*Cu(3d3/2 - 2p1/2) (?) 445.9 /zCu(4d-+ 2p1/2) 445.9 ^Cu(4d^ 2p3/2) 499.1 //Cu(5d5/2 -> 2p3/2) 505.0 ^Cu(5d3/2 -+ 2pi/2) 511.0 annihilation 596. 74Ge(n,n') 670.0 63Cu(n,n') 693. 72Ge(n,n') 834.8 5 4 Cr 843.8 27A1 846.7 5 6 F e 875.8 6 2Ni 908.8 6 1Ni 931.3 6 4 N i 947.6 962.5 63Cu(n,n') 1014.4 27Al(n,n') 1128.8 6 2Ni 1163.4 6 2Ni 1173.1 6 2Ni 1332.5 6 0Ni 1345.7 6 4 N i 1507.7 /iCu(2p1/2 -» l 5 i / 2 ) 1514.1 /xCu(2p3/2 -> l S i / 2 ) 1844.6 /xCu(3p—> Is) 1885.0 6 2 N i TO5 4 o o 10 10 3 d • i i i i i i i i i i i i i i i i i_ b) - i — i — i — i — | — i — i — i — i — | — i — i — I — i — | — i — i — i — i — | — i — I — I — i — | | — i — I — I — i — | — i — i — i — i — | — i — i — r — i — | — I — i — i — i — | — r 200 4 00 600 800 1000 1200 200 400 600 800 1000 1200 CHANNEL NUMBER CHANNEL NUMBER Figure 3.17: Time curves for the Cu lines 1173 and 1514 keV. 3.3.7 Pb Target The target used for this run was just natural lead with isotopic abundances of 52% 2 0 8Pb, 24% 2 0 6Pb, 22% 2 0 7Pb, and 1% 2 0 4Pb. The calibrated spectrum obtained with this target is shown in figure 3.18. There were several nuclear 7-rays observed from /J. capture on the Pb isotopes. Most of these have been identified in the thallium isotopes with 204 < A < 208. Table 3.8 lists strong lines appearing in the above spectra along with their identification whenever possible. The muonic X-ray energies were checked against other literature values [91,92,93] and found to agree within better than ± 0 . 1 keV. Some 7 rays are different from the common capture 7 rays in that they belong to the target isotopes and not to (Z-l) isotopes. These are mainly due to either inelastic neutron scattering, such as the Ge(n,n') lines, or to "inverse internal con-68 Table 3.8: Peaks observed in the lead-target spectrum. Measured energy Identification (keV) 346.4 /xAl(2p -> Is), 2 0 4T1 (?) 350.8 2 0 7 ^ 373.2 415. 205rp i 204rpj 431.3 //Pb(5g9/2 -> 4/7/2) 437.7 /xPb(5g7/2 -* 4/5/2) 453.1 208rpj 511.0 annihilation 435.7 206rpj 569.8 2 0 7 p b 582.8 208Tl(3.1m) -^20SPb* 596. 74Ge(n,n') 649.5 2 0 6 ^ ^ 663.1 X-ray 681.3 X-ray 686.5 693. 72Ge(n,n') 720.1 205rj-iJ 732.6 206rpj 802.5 2 0 6 p b 811. 2 0 5 ^ 846.7 5 6 p e 874. ^Pb(4d3/2 -> 3p3/2) 891. ^Pb(4d^ 3p) 929. ^Pb(4f5/2 - 3d5/2) 938.1 /xPb(4f7/2 -+ 3d6/2) 971.9 /iPb(4f5/2 - • 3d3/2) 1014.4 27Al(n,n') 1331.8 207rpj 1366.2 /iPb(5f5/2 -> 3d5/2), /^Pb(5f7/2 -> 34/2) 1404.5 /zPb(5f5/2 -> 3d3/2) 1438. (^Pb(3d3/2-+2p3/2))" 1507.7 //Pb(3p3/2 -> 3si/2) 1807.8 69 200 400 600 800 1000 1200 1400 1600 1800 2000 ENERGY (keV) Figure 3.18: The lead spectrum. version" processes. Gamma rays belonging to the latter class appear mostly in the "prompt" spectra. They arise from the strong coupling between the muon and the nucleus, especially for such heavy elements as Pb. In these processes, the nucleus is being excited by a radiationless transition of the orbital muon from a higher excited state to the Is state whereby it decays to the ground state with or without neutron emission [92]. Such possible transitions [94] are the lines at 570 keV and 803 keV correspond-ing to the first excited states in 2 0 7Pb and 2 0 6Pb respectively. Radiationless (7^7') on 2 0 8Pb and/or (7 ,7') on 2 0 7Pb could enhance the 570 keV peak while 2 0 6Pb(7 ,7') and 2 0 7Pb(7,n7') could contribute to the 803 keV peak in figure 3.18, see figure 3.19 which shows the prompt and delayed spectra for these two peaks. For more dis-cussions and how to distinguish experimentally between the responsible "prompt" neutrons and the much higher yield //-capture ones see Hargrove et al. [94]. 70 2 4 0 0 1 9 2 0 -1440 4 960 4 8 0 -550 5 6 0 570 580 590 ENERGY (keV) 1700 h 1 3 6 0 -h 1020 H h 680 h 3 4 0 600 775 785 795 805 815 825 ENERGY (keV) 2 4 0 0 1920 1440 960 H 4 8 0 1700 h 1360 h 1020 h 680 h 3 4 0 H 550 560 570 580 590 600 775 785 795 805 815 825 ENERGY (keV) ENERGY (keV) Figure 3.19: Prompt and delayed spectra for the lead lines 570 keV (a and c) and 803 keV (b and d) respectively. 71 200 4 0 0 600 800 1000 1200 1400 1600 1800 2000 ENERGY (keV) Figure 3.20: BGO-target spectrum. 3.3.8 BGO Target This run was made to check for any background associated with muons stopping in the Compton suppression systems. Three prominent fiX—ray lines were used to calibrate the energy spectra. These were the bismuth (5<79/2 — 4/7/2), (4/7/2 — 3/5/2) and (4/5/2 — 3d3/2) lines with energies 442.107, 961.15 and 996.67 keV respectively. The calibrated spectrum is shown in figure 3.20 while the strong peaks are listed in table 3.9. Four of the unidentified peaks are muonic X-rays in the target elements, especially Ge, but since no complete literature compilation for these ele-ments was at hand, these lines were just designated as "X-ray" as they appear only in the prompt spectra 2. 2The identification of the strong muonic X-ray lines in germanium was figured out from systematics. 72 Table 3.9: Peaks observed in the BGO-target spectrum. Measured energy Identification (keV) 346.4 /zAl(2p -»• Is) (?) 382.7 X-ray 402.3 jxGe(3d3/2 -» 2pi/2) 411.5 /xGe(3d5/2 -» 2p3/2) 442.1 //Bi(5g9/2 -> 4/7/2) 448.8 ^Bi(5g7/2 -» 4/5 / 2) 511.0 annihilation , 2 0 8Pb 570.0 2 0 7 p b 583.2 2 0 8 p b 596. 74Ge(n,n') 693. 72Ge(n,n') 803.6 2 0 6 p b 834.8 7 2Ge 843.8 27Al(n,n') 846.7 5 6 F e 897.7 2 0 8 p b 961.1 ^Bi(4f7/2 -> 34 / 2) 996.6 /iBi(4f5/2 -» 3d3/2) 1014.4 27Al(n,n') 1039.6 1063.5 2 0 8 p b 1224.9 1252.2 /wFe(2p1/2 lsl/2) 1257.1 /xFe(2p3/2 -> ls 1 / 2) 1398.4 X-ray 1411.4 1439.5 X-ray 1606.3 1609.6 X-ray 1718.3 1764.2 ^Ge(2p1/2 -¥ ls1/2) 1770.0 2 0 8 p b 1773.5 /uFe(2p3/2 -> l^i / 2 ) 1806.4 73 3.4 Analysis of the Si Target Runs 3.4.1 Summation of Individual Data Runs Due to gain shifts, individual data runs were separately calibrated by measuring 4 well known peaks which occur throughout the energy range. These peaks are the 400.12(2) keV pKa in 2 8Si, the 1014.4(2) keV 7-ray in 27A1, the 1173.238(4) keV in 6 0 Co 3 and the 1779.1(2) keV 2 8Si 7-ray. Nineteen full-tape runs representing approximately 1010 stopped muons in 2 x 10 cm2 Si target were calibrated and summed. 3.4.2 Beam Related Backgrounds In one of the Si runs, the beam was tuned for pions to get an estimate of the pion-induced backgrounds. It was found during this run from the oscilloscope that the beam was mainly electrons, with some muons and a few pions. Figure 3.21 shows the spectrum resulted after the tuning. The only noticeable difference ( if any) from the usual /x~Si spectra is the enhancement of the lines at 440 and 1369 keV. These two lines show up more strongly in the prompt spectrum. The source of this enhancement is not known as there is no corresponding pionic X-rays around these energies. A positive // beam was also used to study effects due to Michel electrons. This was achieved by simply reversing the polarity of the magnets in the beam line. As there is typically 5 times more flux available for fi+ than for fi~, the beam intensity was reduced in order to produce p,+ stopping rates in the target similar to the rates used for the negative muon beam. Figure 3.22 shows a spectrum of /x+Si. Evident is the increase in background continuum from bremsstrahlung of electrons 3It was only realized later ( after analysing the Al target ) that this line is complex one and hence would contribute an additional uncertainty to the line positions ( about ± .1 keV) ; see discussion of this line in § 3.3.4. 74 Figure 3.21: Silicon spectrum resulted after tuning for pions. in fi+ decays. The enhancement of the background doublet at 1274 keV is due to the contribution from the 28Si(n,7)29Si* reaction. The huge line at the end of the spectrum is an artificial peak from a pulser generator. 3.4.3 L i n e Ident if icat ion Identification of lines observed in the /j,~Si runs was generally based on the available information on energy levels of the relevant nuclei. Specific transitions were assigned to each 7 ray based on their measured energies, known associated cascades and proper branching ratios. Comparisons with previous background target runs were most useful. Figure 3.23 and figure 3.24 show the summed spectra obtained with the two detectors. About 100 lines can be seen there. The weak line at 197 keV in figure 3.23a is associated with the decay of the 75 21.9 ms isomer in 71Ge. It represents the summing of the energies of the isomer at 22 keV and the first excited state at 175 keV. Although these two transitions are not, individually, apparent in our spectra as they are below the lower cutoff energy, they were seen in other work [86]. The peaks from neutron inelastic excitation of the germanium isotopes are evident. The time distribution of these 7-rays is similar to that of //-capture 7-rays; indicating that neutrons emitted following muon capture were responsible. This is demonstrated in figure 3.25 which shows the time structure of the 693 keV Ge(n,n') after subtracting the respective background time spectrum. Several nuclei were excited by //-capture in the target and surrounding ma-terials. A major difficulty in determining reaction mechanisms for the different transitions arose from the confusion between the fi capture reactions /T + (A, Z) —> (A - (X + Y), Z - (Y + 1)) + Xn + Yp + v„ (3.4) 76 0 200 400 600 ENERGY (keV) 800 1000 _l I I I I 1 1 1 I 1 1 1— _J I I I 1 u _l • I I I I I I I I I I I I I I I I I I L_ 1(T b) 00 o o IO"" - i — i — i — i — i — i — i — i — i — I — i — i — i — i — i — i — i — i — i — I — i — i — i — i — i — i — i — i — i — | — i — i — i — i — i — i — i — i — I — I — i — i — i — i — i — i — r i — r 1000 1200 1400 1600 ENERGY (keV) 1800 2000 Figure 3.23: ft Si summed spectra for Gel. 77 i o % in groN 10% i i i i I i i i i I i i i i i i i i i I i i i i i i i i i a) 300 T — i — i — i — i — i — i — | — i — i — i — i — i — i — i — i — i — p n — i — i — i — i — i — i — i — i — I — i — i — i — i — i — i — i — i — r 500 700 ENERGY (keV) 900 1100 1100 1300 1500 ENERGY (keV) 1700 1900 Figure 3.24: fj, Si summed spectra for Ge2. 78 I I I i I I I I I I I I i i I I I I I I I I I L cn r -Z> o o \\J —I 1 T 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 2 4 6 8 10 (x10 + 2 ) CHANNEL NUMBER Figure 3.25: Time spectrum for an (n,n') line in Ge. and the neutron induced reactions n + (A,Z)—> (A,Z -Y) + Xn + Yp (3.5) Examples include the confusion between 28Si(/J,, nuj)27Al and 27 Al(n, n'j)27Al or that among 28Si(/J.,pu^)27Mg, 27Al(p,uj)27Mg and 27Al(n,py)27Mg etc. Such confusion is greatest for the lower excited states in the relevant nuclei. Again, the time structure of these transitions are similar, with a time dependence characteristic of muon capture lifetimes. Nine nuclides from 3 elements were excited by p, capture in the Si target. These are 28.27>26A1, 27-26.25>24Mg and 2 4 , 2 3Na. At least seven 2 8 A l transitions were observed at energies 579.2, 865.5, 941.3, 1229.4, 1342.2, 1590 and 1622 keV corresponding to the following transitions, see also figure 3.26,: 2201.5 keV(l+) —• 1622.9 keV(2+, 3+) (3.6) 79 2486.2 keV(2+) —• 1620.3 keV(l+) (3.7) 972.4 keV(0+) —> 30.6fceV(2+) (3.8) 2201.5 keV(l+) 972.4 keV(0+) (3.9) 1373.0 keV(l+) —• 30.6Jfcey(2+) (3.10) 1620.3 keV(l+) —• 30.6fceV(2+) (3.11) 1622.9 keV(2+, 3+) —• 0 fceF(3+) (3.12) Some of these transitions are Doppler broadened [72] while others are effected by the existence of the doublet at about 1621 keV ( 1620.3 and 1622.9 keV). Fig 3.26 shows the lower levels of 28A1. The 28A1(1373.0 keV —> 972.4 keV) transition is also Doppler broadened but is masked by the much stronger muonic Ka in Si. The transition 974.8 keV —> 585.1 keV in 2 5 Mg is probably contributing as well since one observes both 585.1 and 974.8 keV lines. Another seven weaker lines in the spectra have corresponding transitions in 28A1, viz., 1622.9 keV —> 1013.6 fceV (3.13) 2201.5 keV —• 1373.0 keV (3.14) 1013.6 keV —• 30.6 keV (3.15) 1013.6 keV —• 0 (3.16) 2987.5 keV —> 1622.9 keV (3.17) 1373.0 keV —• 0 (3.18) 2656.1 keV —• 1013.6 keV (3.19) However the 7-rays cannot be definitively attributed to these transitions as they are weak and -for most of them- masked by other transitions in other nuclei. 80 J 7T ,+50 50 E (keV) 2987. 25 75 2656.1 22 6 61 11 79 16 5 2201.6 43 50 2138.9 93 7 6 92 1622.9 1620.3 5 55 40 38 62 100 1013.6 972.4 100 30.6 Figure 3.26: Nuclear levels diagram of 2 8 Al (from ref. [95]). 81 Another difficulty one is faced with in assigning these 7-ray lines to their respective transition is the lack of reliable information on 2 8 Al energy levels and branching ratios. Also seen in the spectra are several muonic X ray lines in the Si target and the surrounding materials. Of these are the Ka, Kp, K 7 , Kg, K£ and in the Si target. Figure 3.27a shows the area around the annihilation line where these muonic X rays cluster, while fig 3.27b shows the same spectrum after excluding the prompt events. Other muonic x-rays are from the surrounding materials such as Ka and Kp in Al at 346.9 and 412.2 keV, Ka in Cr and Mn at 1091.8 and 1171.2 keV and Ka and Kp in Fe at 1257 and 1522.1 keV respectively. All of these are observed in the background spectra and are believed to come from either the Al or the steel in the vicinity of the target and detector system. The (J,Ka line from Al is superimposed on the upper side of the delayed capture 7 ray line in Pb(/i, im)207T/(351.0 —> 0) as seen clearly in the delayed spectrum. The 4 strongest muonic X-rays seen in the Pb spectrum 3.18 are also present, though much weaker, in the Si spectra. Figures 3.28a, b and c show different characteristics in time spectra for prompt, delayed and time-independent lines respectively. The first excited state in 2 9Si is probably contributing to the room background peak at 1274 keV as its time spectrum does show some time dependence relative to captured /i's. The line at 1779.1 keV from the decay of 2 8 A l is mainly formed by 28Si(/x, z^)28Al reaction rather than the reaction, 2 7Al(n,7) 2 8Al as in the background spectra. A tabulation of the peaks observed in figures 3.23 and 3.24 is shown in ta-bles 3.10, 3.11 and 3.12, along with the measured energies. The uncertainty in the energies is estimated to be about 0.5 keV. 82 Z) o o 600 H 1980 2020 2060 2100 2140 2180 2220 CHANNEL NUMBER 1400 1200 H 1000 oo t ; 800 Z) 8 600 H 400 200 _ J I L_ I • . . . I b) 0 1980 2020 2060 n — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — r 2100 2140 2180 2220 CHANNEL NUMBER Figure 3.27: Part of the Si spectrum showing the muonic X-ray lines (a). In (b), the same area with prompt events excluded. 83 Table 3.10: Peaks observed in the silicon-target spectrum Measured energy Identification (keV) 197.0 7 1 m Ge 244 Compton edge of 400 keV 264.2 X-ray(?) 346.8 /*Al(2p -> Is) 400.1 /^ Si(2p —* Is) 412.2 /xAl(3p -> Is) 416.4 2 6 Al 431.1 Pb(5g9/2 -> 4/7/2) 439.6 2 3Na 471 2 4Na 476.6 )uSi(3p —> Is) 503.4 ^Si(4p -> Is) 511.0 annihilation , 2 0 8Pb 515.5 //Si(5p —> Is) 522.3 /xSi(6p —> Is) 526.5 ^Si(7p —> Is) 534 i^Si(8p —» Is) 584.5 2 5Mg 596.1 74Ge(n,n') 608.5 685.5 (?) 693.4 (?) 72Ge(n,n') 783.1 X-ray 803.0 X-ray 829.5 2 8 A 1 834.8 7 2Ge 843.8 27Al(n,n') 846.7 5 6 F e 84 Table 3.11: Peaks observed in the silicon-target spect Measured energy Identification (keV) 858.2 (?) 865.5 2 8 Al 873.7 2 4Na 896.2 938.1 ^Pb(4f5/2 3d3/2) 974.1 2 5Mg 984.9 (?) 2 8 A l (?) 984.3 2 7Mg 996.9 (?) 2 4Mg 1003.9 26A1, 2 6Mg (?) 1014.4 27A1 1039.6 70Ge(n,n') 1063.1 1091.8 ^Cr(2p-> Is) 1129.3 2 6Mg 1134.0 (?) 1172.9 ,uMn(2p^ Is), 6 0Co 1229.4 2 8 Al 1238.2 56Fe(n,n') 1252.2 //Fe(2p1/2 -» lsi/2) 1257.1 /iFe(2p3/2 -> ls1/2) 1273.7 2 2Na, 2 9Si 1293.4 4 1 Ar 1303.7 (?) 1308.4 (?) 1332.5 6 0Co 1342.2 2 8 Al 1363.7 (?) 2 8 A 1 1368.6 2 4Mg 85 Table 3.12: Peaks observed in the silicon-target spect Measured energy Identification (keV) 1372.6 2 8 A l (?) 1378.3 2 5Mg 1439.5 X-ray 1398.0 1408 2 7Mg 1434.1 52Cr(?) 1372.6 4 0 K 1522.1 yuFe(3p -» ls1/2) 1528.1 5 5Mn 1589.8 2 8 Al 1608.9 25Mg(?) 1622.5 2 8 Al 1635.4 (?) 2 3Na 1640.4 (?) 2 8 Al 1652.2 (?) 2 6 A 1 1680.2 (?) 1698.4 2 7Mg 1704.8 1721.1 27A1 1754.4 1771.7 5 6 F e 1779.1 2 8Si 1808.8 2 6Mg 1811.2 5 6 p e 1940.2 2 7Mg 86 0 250 500 750 1000 0 250 500 750 1000 Channel Number Channel Number 250 500 750 100C Channel Number Figure 3.28: Time distribution for the three lines seen in Si spectra at 400.1, 1014.4 and 1293.4 keV respectively. 3.4.4 C o n t r i b u t i o n to 1229 keV As stated earlier, this experiment was designed to measure the Doppler broadened 1229 keV gamma ray in 28A1 following fi capture in 2 8Si. The observation of such a Doppler broadened gamma-ray spectrum constitutes a measurement of the 7 — 1/ directional correlation [71]. This measurement is feasible since the recoiling nucleus,28 !^/*, doesn't slow down appreciably before the emission of the 1229 keV 7-ray [71]. Also the width of this 7-ray is considerably larger, (~ 9 keV), than the energy resolution of the available Ge detectors. The only previous measurement of this kind was performed by Miller et al. [72,73,74] at SREL in the late 1960's. The aim of this section is not to extract such correlation, but rather to try to understand the contribution from backgrounds to the specific transition as such understanding is essential for a precise measurement of this nature. The most serious type of backgrounds is that which produces a peak (or peaks) 87 near the 1229 keV line as it could distort the line shape. To start with, no gamma rays in the Si spectra were observed that had either their first or second escape peaks or their Compton edge around the 1229 keV region. ( The amplifier gains were lowered for one run to look at higher 7-energies ). Figures 3.29a and 3.29b show the 1229 keV region for the two detectors (after rejecting the prompt events). The line in figure 3.29a appearing on the upper part of the Doppler broadened 7-ray is the 56Fe(2085.03A;eV —• 846.71fceV) transition. Unlike that in the room background spectrum, figure 3.6, where it is through the 2.6 hr j3~ decay of 5 6Mn, the main source of this line is neutron inelastic scattering off 56Fe. The fact that this line is much stronger in Gel suggests the abundance of iron around Gel and/or BGOl. The lower shoulder below the broadening is not understood yet ! It is present in both detectors and hardly affected by any of the various cuts. One possible explanation is the existence of several non-resolved peaks from /i-capture in the target and/or surrounding materials. Some of the background spectra have some structure near 1229 keV including the empty-target one. Due to the poor statistics in these runs, it was not possible to identify such structures. One effect that might contribute to such structure is any existence of nearby triangular peaks from the (n,n') reactions in the Ge crystals. Possible -but unlikely in terms of relevant branching ratios- lines are the 1204 keV and 1216 keV due to the inelastic excitation of the second excited states in 7 4Ge and 7 0Ge respectively. Beside the empty-target contribution, Cu, stainless steel, BGO and Pb spectra have weak lines around 1229 keV. The Cu and Pb contribution could safely be excluded as the much stronger (2p-ls) and (5f-3d) ^X-ray doublets in Cu and Pb respectively are not seen in the Si spectra. The unidentified line at 1225 keV seen in the BGO spectrum could be one of the contributing lines provided it is not related 88 1lV oo i — z: ZD o o io-' I 1 I I I I I l_ _ l I l_ a) Ge1 ft - i 1 1 1 1 1 1 1 1 1 1 r 1150 1200 1250 ENERGY (keV) ~T 1 1 1300 i 1 1 r 1350 10 oo o o _1 I I I | I I I I I I I I L _ _ l I l _ b) Ge2 — i 1 1 1 | 1 1 1 1 1 1 1 1 r 1150 1200 1250 ENERGY (keV) — i — i — i — i — i — 1300 1350 Figure 3.29: The 1229 keV energy spectra for the two Ges. 89 00 I — 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1150 1200 1250 1300 1350 ENERGY (keV) Figure 3.30: The vicinity of 1229 keV in the steel spectrum (for Gel). to 2 0 9 Bi as we don't see the //X-ray in Bi. The most likely background contributor is the stainless steel as we see almost every single line present in its spectrum. Figure 3.30 shows the steel spectrum for the same region as figure 3.29a (and with the same cut). The ratio of the two lines below 1229 keV to the 1238 keV and/or to the fiKa in steel is similar to that of the shoulder to the same lines in the Si spectra. Other possible target-related transitions are the weak transitions at 1222 keV in 27A1 and 1208 keV in 2 3Na. The counting rate of the 1229 keV gamma-ray transition could be measured directly using the formula : 7Y7 = N^eCt (3.20) where JV7 is the number of 7 rays detected. iV^  is the number of /J'S stopped, eil is the acceptance of the associated detector. Ky is the yield of 7-ray per stopped 90 The average number of stopped muons,(= 1.2.3), per run is about 5 x 108/^ 's and hence the total number of //'s stopped, JVM ~ 1010. The quantity Ny is simply the background-subtracted peak area of the 1229 keV line. Taking an 11 keV energy window around the 1229 keV and including the BGO, PROMPT and timing cuts we have obtained4 about 7 x 103 and 3 x 104 counts in the 1229 keV peak in about 50 hours of running which would give, with Ge's about 25 and 17 cm from the target, 7.0 x 10 - 7 and 2.7 x 10 - 6 1229 keV 7//istop for Gel and Ge2 respectively. Using the measured yield for the 1229 keV by Miller et al [72] 0.011 7's//i cap-ture and correcting for the fraction of muons which decay in the target (~34.2%), acceptances of about 1.1 X 10~4 and 4.0 x 10 - 4 are obtained for Gel and Ge2 respec-tively. This procedure was repeated for the 1014.4 keV 27A1 peak, with Ky=0.103 7 's//istop [72], and gave consistent results. 4i.e. for 50% of our data, we have obtained double (same) the statistics of Miller et al. [73,74] with Ge2 (Gel). 91 Chapter 4 Conclusion The present work was designed to measure the X- and 7-ray energies following muon capture on 2 8Si and to investigate the potential backgrounds contributing to a transition sensitive to the induced pseudoscalar coupling constant (gp ) of the weak hadronic current. To do this several other targets were investigated and the sources of many lines have been identified. Using a precise energy calibration it has been possible to definitively attribute the origin of a large number of peaks; many more than were identified in the previous study of Miller. This work should provide valuable input for subsequent extraction of the 7 — v correlation and succeeding spectroscopic work. The only puzzle which remains is the plateau underneath the 1229 keV line in the silicon spectrum. It is partially visible in the stainless steel spectrum, so it is the best identification that we have. 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