.. :v‘ WWWWMWW. , fifir. ‘ MW a: awn... .. “Mm. , ‘ . n . . . . a: a... . . ”35.4. I I - . aJfix .... q. _ I u” 2 . 1. 3. “Cu fimufi... .. «5.2%. 5;“ 2.9% Lute; am £wa a :3; . i ”fix“. .14» 52.; 5, .. _ .5 ‘ $5: 2. i. 5.5%”, .. an“: I...) .1... A: I. I. .I :3: 11¢ .2 a. .. 1 v2 . V ‘1 ‘1‘. .5. 1...: - n. i; £54.. 7;... . .1511 v...) o a... a. 13:52.“. .5 A. . urn. u . 2 . . . . V . 1? 6.. , . . A . . Q . Ill ‘ V , l t... 6..» 31?. 3.5.1:: k .539. 13.3.1.1. 1.: 5 y ‘ :1: .u ‘2: .1 Stir... . .. BETA DECAY STUDIES OF 69Ni AND 58V: DEVELOPMENT OF SUBSHELL GAPS WITHIN THE N = ‘28 - 50 SHELL By Joann I. Prisciandaro A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY Department of Chemistry 2001 ABSTRACT BETA DECAY STUDIES OF 69Ni AND 58V: DEVELOPMENT OF SUBSHELL GAPS WITHIN THE N = 28 - 50 SHELL Bv v Joann I. Prisciandaro Macroscopically, nuclei with magic proton or neutron numbers (N, Z = ‘2, 8, '20, ‘28, 50. 8‘2 and 1‘26) may be described with spherical charge distributions and modest collective features at low excitation energy. Between the magic shell closures, collec- tive interactions amid nucleons becomes evident, inducing quadrupole deformation. This deformation becomes apparent in the form of vibrational and rotational ex- citations within the low-energy level spectrum and are expected to be maximum at midshell. However, the development of collectivity away from major closed shells may be inhibited by the presence of subshell closures, or minor shell gaps. In the framework of this thesis, the development. of subshell gaps at N = 32 and N .—: 40 for neutron-rich nuclides within the N = ‘28 — 50 shell were investigated. A conventional beta detection system was used to examine the beta decay proper- ties of neutron-rich nuclei near N : 40. An N : 40 subshell was first suggested for ggNim by Broda cf (11. [1] due to the rise of the first excited 2+ state relative to its N - ‘2 neighbor, 66Ni. The presence of an N = 40 subshell would inhibit the development of collectivity in this midshell region. During this study, a 3.4(7) s isomeric state in 69Ni was directly produced via the fragmentation of a 70 MeV/nucleon 7'6Ge beam in a 9B6 target at. the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University. The beta decay of the 1/2’ isomer was observed to mainly populate the excited 3/2‘ state at 1296 keV in 69Cu. By comparing the total number of 69Ni nuclei implanted with the intensities of the beta-delayed 7 rays following the decay of the 1/2" isomeric state and the ground state of 69Ni, a 36% upper limit has been extracted for the beta. branch from the isomeric state in 69Ni to the ground state of 6QCu. Based on this branching ratio. a small ‘2p-‘2h mixture into the ground state of 69Cu may be deduced. This small admixture suggests that the ground state of 69Cu is predominately single—particle in nature and may be described as a proton coupled to a 68Ni core. The dominance of the “SNi core provides a strong case for the N = 40 subshell. A new beta. detection system was employed to study the decay properties of neutron-rich nuclides near N = 32. An N : 3‘2 subshell gap was first suggested following the measm'ement of the high—energy 121+ state of 52Ca32 [2]. Similar to the case of 52Ca. the first excited 2+ state of 5“(‘r lies higher in energy relative to its N — ‘2 neighbor. 54Cr. To determine whether the first excited 2+ state continued to rise or is peaked at N 2 32, it. was necessary to measure E(21+) beyond N = 32. 58V was produced following the fragmentation of 70Zn at 70 MeV/nucleon in a 9Be target at the NSCL. The ground state beta decay of 58V was observed to mainly proceed into the 880 keV state of 58Cr. In comparison to the first excited 2+ state of 33C1'32, a peak in this energy for even-even neutron-rich chromium isotopes is now evident at. 56Cr. The current measurement provides the first conclusive evidence for a significant subshell gap at N = 32. The presence of the N = 32 subshell gap has been attributed to a strong 7r1f7/2-1/1f5/2 proton—neutron monopole interaction. Per 27 mici genitorz’, [anti [met 6 abbracci. iv ACKNOWLEDGMENTS First. and foremost, I would like to thank my advisor, Paul Mantica. Thank you, Paul, for your guidance, wisdom and support. Without you, none of this would have been possible. The research described within this dissertation was performed at the National Superconducting Cyclotron Laboratory at Michigan State University and involved the collaborative efforts of many at the NSCL and abroad. I would like to thank the operations staff at the NSCL for allowing my experiments to run so smoothly and the National Science Foundation for their generous financial support. In addition, I owe a debt of gratitude to my collaborators: Don Anthony, Matt Cooper, Alejendro Garcia, Daniel Groh, Mika Huhta, Alexander Komives, VVasantha Kumarasiri, Patrick Lofy, Anca Oros—Peusquens, Reg Ronningen, Samuel Tabor, William Walters and Mathis VViedeking. Their assistance during my thesis experiments was invaluable. I would like to thank B. A. Brown for performing the shell model calculations discussed within this dissertation for the N = 29 isotones in the region 20 g Z _<_ ‘28. I would also like to express my gratitude to Thomas Baumann for addressing my Em and GEANT questions. You have proven to be a [MEX and GEANT guru! Special thanks to David Morrissey, Thomas Glasmacher and Michael Thoennessen for serving on my guidance committee. Without my family, I would be nothing. They have been a constant source of love, support and encouragement. Mom and dad, although you weren’t fond of the idea of my moving away from New York and living an hour from Detroit, you were still very supportive. You have always been there for me when I needed you the most, thank you! And trust me, I will always remember where I came from with pride! Annette and Frank thank you for being there to lift my spirits. You always believed in me even when I did not, thank you! To my sister Isabella, thank you for your many words of encouragement and for your moral support. Thank for you flying out on Thanksgiving \7 so I wouldn’t be lonesome, even though you told me about your plans the day before your flight. You always were the spontaneous one! And Jack, I don’t know where to begin. Growing up, I always felt like I was trying to live up to you. However, as an adult I finally realized that would be impossible. You are an intelligent, kind and wonderful person. You have been dubbed the “successful" one in our family, and I certainly agree. However, what I admire the most about. you is not what you have become, but whom. Throughout it all, you always seem to remember what is truly important in life, your family and friends. Thank you for teaching me the finer points in life. I don’t think I would be able to muster up enough courage each morning to drag myself into work without my fellow graduate students and friends. Although the list. is lengthy, I would like to name just a few friends to which I am forever indebted. Pat, we started our graduate career together and struggled through the same classes and exams. You were certainly a better sport than I. Thanks for putting up with my grumbles and gripes, and thank you for bringing a little humour to the lab (I still can’t seem to manage to get that song from “The Sound of Music” out of my head). I don’t think I will soon forget your many antics. You always knew how to make me laugh, even at myself. I still chuckle when I think about the time you flipped the canoe over during that trip to Alma with the other first year chemistry students. Now that I think about it, wasn’t I the only one that ended up sopping wet?!! Graduate school can be a very challenging and stressful period, especially when you are one of several female graduate students in a male dominated program. Katie, you certainly made my time here a lot easier. You gave me the strength to believe in myself and also taught me a few lessons about taking time to enjoy myself and relax. I don’t think I will ever forget our camping trip out west. From the outhouses, to the smores, to the little incident in Colorado. Sorry about your CD’S. Thank you for being a terrific friend. Being the first graduate student in a group is like being the first. born child, it isn’t easy. You feel like mom and dad’s guinea pig as they get their parental bearings. vi Although most. siblings are resentful of their younger siblings. that was certainly not the case with my academic brother, Daniel. I was grateful when you joined Paul‘s group. It was nice to have a. comrade and friend that I could confide in. Thank you for all of your help during my thesis experiment and for your kindness afterwards. I still have the card that you and Michelle gave me after my experiment with the cartoon elephant chained to the S2 vault. It ren'iained on the wall in front of my computer throughout the remaining years of my graduate career to remind me of the more challenging times I‘ve experienced at the laboratory. In addition. it was a constant reminder that even when things were rough. I have friends around me that. could lift my spirits. Thank you for lending me a helping hand when I needed it the most, especially when I needed someone to proof read my thesis. To my dear friend Irene, although I did not continue on to medical school with you as I originally planned, you were always there for me. You had the confidence in me that I certainly lacked. Thank you for being such a wonderful friend. Last but certainly not least, I would like to thank Mike. The last few years have been among the happiest because you have been a part of my life. Thank you for knowing just when I needed a hug and for making me laugh when I wanted to cry (although at this point your story about the leaves is just about ready to make me cry :—). Thank you for being you! vii Contents LIST OF TABLES x LIST OF FIGURES xii 1 Introduction 1 1.1 The Atomic Nucleus ........................... 1 1.2 Development of the Nuclear Shell Model ................ 2 1.3 The Structure of Nuclear Systems .................... 5 1.3.1 Nuclear Structure Near Shell Closures ............. 6 1.3.2 Quadrupole Deformation ..................... 7 1.4 Probing Nuclear Structure ........................ 8 1.4.1 E(2;‘) ............................... 8 1.4.2 Ratio of E(4f) to E(2}L) ..................... 10 1.5 Motivation ................................. 12 2 Technique 15 2.0.1 Beta Decay ............................ 15 2.0.2 Beta-Delayed Gamma Ray Transitions ............. 18 2.0.3 Summary ............................. 20 3 Experimental Setup 22 3.1 Production of Radioactive Beams .................... 22 3.2 Beta Detection System .......................... 23 3.2.1 Pulsed Beam Method, Experiment 97004 ............ 23 3.2.1.1 Electronics ....................... 26 3.2.2 Continuous Implantation Method, Experiment 98020 ..... 26 3.2.2.1 Electronics ....................... 32 4 Sample Data Analysis for Continuous Beam Implantation 35 4.0.3 Test study, beta decay of 57V .................. 36 4.0.4 J1r discussion ........................... 45 4.0.5 Summary ............................. 47 5 Experimental Results & Interpretation 48 5.1 Subshell Gaps and Neutron-Rich Nuclei ................. 48 5.1.1 Neutron-Rich Nickel Near N = 40 ................ 49 viii 5.1.1.1 Configuration mixing in 69Cu ............. 60 5.1.1.2 Summary ........................ 6-1 5.1.2 Neutron-Rich Nuclides Near N = 32 .............. 65 5.1.2.1 Beta decay of 58V" .................... 66 5.1.2.2 Summary ........................ 76 Summary 78 6.0.3 Outlook .............................. 81 Beta Efficiency Calculations 82 A04 Experimental Efficiency for Exp. 97004 ............. 82 A05 Simulated Beta Efficiency for Exp. 98020 ............ 82 A051 GEANT Program .................... 85 A052 Sample Input File ................... 112 A.0.5.3 Running the GEANT simulation ........... 113 Gamma-ray Efficiency Calculations 116 B.0.6 Experimental Efficiency for Exp. 97004 ............. 116 B0? Experimental Efficiency for Exp. 98020 ............. 124 B.0.7.1 Computer Simulation ................. 124 8.0.7.2 Sample Input File ................... 129 Gamma ray Summing Corrections 136 D Single-Particle Calculations for N = 29 Isotones 139 BIBLIOGRAPHY 150 ix List of Tables [0 N; [v t-‘ 4.1 5.1 A.1 B.1 B2 B3 B4 B5 8.6 B7 B8 B.9 D1 D2 D3 D4 Selection rules for beta decay transitions ................. I9 Weisskopf single-particle reduced transition probabilities and estimated transition rates ............................... 21 Calculated beta efficiencies for the nuclides produced in Exp. 98020. In addition, the decay energies and previously measured T1/2 are provided. 39 Comparison of the number of experimental and simulated single-sided beta events. ................................ 42 Estimated single—particle energies for the N = 29 isotones in the region 20 3 Z s 28. .......................... 73 Calculated beta efficiency for Exp. 97004 ................. 83 Sources used for total efficiency measurement. ............. 117 Summing corrections for the prominent gamma rays emitted by the mixed gamma ray source. ........................ 120 Summing correction coefficients for the 583 keV and 2615 keV gamma rays emitted following the decay of 208T1, a member of 228Th decay chain. 121 Peak efficiency data for the 120% and 80% Ge detector used in Exp. 97004. ................................... 123 Peak efficiency data. for the 120% and 80% Ge detectors used in Exp. 98020. ................................... 124 Peak efficiency data for the Ge clover detectors used in Exp. 98020. . 125 A fit to the simulated peak efficiency for an extended source for the Ge detectors used in Exp. 98020. .................... 129 Comparison of the experimental and simulated ratios of the 511 keV peak area for the 22Na. at the four corners of the DSSD position to its central position ............................... 129 Continued:Comparison of the experimental and simulated ratios of the 511 keV peak area for the 22Na at the four corners of the DSSD position to its central position. .......................... 130 Calculated single-particle energies (s.p. E(keV)) for 49Ca ........ 140 Calculated single-particle energies (s.p. E(keV)) for 51Ti. ....... 140 Calculated single-particle energies (s.p. E(keV)) for 53Cr ........ 141 Calculated single-particle energies (s.p. E(keV)) for 55Fe. ....... 142 7 D.5 Calculated single-particle energies (s.p. E(keV)) for 5 Ni. ....... xi List of Figures 1.1 Systematics of the first ionization energy as a. function of atomic number. 2 1.2 Systematics of two-proton and two-neutron separation energies . . . . 3 1.3 Calculated nuclear shell structure for an infinite square well and har— monic oscillator nuclear potential ..................... 4 1.4 Modified nuclear shell structure with the inclusion of the spin-orbit interaction. ................................ 5 1.5 The ground state single—particle configurations and the low—energy level structure for 41Ca. ............................ 6 1.6 Experimental E(2T) systematics for a. series of isotones and isotopes. 9 1.7 E(2f) systematics for even—even N = 50 isotones and neutron—rich zirconium isotopes. ............................ 11 1.8 The E(2'lf) systematics for Fe, Ni, Zn and Ge in the vicinity of 28 S N S 50 ..................................... 13 3.1 Schematic diagram of the beta detection system utilized in experiment 97004. ................................... 25 3.2 Plastic scintillator, Ge and PIN electronic diagrams for experiment 97004. ................................... 27 3.3 PPAC and master gate electronic diagrams for experiment 97004. . . 27 3.4 Schematic diagram of the detector positions for experiment 98020. . . 29 3.5 Implant multiplicity for the DSSD. ................... 30 3.6 Decay multiplicity for the DSSD. .................... 31 3.7 Beam profile on the strip detector. ................... 32 3.8 DSSD electronics diagram for experiment 98020 ............. 33 3.9 PIN and PPAC electronics diagram for experiment 98020. ...... 33 3.10 Ge and master gate electronics diagram for experiment 98020. . . . . 34 4.1 (a) Energy loss versus time of flight plot representing all nuclei im- planted within the DSSD. (b) Implantation spectrum correlated with subsequent beta events ........................... 36 4.2 The decay scheme for 23217 ......................... 38 4.3 (a)The 57V half-life curve following the correlation of 57V implants and their subsequent beta decays. (b)Beta delayed gamma ray spectrum obtained by gating the total gamma ray spectrum on beta correlated 57V implants. ............................... 40 4.4 [SC-delayed gamma-ray spectra for 57V ................... 44 xii 4.6 Cfi CI! 05 U1 *1 R] 5.14 5.15 6.1 A.1 B1 B2 B3 8.4 B5 C.1 Beta-delayed gamma ray spectrum observed by Sorlin (it (11. following the decay of 57V. ............................. 268-") coincidence spectrum. ....................... The first excited 2+ energies, E(-'11+)/E(2}1) and the reduced transition probabilities for nickel isotopes in the region 28 S N S 40. The 69Ni levels identified by Grzywacz cf (1]. and the 69Co - 69Ni [3 decay sequence as proposed by Mueller et (1].. ............. ,3—delayed 7—ray spectrum obtained when the A1200 separator was tuned for peak production of 69M and “Cu. .............. Decay time curves for selected y-ray transitions identified during im- plantation of 67Co, 68 69Ni, 70 71Cu, 7'zZn. ................ 1298 7 coincidence spectra for the 80 and 120% Ge detectors. A portion of the 13— delayed gamma ray spectrum when the A1200 was tuned for the peak production of 69Ni and the peak production of 71C11. The ratio of gamma ray intensities during beam on and beam off cycles as a function of energy ........................... The particle identification spectrum during the second tune of the A1200 and energy-loss PIN spectrum gated on the 69Ni implants. Schematic of the ,3 decay of 69Ni. .................... The low-energy level scheme of 67Ni following the beta decay of 67Co. Beta-delayed gamma ray spectrum following the decay of 58V observed by Sorlin et (11.. .............................. The 58V half-life curve and the background subtracted ,d-delayed gamma- ray spectrum for 58Cr. .......................... Low- -energy level scheme for neutron— rich chromium isotopes in the range 28 S N S 36 ............................. E (2") systematics for neutron- rich nuclides between 20 _<_ Z S 28. Low-energy states for the odd- A Ar- — 29 isotones in the range 20 S Z < 28. .................................. Table of the isotopes ............................ GEANT simulated DSSD setup ...................... Total efficiency for the 120% Ge detector at a source-to-detector dis— tance of 45 mm ............................... Sum corrected peak efficiency for the 120% Ge detector at a source- to-detector distance of 45 mm. The solid line represents a fifth order polynomial fit to the data. ........................ The simulated Ge detector orientations .................. The experimental and simulated peak efficiencies for a point source. . The simulated peak efficiencies for an extended source. ........ Simple two photon decay scheme used to illustrate sununing corrections calculation. ................................ xiii 55 56 57 58 r 59 61 63 115 119 126 127 Chapter 1 Introduction 1.1 The Atomic Nucleus The atomic nucleus lies at the heart of all matter that surrounds us. It is a system on the order of 10—15 m, consisting of a collection of protons and neutrons. Considering that protons are positively charged, it would seem impossible to confine these parti- cles within such a small volume; the electromagnetic interaction among the similarly charged protons should cause them to repel. However, the predominant force within the atomic nucleus is the strong force. This attractive, short-ranged force counteracts the repulsive electromagnetic interactions, thereby enabling the nucleus to survive. The subatomic particles comprising the nucleus, the protons and neutrons, make up the class of particles known as nucleons. With the exception of their charge, qp :2 +1 and qn = 0, protons and neutrons are essentially indistinguishable. Pro- tons and neutrons have a spin of 1/2, are composed of three quarks (p = uud and n = udd, where u and (1 represent up and down quarks) and have a mass of 938.3 and 939.6 MeV/cz, respectively. Considering the atomic nucleus as a charge independent system, protons and neutrons can be treated as degenerate nucleon states. They are distinguished from one another with the assignment of a fictitious spin vector known as isospin [3] and they are given different projections within isospin space, :t1/2. This enables nuclear scientists to consider protons and neutrons independently of one another. 1.2 Development of the Nuclear Shell Model During the early studies of the atom, discontinuities were observed in the first ioniza— tion energy as a function of atomic number, where ionization energy is the amount of energy required to remove an orbital electron from an atom. The discovery of these discontinuities, see Fig. 1.1, at Z = 2, 10, 18, 36, 54 and 86 provided the first em— pirical evidence for the existence of an electronic shell structure for the atom. Using ao-— ~ , 7 , ~ 0 10 20 30 40 50 60 70 80 90 100 110 Atomic Number Figure 1.1: Systematics of the first ionization energy as a function of atomic number [4]. such models, atomic physicists were able to predict the properties of the atom in good agreement with experimental measurements. In the nuclear system, trends in nuclear masses and binding energies, B(Z,A), have suggested enhanced stability for nuclei associated with nucleon numbers 2, 8, 20, 28, 50, 82 and 126 (the magic nu- cleon numbers). For example, Fig. 1.2 depicts the difference in the experimental and theoretical two-nucleon separation energies versus nucleon number, where separation energy, S(p) or S(n), is the energy required to remove a nucleon, proton or neutron, from the nucleus. The peaks in AS(2p) and AS(2n), where S(2p) = B(Z,A) - B(Z-2,A- 2) and S(2n) = B(Z,A) + B(Z,A-2), suggest enhanced binding at the magic nucleon numbers. As in the atomic case the existence of these magic numbers have led to the 206) 15 $10] @ (u. 9 A9429) 0 is" ‘ >0 %® is A...) 3 1*, 21’s) % {S J \ C e,“- A8(2n) b O Figure 1.2: (TOp) The difference between experimental and theoretical two-proton sep- aration energies for a sequence of isotones. The lowest A members are noted. (Bottom) The difference between experimental and theoretical two—neutron separation energies for a sequence of isotopes. The theoretical two—nucleon separation energies were calculated based on the semi-empirical mass formula and the experimental values were obtained from Ref. [5]. This figure was adapted from Ref. [3]. development of the nuclear shell model, where the magic numbers correspond to the filling of major nuclear shells. To model the phenomenological trends of the nucleus, theorists tried to develop a mathematical formulism to reproduce the known magic numbers. A large energy gap was expected between adjacent single-particle orbitals at major shell closures. Thus, such energy gaps should be apparent within the shell model at the magic numbers. However, in order to construct a shell model, an estimate of the nuclear potential was necessary. Unlike the atomic case, in which the potential is supplied by the Coulomb field of the nucleus [3], the nuclear potential is unknown. Some early candidates for Infinite Well Harmonic Oscillator zg 1‘ 3p 4s,3d,29,1i .. —— @ 2f @ 2p,2f,1h 3s “—4— 2d 351M119 1. 2" @ 2p,1f .. 0 zs,1d 28 ...——— 1° 11 (D o . 13 Figure 1.3: Calculated nuclear shell structure considering the infinite square well and harmonic oscillator potentials [3]. the nuclear potential were the infinite square well and the harmonic oscillator. The single—particle orbitals calculated with these potentials are shown in Fig. 1.3. Not only were these potentials unrealistic (V —-> 00 at the boundaries of the nucleus), they did not reproduce the correct magic numbers above 20. As a next step, theorists considered the Woods-Saxon potential [6], —V0 V”) = 1+ 6.17p[(1' _ Roval (1.1) where V}, represents the depth of the potential, r is the distance from the center of the nucleus, R0 is the mean radius (R 1.25 fm A1/3), A is the atomic mass, and a is related to the “skin thickness,” 4a In 3, the distance over which the potential changes from 90 to 10% of V0. Unlike the infinite square well and the harmonic oscillator, the Woods-Saxon potential smoothly falls off to zero at large values of 7'. Although the Woods—Saxon potential is a more realistic form of the nuclear potential, it could not. reproduce all of the known magic numbers. The correct reproduction of the known A @ A — 99/2 __ __ d _— _ 21" _ sit: — 5’2 9712 — — 9312 (15,; _ as: _ _ — é _ __ > P: 2 g 63/2 2! {SI/2 _ _ ‘11: — ” — pa 2 — In -— IE — lull: — ‘5” hm _"‘ I712 — 91/2 — h11/2 --— p 3/2 _- 3/2 ,1” _ 9m —- O is” _ _ ’m _ Figure 1.4: Modified nuclear shell structure with the inclusion of the spin-orbit interaction [7,8]. This figure is not drawn to scale. —0 magic numbers was not achieved until the spin-orbit. interaction, -V(, r-é‘, where Vgs is a strength constant, was included within the overall nuclear potential [7, 8]. The 7'- 5? term of the spin-orbit interaction breaks the degeneracy for any pair of f > 0 states, drawing the f + 1/2 state lower in energy relative to the f — 1/2 state. This results in the reordering of the single‘particle orbitals as shown in Fig. 1.4. 1.3 The Structure of Nuclear Systems To the layperson, there is hardly a distinction between an atom and its nucleus. To a. scientist, the atomic nucleus is often thought of as a spherical body consisting of protons and neutrons. Nuclei with magic proton or neutron numbers may be described with spherical charge distributions and modest collective features at low excitation energy. Following the spherical symmetry of the potential away from major shell closures, the nucleus has been found to deviate from sphericity, evolving into oblate (discus-like) or prolate (football—like) bodies. 1.3.1 Nuclear Structure Near Shell Closures Nuclei near major shell closures may be described microscopically by the shell model. The properties of these nuclei have been predicted in good agreement with experi- ment considering an extreme single-particle shell model. According to this model, the properties of the nucleus are dictated by the behavior of a single unpaired nucleon. To illustrate this point, consider as an example 41Ca, which has 20 protons and 21 neutrons (see Fig. 1.5). In its ground state, the odd, 213’ neutron would reside in the 1f7/2 single-particle orbital. The predicted spin and parity for this state is 7/2" (J"' = Jf‘lll, where J and 6 represent the total and orbital angular momentum of the odd neutron). Experin‘ientally, the ground state spin and parity of 41Ca have been determined to be 7/2". S (a) —— 11' b ——- 2347: ”w :23: O— 19,” 5I2; 3/2 2010 “0-.- O-O-O-O- 1‘3]: :3 [:3 m- .. o ”5 ® Q) ”can Figure 1.5: (a)The ground state single-particle proton and neutron configurations and (b)the low-energy level structure for 41Ca [9]. The spectroscopic factor, S, is listed for the ground and first excited state of 41Ca. The parentage of a nuclear state is the fraction of that state that originates from a given nuclear configuration. To determine the parentage of the 7 / 2’ ground state of 41Ca, it is necessary to examine the spectroscopic factor of this state. Spectroscopic factors provide a way to describe the fragmentation of single—particle configurations among the states of a given nucleus [10]. These values are typically extracted from data obtained in transfer reactions, either involving the pickup or stripping of a nucleon by the fragment of interest. Thus, the spectroscopic factor is the overlap between the final state configuration and the configuration obtained by coupling an odd nucleon 6 with a (Z — I) or (N — 1) core. If there is no fragmentation of single-particle configurations, then S 2: 1. In reality, all states have some configuration mixing, thus 5' < 1. For 41Ca, several states have been assigned a spin and parity of 7/ 2‘, however, a spectroscopic factor has only been extracted for its ground state [11], providing an upper limit of 0.85. This suggests that the ground state of “Ca has at most an 85% component from the f7/2 single—particle orbital. In addition. the first excited state observed for 41Ca at 1.9 MeV has a spin and parity of 3/2'. This experimentally extracted J1r is in agreement with the excitation of the odd neutron to the lowest unoccupied single-particle neutron orbital. 2})3/2. Although the spectroscopic factor for this state is lower, 5' = 0.75 [11]. its configuration is predominately p3/2 in nature. This example of 41Ca represents a relatively simple configuration, however, most nuclei are more complex. 1.3.2 Quadrupole Deformation Between the magic shell closures, more complex excitations develop. Microscopically, it is difficult to calculate the configurations of these new excited states. However, macroscopically these states can be described as the result of collective interactions amid nucleons, which induce quadrupole (prolate/oblate) deformation. The extent of quadrupole deformation is quantified by the quadrupole deformation parameter, 132, and the Sign of ,62 provides information on the shape of the nucleus. Values of B; > 0 are indicative of a prolate shaped nucleus, while 132 < 0 suggests the nucleus is shaped like an oblate ellipsoid. Spherical nuclei have 132 z 0. Nuclear shapes may also be specified by 7 deformation, which is a measure of axial asymmetry. However, most known nuclei are believed to be axially symmetric, at least in their ground state [12]. Thus, for this study, the focus will be on quadrupole deformation. ‘1 1.4 Probing Nuclear Structure Quadrupole deformation is expected to be maximum at midshell. In order to study such phenomena, experimental probes of quadrupole deformation may be utilized. There are a number of experimental probes that can be employed to determine the extent of quadrupole collectivity for a given nuclear system. The probes that have been considered for this study include the energy of the first excited 2+ state, E(2T), and the ratio of the energies of the first excited 4+ and 2+ states, E(4T)/E(2f). 1.4.1 E(2fr) One measure of quadrupole collectivity in even-even (even number of protons and neutrons) nuclear systems is the energy of the first excited 2+ state, E(2f). This value has been shown to be sensitive to the overall coherence and collectivity in the wave function of the first excited 2+ state [13]. Figure 1.6 depicts the systematics of E (2?) versus nucleon number for a series of isotopes and isotones, nuclides with the same number of protons and neutrons, respectively. Similar to Fig. 1.2, peaks in E(2f) are apparent at the known magic numbers 8, 20, 28, 50, 82 and 126. Nuclei associated with a magic number of protons or neutrons exhibit an extra degree of binding, suggesting that excited nuclear states would lie high in energy. From a microscopic perspective, the peaks observed in the first excited 2+ states for even-even nuclides near shell closures are relatively easy to explain. A sufficient amount of energy must be supplied to the nuclear system to break a pair of nucleons and excite one member of the pair to a higher—lying single—particle orbital. Promoting a nucleon across a shell gap will require a significant amount of energy, resulting in high E(2f) values. Away from shell closures, anomalously “low” 2+ states were observed at energies even below that needed to break a pair of nucleons. Microscopically, this lowering may be attributed to multi—state mixing which draws collective quadrupole states lower in energy [13]. Macroscopically, the first excited 2+ state is lowered as the potential energy surface softens, allowing for deformation to set in. L (REV) l A 1 1 1 1 Atomlc Number Experimental E(21*) 5 m i\ O (E) l 1 1 1 120 140 Neutron Mmbor Figure 1.6: Experimental E (211') systematics for (top) a series of isotones and (bottom) a series of isotopes. Peaks in E (21*) values are apparent at nucleon numbers 8, 20, 28, 50, 82 and 126. The data was taken from Ref. [9]. Based on the trends of the first excited 2+ energies, Grodzins [14,15] derived the following empirical relation: 1225 MeV (1.2) Near major shell closures, nuclei are near—spherical, 132 z 0, and E(2f) values are large relative to neighboring even-even isotopes as shown by Eq. 1.2. As nucleons are added or removed from a closed shell, E (2?) will decrease, a result of the dominance of collective interactions among nucleons. As stated earlier, collective excitations should 9 be maximum at midshell. However. the development. of collectivity away from major closed shells may be inhibited by the presence of subshell closures. or minor shell gaps. Although the energy gaps between single—particle orbitals for subshells are not as dramatic as major shell closures, AB R 2 MeV as opposed to > 3 MeV [16], the properties exhibited by nuclei at or near subshell closures resemble those near major shell closures. For instance, similar to shell gaps, the structure of nuclei near minor shells are expected to be spherical, thus inhibiting the development of quadrupole deformation within a major shell. Therefore, in regions where one may expect large deformations, the contrary may be observed. The existence of subshells between major shell closures should result in similar E(2T) trends. As an example, the E (2?) systematics for even—even N 2 50 isotones are shown in Fig. 1.7a. The depicted E(2fL) values were obtained from Ref. [9,17]. Although the major proton shell spans from Z 2 28 — 50, there is a clear increase in E(2T) at 90Zr, Z = 40. This peak in E(2f’) suggests a substantial energy gap between the 7r2p1/2 and 71'199/2 single-particle orbitals, indicative of a Z = 40 subshell. An inspection of the E (21') values for neutron—rich, even-even zirconium isotopes reveals a similar peak at N = 56 (see Fig. 1.71)). Sadler et al. [18] have suggested that the significant energy gap between the V2d5/2 and the Vlg7/2 orbitals may be attributed to the N = 56 subshell. Thus, by examining the systematics of the E(2f) values, one may explore new features in nuclear shell structure, i.e. the development of quadrupole collectivity away from shell closures, the presence of subshell closures and changes in major shell closures away from beta stability. 1.4.2 Ratio of E(4f) to E(Zf“) Another method of exploring quadrupole collectivity in nuclear systems is by exam— ining the ratio of the first excited 4+ to 2+ states. This ratio indicates the type of deformation a nuclear system undergoes, whether it may be vibrational or rotational. Time averaged, a vibrationally deformed nucleus would appear spherical, as the 10 2+ 0.5‘ Excitation Energy (MeV) o~———————————————o+ 25 szceso 343350 361950 3331'» aozrso 42M°so «Ruso “Pd” 43de (1)) :—~. “Zr isotopes 9 2: E ' 8 ‘ 5 I” 1‘ s __..= a g 5 .8 005‘ —...‘_—'.' :5 " 1.— “ '——2+ 0 40 42 44 46 48 50 52 54 56 58 60 62 64 0+ Neutron Number Figure 1.7: E(2f) systematics for (a) even—even N = 50 isotones and (b) neutron-rich zirconium isotopes. The E(2f) values for Ge to Pd were obtained from Ref. [9,17] and Cd from Ref. [18]. system undergoes dynamic shape deformations. Such a system may be identified by examining the systematics of E(4f)/E(2l+). In a. vibrationally deformed system, the energy of the phonon state is: Em}, : (11+ 1/2)fi.w (1.3) where v = 0, 1, 2,..., w = (ls/11,)1/2, k is the force constant and 11 is the reduced mass. Thus, each of the states would be separated by an energy of 111.0. In an even—even nuclear system, the first excited 2+ state should be the lowest excited state, followed by a degenerate triplet of states, 03‘, 23' and 4;“ state. For an axially symmetric, vibrationally active system the E(4f) to E(21+) ratio should be m 2. As one continues to move away from major shell closures, the nucleus becomes increasingly deformed. As more valence nucleons become available, collective interac— 11 tions enhance. The nucleus undergoes a transition from dynamic to static deformation with the onset of rotational motion. In a. rotationally deformed system, the energy of a given state is: 152.1 (J + 1) ErratquJltl+ll (1.4) where I is the moment of inertia, Z,/1,ff, 1,1,- is the reduced mass of particle i, r,- is the perpendicular distance of particle i to the axis of rotation and J is the spin of the state. Based on this equation, a rotationally deformed axially symmetric system has a ratio of the first excited 4+ state to the first excited 2+ state m 3.3. 1.5 Motivation The aim of the present work was to explore the development of quadrupole collectivity for neutron-rich species within the N = 28 — 50 major shell. This shells extends over 22 neutrons, thus one would expect very deformed nuclear systems at midshell. However, the N = 28 — 50 shell has been shown to exhibit interesting features. For example, a clear increase in E(2,+) at N = 40, Z = 28 (see Fig. 1.8, data from Ref. [1,9,19,20]) has been observed by Broda et al. [1]. They suggested this peak was the result of an N = 40 subshell closure for nickel, which would inhibit the development of collectivity in this midshell region. Although a peak in E(2f) is not apparent at N = 40 for Fe, Zn or Ge, this may be due to the predominately proton nature of their configurations. If N = 40 is indeed a viable subshell closure, then the N = 28 — 50 shell is effectively split into two subshells, N = 28 — 40 and N = 40 — 50, which inhibits the full development of collectivity in this major shell. To determine the robustness of the N = 40 subshell, neutron-rich species near N = 40 were explored in this work. One such nuclide was 33C3u40, which was produced by the beta decay of ggNi“. If N = 40 is a good subshell closure, then the properties of 69Cu could be described by the extreme single-particle shell model as a. proton coupled to a 68Ni core. Details of this study will be discussed in section 5.1.1.2. 12 E(zi) .§§§§§§ / ll T V T l I l l l I T T I j 2628303234363840424446485052 NeutronNumber Figure 1.8: The first excited 2+ energies for Fe (orange circles), Ni (green diamonds), Zn (blue triangles) and Ge (purple squares) as a function of neutron number. Data were taken from Ref. [1,9,19,20]. Please note that images in this dissertation are presented in color. To investigate whether the N = 40 subshell strengthens for increasingly neutron- rich nuclides, an extension of the N = 40 study to lighter mass systems was of interest. Therefore, neutron-rich species within the N = 28 —- 40 midshell were examined. Similar to major shells, collectivity should be at a maximum in the middle of a subshell. Thus, one would expect deformed nuclear systems in the middle of the N = 28 — 40 subshell. However, following the fl-decay study of 58V, new empirical evidence for an N = 32 subshell was observed. Such discoveries warrant the need for further experimental studies into nuclear structure. Much of what is known about the properties of radioactive species approaching or near the neutron drip-line has been attained through the extrapolation of experimentally derived measurements of stable nuclei. By experimentally probing regions away from stability, theorists are presented with new data to check and refine their current models to better predict the properties of nuclei away from the valley of stability. For this study, it was of interest to populate the first excited 2+ and 4+ states in neutron-rich nuclides in the N = 28 - 40 subshell. As discussed above, the first excited 2+ and 4+ states are key to unveiling the structure of the atomic nucleus. The 13 method that was utilized to populate these states was 1'3 decay. 14 Chapter 2 Technique An important technique for studying the pr01.)erties of 1'1eutron-rich nuclei is beta- delayed gamma ray spectroscopy. Using this method, a nuclide of interest. is produced following the beta decay of its §_1X,\r+1 parent. During the course of beta decay, the parent nuclide may populate an excited nuclear state in the daughter. When this state de-excites, a gamma ray is emitted. providing a measure of the exact energy difference between nuclear states. By correlating the observed gamma ray transitions, one may construct an energy level scheme for the daughter nucleus. 2.0.1 Beta Decay Beta decay is a radioactive decay process that. involves the transformation of a neutron (proton) within the nucleus into a proton (neutron). In addition, two particles are emitted, a beta particle, which is a fast electron that originates in the nucleus, and a neutrino, an electrically neutral subatomic particle. Although the atomic number and neutron number will change by Z + (——) 1 and N — (+) 1 during this process, the mass number, A, will remain constant. There are three types of beta decay processes: 1. Electron capture : QXN + e‘ —) §_,YN+1 + l/ + QEC' [\D . 5+ decay : ‘QXN —> §_1YN+1 + 13+ + u + (2,34, 3. ,3" decay : ‘i/jXN —> §+1YN_1 + ,3" + D + Q3- where e‘ is an electron. 3* are beta particles, 1/ is a neutrino, D is an anti-neutrino 15 and Q5 is the difference between the initial and final nuclear mass energies [3]. Both 13+ decay and electron capture occur in nuclides that are neutron-deficient, however, they may not both be energetically possible. In order for beta decay to occur, the decay energy, Q3. must be greater than zero. In electron capture, the nucleus captures an atomic electron, producing a bound neutron. The only particle emitted from the nucleus following this process is a neu— trino. As the mass of a neutrino is extremely small, 2 0.1 eV [21,22], it is nearly impossible to observe this particle. In reality, electron capture is tracked not through primary particle emission, but rather secondary. When the atomic electron is cap- tured, it leaves a vacancy in the electron shell (typically the K shell). This is an unstable electronic configuration, and the electrons quickly reconfigure. A higher— lying electron de—excites to fill the vacancy and in the process gives rise to either detectable x-rays or Auger electrons. When the Q3 value is greater than 2mccz, twice the rest mass of an electron, 13+ decay becomes energetically possible. During this process, a bound proton is converted to a bound neutron. In addition, a neutrino and a 13+ particle are emitted. In 13+ decay, the beta particle is a positively charged electron, a positron. Since neutrinos are nearly undetectable, [3+ decay is monitored through the emission of positrons. Positrons are very reactive species. Unbound, they quickly combine with an electron and annihilate, emitting two 0.511 MeV photons in opposite directions. In addition, 13+ particles may be directly observed. Beta particles will interact directly with atomic electrons within the detection material. When the neutron-to-proton ratio in a nucleus is significantly larger than the ratio of the stable isobar, [3‘ decay is possible. During this process, a bound neutron is converted to a bound proton. In addition, a [3" particle (an electron) and an anti- neutrino are emitted. To monitor such a decay, the [3‘ particle must be observed. As in the case of 13+ decay, these particles are detected as they interact directly with the orbital electrons within the detection medium. For the present. study, _1’3’ decay will be the decay mode of interest. 16 By monitoring beta activity, the half-life of the initial decaying nuclide (the mother) may be deduced. The half-life is the time over which the initial number of atoms is reduced on average by one half [23]. Consider the first-order rate law, dN , N _ , where N and .N'YO represent the final and initial number of atoms of a given radioactive species and A is the rate constant. At 1N7NO = 1/2, tv [0 V I: fl/‘z Z —. (i. j3—decay half-lives typically range from a. few milliseconds to seconds or longer. This time is dependent on the differences in the spin, parity and energy of the original and final state to which the mother decays. During the process of beta decay, two particles, an electron and a neutrino, are emitted from the nucleus. Each particle has a spin of 1 / 2 and can carry orbital angular momentum. If their spins are anti-parallel (T1,, S = 0), the nuclear system will undergo a Fermi decay [3]. In an allowed/favored Fermi decay, the electron and neutrino are emitted with zero units of orbital angular momentum. Thus, there will be no change in the nuclear spin, AJ = [J3 — Jf] = 0. In addition, when f = 0, the parities of the final and initial states will be the same, 7r 2 (-1)f. If an electron and a neutrino have their spins aligned parallel (TT or 11, S = 1), then the system may experience a Gamow—Teller decay [3]. For an allowed Gamow-Teller decay, the electron and neutrino must carry away one unit of angular momentum. Thus, §XH+ QHY+43‘+D) (2m £=L+f mm and Uy—HSJfi§h+4,AJ=Q1 95) As for allowed Fermi decays, the initial and final states following an allowed Gamow- Teller decay will have the same parity (An = no). 17 Allowed 1‘3—decay transitions are among the fastest. However, it is also possible to undergo beta transitions in which AJ > 1 and/or the initial and final states have opposite parities. These transitions are classified as “forbidden.” Unlike the name suggests, forbidden transitions are feasible, however, they are slower than allowed transitions. Table 2.1 provides a list of known 1'3-decay transitions and a corresponding log ft range. log ft values can be used to provide a comparative half—life for a given transition. The log f term corrects the half-life measurement for the atomic number of the daughter and the maximum energy of the beta transition [23], due to the atomic interactions of the emitted electron, log f,3_ = 4.0 log Em” + 0.78 + 0.02 Z — 0.005 (Z — I) log Enzar (2.6) where Em,” is the difference in energy in MeV of the initial state in the mother and the final state in the daughter and Z is the atomic number of the beta daughter. logt is the logarithm of the partial half-life for the beta decay branch to a given state, total Triagt‘ial : Tl/f.’ (2.7) 1/ BR where BR is the branching ratio. Although some beta transitions may be classified as pure Fermi or Gamow-Teller decays, beta decays may also be characterized as mixed Fermi and Gamow-Teller transitions. 2.0.2 Beta-Delayed Gamma Ray Transitions Following 13-decay, the daughter nuclide may be left in an excited state. This state will de-excite through the emission of one or more photons, either directly or through a cascade of gamma rays to the ground state. The emission of gamma radiation is the result of changes in the charge and current distribution of the nucleus [23]. These changes give rise to electric and magnetic moments, respectively. Thus, 7—ray transitions may be classified as electric or magnetic in nature. Similar to beta particles, 7-rays may carry orbital angular momentum as they are emitted from an excited nuclear state. In general, the favored transitions are associated with the transfer of 18 Table 2.1: Selection rules for beta decay transitions [23]. Type A J A 71' log ft Superallowed 0,1 N o 3 Allowed (normal) 0,1 No 4-7 Allowed (f—forbidden) 1 No 612 First forbidden 0,1 Yes 615 First forbidden (unique) 2 Yes 9—13 [\9 Second forbidden No 11-15 Second forbidden (unique) 3 No 13-18 Third forbidden 3 Yes 17-19 Third forbidden (unique) 4 Yes Fourth forbidden 4 No ~23 Fourth forbidden (unique) 5 No the lowest amount of angular momentum. Gamma rays ejected with t” = 1, 2, 3, 4, A h of angular momentum are referred to as dipole, quadrupole, octupole, hexadecapole and 2’X-pole radiation. Transitions may be electric, magnetic or a combination of electric and magnetic in character. Electric and magnetic transitions may be differentiated by the relative parities of the initial and final states. Following an electric transition, the initial and final nuclear states will experience a change in parity when the emitted gamma ray carries off an odd value of angular momentum. In a magnetic transition, the initial and final states will have opposite parities if the gamma ray is emitted with an even unit of angular momentum. Thus, the selection rules for a gamma ray transition are as follows: [Ji —Jf] S /\ S [Ji-l-Jf] (2.8) AME) = (—1)“ (2.9) .37.:(111) -_— (-1)"+1 (2.10) A reasonable single-particle estimate for electromagnetic transition rates may be 19 calculated as follows [24]: , 87r(A +1) 1 l 2\ . ., .. . .7 ‘, E/N : f .' _ __ ,+l 412A+1 . .'/\ 2 Hf ) 0“A[(2A+l)!!]2h(hc) f 1311”” l f 11) f1. 87r(A +1) 1 1 . . . TW(MA) = 0M 9 «11 C)2/\l(")\ +1)”1'2 E(EVMIEZHIEMMA) (2.12) “1' p 4.: .o , where a is the fine structure constant (z 1/137), c is the speed oflight (2.998 x 1023 fm/s), Mp is the mass of a proton (938.3 MeV/c2), h is Planck’s constant divided by 271 (6.582 x 10‘22 MeVs), A is the multipole order and BW(EA) and BW(MA) are the Weisskopf single—particle estimates to the A” multipole reduced transition probability. The reduced transition probabilities are defined as: 1 3 B , EA 2 — —— '2 1.2 25,423“ '2 . .2" 2.13 u( ) “(ANN ) 6fm ( ) 10 3 . _. 2,\_—3 . _ EMMA) = ;(,—,;—3)2(1.2)2" 2.4 . #3., f7712’\ 2 (2.14) where [AM is the nuclear magneton, 233,,' The transition rates are calculated in inverse seconds. Transition rates can also be expressed in Weisskopf units. One Weisskopf unit for a At" multipole is equivalent to le(EA) or le(MA) depending upon whether the transition is electric or magnetic. Deviations from the single—particle estimate of the transition rates are calculated as the ratio of the experimentally extracted reduced transition probability and the single-particle estimate, Bap/8w. In addition, one may predict the lifetime of an isomeric state, a long-lived excited nuclear state, by multiplying the inverse of the transition rates by In 2. Table 2.2 lists the Weisskopf single-particle estimates for the reduced transition probabilities and EA and MA transition rates for several multipolarities, where E, is in units of MeV. 2.0.3 Summary To investigate subshell gaps in the midshell region of N =2 28 — 50, beta—delayed gamma ray spectroscopy was utilized. Using this technique, a nuclide of interest was produced by the 13‘ decay of its (Z - 1), (N + 1) parent. Since beta decay is a selective decay process following the rules indicated in Table 2.1, states in the daughter nuclide 20 Table 2.2: Weisskopf single—particle reduced transition probabilities and estimated transi- tion rates [24]. A Bttr(EA) (eff/n22) Bn'(:l-IA) (pafmz'vfz) 1 6.446 x 10-2 A‘Z/3 1.790 2 5.940 x 10-2 AW 1.650 A?” 3 5.940 x 10-2 A'2 1.650 A4/3 4 6.285 x 10“2 A3/3 1.746 A2 5 6.929 x 10-2 AW3 1.925 A8/3 A TleA) (S71) TwlMA) (S71) 1 1.025 x 10” E3 3.157 x 1013 E3 2 7.279 x 107 13: 2.242 x 107 E: 3 3.391 x 101 E: 1.044 x 101 E: 4 1.066 x 10-5 153 3.284 x 10-6 E3 5 2.396 x 10'12 E11 7.378 x 10‘13 E111 are preferentially populated if their spin, J], is equal to the spin of beta decaying parent state, J,- or if .1; = [.13 d: 1]. In addition, in allowed beta decay transitions the parities of the parent and daughter states are the same (A77 2 no). Beta decay may populate an excited nuclear state in the daughter. As this state de—excites, a gamma ray is emitted. The goal of this study was to populate the first excited 2+ and the first excited 4+ states via beta decay of even-even neutron-rich nuclei in the N = 28 —- 40 subshell. The energies of the 2;“ and 4;" states would be useful in extracting structural information concerning the nuclides of interest. 21 Chapter 3 Experimental Setup 3.1 Production of Radioactive Beams With the exception of several long-lived transuranic isotopes and a few other corn- mon radionuclides (i.e. 40K and MC), radioactive nuclides are not readily available on earth. In nature, these nuclides are produced within a stellar media during the course of their evolution. One method of producing radioactive nuclides within a lab- oratory setting is using a technique known as projectile fragmentation. The National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University is one of several facilities worldwide that utilizes this method for the production of radioac- tive beams. This technique, at the NSC L, entails the acceleration of a primary, stable beam within the K1200 cyclotron. Once the primary beam has been accelerated to a sufficient energy, it is impinged upon a thick, stable target (typically 9Be). As a result of this collision, the target will abrade nucleons from the initial projectile pro- ducing both stable and radioactive secondary beams ranging from the A and Z of the primary beam to hydrogen. To study the decay properties of a given subset of secondary beams, these nuclides must be isolated from the other reaction products. This separation was achieved by transporting the secondary fragments through the A1200 fragment analyzer [25]. The A1200 was designed to be achromatic, with two intermediate images between two sets of dipoles, whose bending radii were in oppo- site directions. Momentum slits were inserted at the first dispersive image to filter nuclides based on their momentum to charge (p/q) ratio. In addition, an aluminum 22 wedge was placed at the second dispersive image of the device to purify the secondary beams. This was accomplished by differentially degrading the energy of the secondary fragments as they traverse the wedge. By inserting a position slit at the focal point of the fragment separator, further constraints were placed on the secondary fragments, limiting the number of transmitted fragments. Once the secondary beams of interest were isolated from the other reaction prod- ucts, they were transported through the Reaction Products Mass Separator (RPMS) and finally to the S2 experimental vault where the beta detection system was located. The RPMS may be used to provide mass / charge separation of secondary fragments, however, during the two studies that will be discussed, the RPMS was not utilized for this purpose. Although some separation was achieved by applying a voltage of :1: 140 kV to the Wien filter, position slits were not inserted at the end of the RPMS. Therefore, for all practical purposes, the RPMS can be viewed as a beamline con— necting the S1 and S2 vaults. 3.2 Beta Detection System 3.2.1 Pulsed Beam Method, Experiment 97004 In conventional beta detection systems, a radioactive beam is implanted within a collection target for an implantation time, t,,,,p,a,,,. The beam is then inhibited for a period tdecay when the bulk activity of the beta decaying implants is monitored with a series of beta detectors surrounding the implantation foil. For this particular study, the collection foil was mounted on a rotating target wheel. The target wheel was 40 cm in diameter with nine Al collection foils, 165 mg/cm2 in thickness and 5 cm in diameter, equally spaced along its circumference [26]. The wheel was aligned at an angle of 450 with respect to the beam axis and located downstream from the end of the beam line, which was sealed with a kapton window. Two 3 mm plastic scintillators coupled to photomultiplier tubes were used to monitor the emission of 3 particles. In addition, two high-purity Ge (HPGe) detectors with 80 and 120% photopeak efficiency relative to a 3" x 3” cylindrical Nal(Tl) crystal were utilized for the detection of “prays. One plastic scintillator—Ge pair was aligned parallel to the beam axis and approximately 40 mm from the center of the collection foil. The second plastic scintillator—Ge pair was located directly behind the collection foil, such that the Ge detector was 15 mm. from the center of the foil. In this orientation, a total 13 efficiency of 40(2)% and a peak y-ray efficiency of 4.5% at 1.274 MeV was attained (see discussion in Appendix A—B). Further upstream from the beta detection system was a 300 um Si PIN detector. Secondary fragments were identified by their energy loss within this Si detector and their time of flight (TOF) from a plastic detector inserted at the first dispersive image of the A1200. Particle identification was also determined at the focal plane of the A1200 where a second 300 pm Si PIN detector was located. In addition, a parallel plate avalanche counter (PPAC) was placed upstream from the beta detection system. The PPAC detector consists of two parallel plate electrodes separated by a small gap [27]. The electrodes are encased between two thin mylar windows in a container filled with iso—octane gas at a pressure of z 5 torr. This gas-filled cell was used to determine the position of the secondary beams as they passed through the detector. Figure 3.1 is a schematic of the detector endstation used for this experiment. A cocktail beam consisting of 5.2% 67Co, 18.8% 69Ni, 12.9% “Cu, 25.7% 7Von and 37.4% of 68Ni + 70Cu was produced following the fragmentation of a 70 MeV / nucleon 76Ge19+ beam, provided by the K1200 cyclotron, in a 202 mg/cm2 Be target. The primary beam current was z 1.6 enA, resulting in the production of 69Ni at a rate of 86.7 s“. The magnetic rigidity, Bp, of the dipole magnets of the A1200 fragment analyzer were set to 2.505 Tm and 2.250 Tm, respectively. B represents the magnitude of the magnetic field and p is the radius of curvature of the fragments as they traverse the B field. The full momentum acceptance of the A1200 was set to 0.5% using momentum slits at the first dispersive image of the device. A 70 mg/cm2 Al degrading wedge was inserted at the second dispersive image of the A1200 to separate the fragments of interest from other reaction products following fragmentation. 24 PPAC Beam from RPMS Si PIN 3 mm plastic scintillators Ge Figure 3.1: Schematic diagram of the beta detection system utilized in experiment 97004. To study the beta decay properties of the nuclides of interest, the secondary beams were transported to the experimental endstation. After penetrating the PPAC detec- tor and the Si PIN detector, the fragments were transported through a kapton barrier which separated the beam-line vacuum from the beta detection system that was at atmospheric pressure. The secondary fragments were implanted within one of the nine aluminum collection foils of the rotating target wheel for twp)“, = 24 s. The beam was then pulsed off for 36 5. Once this cycle was completed, the target wheel was rotated to a new collection foil using a stepper motor whose controller was interfaced with the data acquisition system. The rotation of the target wheel required 250 ms. A second pulsing sequence was used with timplan, = 4 s and tdecay = 4 s to measure the half-lives of short-lived radioactive species. Data were collected only during the implantation and decay periods. Using a second tune of the A1200, a different subset of nuclides were produced. The new Bp setting for the second set of dipole magnets, 2.245 Tm, and a slightly larger full momentum acceptance, 1%, produced a cocktail beam of 68Co, 69’mNi, 71'72Cu and 7'3Zn. For the second tune, several different timpgant/tdmy sequences were used: 1.7 s/1 s, 1 s/l s, 24 s/36 s, 0.3 s/0.3 s and 33 ms/100 ms. 25 3.2.1.1 Electronics Figures 3.2 and 3.3 show the electronics diagram used for experiment 97004. The mas- ter gate was triggered by an event above threshold in either the germanium detectors, the plastic scintillators or the PIN detector. The master gate trigger from the PIN de- tector was downscaled by a factor of ten to prevent these triggers from dominating the master gate, as the beam implantation rate was rather high (z 1000 particles/sec). 3 — 'y coincidence events were identified, in software, as events that triggered one of the plastic scintillators and the non-adjacent Ge detector. 3.2.2 Continuous Implantation Method, Experiment 98020 Although the conventional beta detection method has proven to be quite useful in extracting beta decay information for radioactive species, it has two shortcomings. In this technique, (1) the bulk activity of the implanted species is monitored rather than monitoring the activity on a nuclide—by-nuclide basis; and (2) the beam is pulsed. Cycling the beam on and off reduces the overall counting statistics. To avoid these two limitations, a new beta detection system was developed. This system employed a Micron Semiconductor Ltd. type BB1 double-sided silicon strip detector (DSSD). The DSSD is a single silicon wafer segmented in 40 1-mm wide strips in both x and y dimensions, yielding 1600 pixels. These 1600 pixels behaved as 1600 individual detectors. A bias of -140 V was applied to the front of the strip detector, resulting in the collection of holes on the front and electrons on the back of the detector. The purpose of using this new beta detection system was to take advantage of the high pixelation of the microstrip detector to continuously implant short-lived activities over as much of the active area of the detector as possible and correlate implant and subsequent beta decays on an event-by-event basis. A 985-pm thick DSSD was selected to ensure sufficient Si for the detection of high-energy beta particles expected from the decay of nuclei far removed from the line of 13 stability. The DSSD was positioned between two 5 cm X 5 cm Si PIN detectors, placed at a distance of 1.9 cm and 5'" wi—lmwfl—lm NC I“! Am cro Fen Del-v rec Feet P \_> 5'” M, m A. a (a: or 52) a! P ”m May an Register CFO Fan Fm Del-v roc c, o (Ge1 or Ge!) ADC Slow Start Ste Rate ADC mac om +20 v PIN 9 Delay en Regleter ] cm Fen Del-v rec Feet Sealer Trigger downeoeled E by e factor of 10. Figure 3.2: Plastic scintillator, Ge and PIN electronic diagrams for experiment 97004. Bit Register I A Bit Register Gatel B - C Master Gate __; D E AND Fm ADC All Gates I Computer . TDC Start PA - Pie-Amplifier TFA - Time Filtering Amplifier PMT - Photo Multiplier Tube ADC - Analog-to-Digltal Converter TDC - Time-to-Digltal Converter TPHC - fime-to-Pulse Height Converter CFD - Constant Fraction Discriminator Figure 3.3: PPAC and master gate electronic diagrams for experiment. 97004. [\D ‘1 2.2 cm, respectively from the center of the DSSD. The upstream PIN detector had a thickness of 503 pm, while the downstream detector was 309 pm thick. The PIN detectors and the DSSD were mounted on an ISO—160 flange for easy coupling to the beam-line vacuum. Two 50-pin feed-throughs on this flange were used to bring the DSSD signals to a grounding board placed immediately outside the vacuum chamber. The grounding board provided a common ground for each output channel and six 34-way ribbon cables to transmit the DSSD output to the shaping amplifiers. During this experiment, NSCL fabricated preamplifiers with gains of 60 mV/MeV and rise and fall times of 50 ns and 100 ps, respectively, were utilized. These pre—amps were chosen because of their high gain and short rise time, which was necessary to trigger the electronics, namely the constant fraction discriminators (CFD’S), on the DSSD signals. In an earlier test run, preamplifiers obtained from Washington Univer- sity were used. Although these pre—amps were equipped with both fast (Trise = 7 ns and Tfall = 200 ns) and slow (TN-,6 = 1 [LS and 7'10” = 100 its) outputs, only the slow output signals were processed. The noise level from the fast output was considerably larger than that from the slow output, 125 mV peak-to-peak as compared to 3 mV peak—to—peak. Although the slow pre—amp signals were originally teed to provide both energy and timing signals for each DSSD channel, the signals could not trigger the CFD’s due to their relatively long rise time. The pre—amps, the DSSD and the vacuum chamber were all on a common electrical ground. The N SCL pre—amp signals were teed to yield an energy and time signal for each DSSD channel. The energy signal was recorded by processing the pre-amp output through a variable gain Washington University CAMAC shaper and then digitalized using a Philips 7164H ADC in CAMAC. Each of the 80 channels of electronics from the DSSD (40 strips x and y) were gain matched using high-energy alpha peaks from a 232U source. A timing signal was produced by first passing the pre—amp output through a fast amplifier. The amplified signal was sent through a Lecroy 3420 CF D with 100 ns delay chips. This signal was delayed 100 ns and teed to provide inputs for a Lecroy 4434 scaler, a Lecroy 4448 coincidence register and a Philips 7186H time- 28 to—digital converter (TDC). The master gate, defined as any trigger from the DSSD, served as a common start for the TDC. Further upstream from the PIN—DSSD-PIN detector telescope was a 300 um Si PIN detector. This Si detector provided energy loss and, in conjunction with the cyclotron radio frequency, time of flight (TOF) necessary for particle identification. In addition, two PPAC’S were placed upstream from the silicon telescope. The PPAC detectors were used for beam diagnostics, providing information concerning the beam position. Gamma ray emission was monitored by an array of Ge detectors. A 120% HPGe detector was positioned directly behind the ISO-flange. In addition, an 80% HPGe detector and three HPGe clover detectors (each Ge crystal within the clover had a relative efficiency of z 25%) were oriented in the plane perpendicular to the beam axis. The 80% HPGe detector was placed 8.5 cm from the center of the DSSD at an angle of 104° relative to the beam line. The three clover detectors were 8.1 cm from the center of the DSSD. offset by an angle of 4" relative to perpendicular. A depiction of the experimental endstation is shown in Figure 3.4. Ge Clover Detectors PPAC'S DSSD Figure 3.4: Schematic diagram of the detector positions for experiment 98020. 29 As a consequence of using single. high—gain electronics to process the DSSD energy signals, the high-energy implant events (E > 17 MeV) fell outside the maximum input voltage range of the ABC's and were recorded as overflow events. Moreover. the large pre—amp signal for a given strip induced signals in neighboring channels. This resulted in an implantation multiplicity greater than one in both the front and back channels. An average multiplicity of six in both x and y were recorded for a given implant event within the DSSD (see Fig. 3.5). To determine the pixel of each implant, the sum of Consecutive strip numbers recording an overflow were tallied and divided by the multiplicity for both the front and back of the DSSD. The most central pixel in the overflow array, along with its iii neighbors, where i is the implant strip, were identified as the implant pixels. 1000000 1 100000 i 10000 r 1000 iElFront lIBeck 100 10 1 8 7 8 9 1o 11 12 13 Multipllclty Counts Figure 3.5: Implant multiplicity for the DSSD. Multiplicity refers to the number of strips that were triggered for a given event. On average, six strips fired on the front and back of the strip detector during implantation. Unlike implant events, beta events could be isolated to the nearest pixel (see Fig. 3.6). This was due to the fact that the emitted beta particles were far less energetic than the implanted ions. In addition, rather than depositng their full energy within the DSSD, the beta particles were depositing a fraction of their total energy, AE, as they were emitted from a given pixel in the DSSD. These beta decays were then 30 1000000 i 100000 i 10000 , e a 100° , DFront 0 IBeck 100 i 10 i 1 L a 1 2 3 4 5 6 7 8 9 10 Multlpliclty Figure 3.6: Decay multiplicity for the DSSD. correlated with previously identified implants within a given pixel. Neighboring iz’cl pixels that had been labelled as implants for the same event were then zeroed. A cocktail beam consisting of 0.3% 54Sc, 1.5% 55Ti, 2.6% 56Ti, 37.1% 57V, 1.9% 58V, 3.8% 58(‘r. 47.2% 5E’Cr, 2.1% 60Mn and 3.4% 61Mn was produced by fragmenting a primary, stable beam of 70Zn18+ at 70 MeV/nucleon in a 155 mg/cm'2 9Be target. The primary beam current was z 40 enA, resulting in the production of 57V at a rate of 240 S“. The Bp setting for the dipole magnets of the A1200 fragment analyzer were 2.771 Tm and 2.645 Tm. The full momentum acceptance of the A1200 was set to 0.5% using momentum slits at the first dispersive image of the device. A 70 nig/cm‘2 Al degrading wedge was inserted at the second dispersive image of the A1200 to separate the fragments of interest from other reaction products following fragmentation. The secondary beams were then transported through the RPMS to the S2 vault where the experimental endstation was located. On average, ions were implanted into the strip detector at a rate no greater than 100 5‘]. The secondary beam was defocused in both x and y to illuminate z 2/3 of the active detector area. This beam profile, shown in Fig. 3.7, resulted in an average two—second time window between successive implants in the central most portion of the DSSD, ample time for measuring half-lives 31 Front Strips Figure 3.7: Beam profile on the strip detector. of the nuclides of interest. 3.2.2.1 Electronics A schematic of the electronics diagram is depicted in Fig. 3.8—3.10. The master gate was triggered by an event above threshold in the x and y strips of the DSSD. Implant events were identified in software as any event that triggered the strip detector and the first PIN detector without firing the third PIN detector. Decay events were identified in software as events that triggered the strip detector and either the second or third PIN detector without firing the first PIN detector. 32 ' 5'"... m ""1 +20V P Am Delay BitRegieter mm Delay Bit Register Figure 3.9: PIN and PPAC electronics diagram for experiment 98020. 33 Figure 3.10: Ge and master gate electronics diagram for experiment 98020. A and B are the front and back triggers as shown in Fig. 3.8. 34 Chapter 4 Sample Data Analysis for Continuous Beam Implantation The bulk activity measurement discussed in Sec. 3.2.1 made use of a Si PIN detec- tor to identify fragment implants and plastic scintillators for beta detection. When a fragment of interest was implanted into one of the nine Al collection foils, the primary cyclotron beam was stopped for a fixed time to reduce the beam-induced background in the scintillators during the beta detection period. To study the decay properties of short-lived, low intensity radioactive beams more efficiently, a new beta counting system has been developed. As discussed in Sec. 3.2.2, this new system employs a double-sided silicon strip detector (DSSD) to correlate fragment implants with sub- sequent beta decays. The goal was to take advantage of the high pixelization of the strip detector to continuously implant short-lived activities over the entire active area of the detector. This results in a two-fold improvement over the conventional beta detection system. (1)Each of the pixels can be treated as individual detectors, there— fore, an implant and its subsequent beta decay may be correlated within a given pixel on a nuclide-by-nuclide basis. (2)By maintaining an implantation rate of less than 100 s", the beam may be continuously implanted into the strip detector resulting in a duty factor on the order of 100%. 4.0.3 Test study, beta decay of 57V To ensure that the DSSD beta detection system was working properly. the decay prop- erties of a known nuclear system were compared with previously published results. The nuclide utilized for this test was 57V. which represented 37.1% of the implanted cocktail beam. 57V was identified based on its energy loss in the upstream Si PIN detector and time of flight from the cyclotron. see Fig. 4.1a. By placing a gate around the 57V contour in the particle identification spectrum and requiring coincident events in the other detectors within the experimental setup. the decay properties of 57V were extracted. AE (m. Units) “me of fllght (Arb. Unlts) . Time of flight (m. Units) Figure 4.1: (a) Energy loss versus time of flight plot representing all nuclei implanted within the DSSD. (b) Implantation spectrum correlated with subsequent beta events. As discussed in Sec. 3.2.2, implant events were identified in software as any event that triggered the DSSD and the first Si PIN detector, without firing the third PIN detector. The high-energy implant events were recorded as overflow events and re- sulted in an average implant strip multiplicity of approximately six, see Fig. 3.5. To determine the pixel of each implant, the sum of consecutive strip numbers were tallied and divided by the multiplicity for the front and back of the DSSD. The most central pixel, along with its ii] neighbors were labelled as implant pixels. In addition, each of the implant pixels were tagged with an absolute time stamp, the corresponding en- ergy loss of the implant in the first PIN detector and the time of flight of the implant from the cyclotron to the first PIN detector. If a second implant was identified in the 36 pixel within a 6 s time window before a. decay. the pixel was zeroed to reduce the chance of random implant-decay correlations. A timestamp was acquired by running two 16-bit clocks in parallel. One clock was incremented 65536 channels every two seconds, clock 1, and the other was incremented one channel per second, clock 2. An algorithm was written to create a. timestamp such that, clock. 2 * 65536 Timestmnp 2 clockl + H Overall, the timestamp had a 30 HS resolution. Ideally, a beta particle would be identified as an event that triggered the strip detector without triggering the upstream Si PIN detector. However, prior to the experimental run, the DSSD was energy calibrated with an open 232U source. The source was exposed to the DSSD within close proximity while the chamber was under vacuum for an extended period of time. Alpha peaks ranging from 5 — 8 MeV were observed in the DSSD energy spectra. To determine the origin of these alpha peaks, two background measurements were performed within % 18 hours of one another. During the first measurement an activity of 15.9 s‘1 was calculated by taking the ratio of the number of counts observed in the alpha peaks (1.40 x 105) to the total run time. The measured activity during the second background run was 13.2 3". Based on Eq. 2.1, a half-life of 2.79 d was calculated. Considering the decay chain of 232U (see Fig. 4.2), this half—life is close to the known half-life of 224Ra, suggesting that the DSSD was contaminated with traces of 224Ra. To isolate the DSSD triggers generated by beta particles from the 0 particles, beta decay events were identified in software as events that triggered both the front and the back of the strip detector and either the second or third Si PIN detector without firing the first PIN detector (see Fig. 3.4). This condition was imposed under the assumption that alpha particles would not have sufficient energy to exit the DSSD and trigger either PIN detector. By requiring additional conditions to satisfy a beta event, the overall beta efficiency of the DSSD was reduced. Table 4.1 lists the 63 values determined by taking a ratio of the correlated fragment—,3 spectrum, Fig. 4.1b, 37 232 u T1I2= 69.8 y Y 22811. T112: 1.91 y [7 224 Ra 1.1/2: 3:“ d (X. 220 Rn T1”: 55.6 s (I. 212Po DL 1' = 0.3 118 B 216”, l/ 112 64 212” 71/2: 0.15 s 208 a Pb 0‘ 13 / Stable B 20, $6 °lo TI 212 Pb 13,2: 3.05 min 1.1/23 10.“ h Figure 4.2: The decay scheme for 23211. to the implantation spectrum, Fig. 4.1a, on a nuclide-by-nuclide basis. The Q5 values and previously measured T1/2 are also listed for the readers convenience, where data were taken from Ref. [9,28—30]. In an attempt to simulate the beta efficiency, a Monte Carlo based simulation program, GEANT, was utilized. To ensure that the simulation program was working properly, a 90Sr source run was performed after the 224Ra contamination had decayed. Thus, the master gate was triggered only by beta events above threshold within the DSSD. The efficiency calculations using this point source are detailed in Appendix A. Using a source-to—detector distance of 26.7 cm, a lower limit experimental beta efficiency of 0.291(9)% was determined. To determine the intrinsic efficiency of the detector, the calculated efficiency was divided by the geometrical efficiency of the detector, 0.175%. An intrinsic efficiency of 166.3% has been determined. The intrinsic Table 4.1: Calculated beta efficiencies for the nuclides produced in Exp. 98020. In addition. the decay energies and previously measured Tl/‘Z are provided. Data were taken from Ref. [9,28—30]. Nuclidc c3 (%) Q3 (MeV) [9] T )2 (s) 548.: 1.723(3) 11.3 0.2 3(40) [29] 5613 1.531(2) 7.11 0.150(: 30) [23 ] 0. 190( (40) [30] 55Ti 1.431(5) 7.34 0.600(4 0) [23 ] 0.320 (60) [30] 58v 2.022(3) 11.6 0.203(20) [24,3] 0. 200( (20) [30] 57v 133(1) 3.02 0.323(30) (29 ] 0. 340 (30) [30] 5901 1.74(1) 7.77 0 7(40 240) [9] 580. 194(3) 3.97 .00( 30) )[9] 6% 192(2) 7.13 0. 710( 10) )[9] 60Mn 136(3) 3.24 510(6.() )[9] 60Mn’"1 8.51 1. 77(2 ))[9] efficiency is believed to be greater than 100% as a result of beta particles scattering off of the Al vacuum chamber and the A1 degrader to which the source was mounted. The scattered particles were effectively collimated, increasing the total beta efficiency of the DSSD in the given geometry. The GEANT simulation confirmed this hypothesis. The details on this simulation are also discussed in Appendix A. From this simulation, a 135.9% intrinsic beta efficiency was determined, which is 82% of the determined experimental intrinsic efficiency. To simulate the beta efficiency for Exp. 98020, the current FORTRAN code would need to be modified to account for the distribution of the beta source in the x-y plane within the DSSD. In addition, a distribution in implantation depth and straggling of the secondary beam should to be considered. An algorithm has been included in the GEANT code to vary the position of a beta particle in the z axis, however, at present, this routine has been commented out. Unlike implant events, beta particles deposited a small amount of energy, 0 S AF. S 0.56 MeV (considering a Q73 2 10 MeV), within the DSSD, thus a beta event could be isolated to the nearest strip. As depicted in Fig. 3.6, beta. events were predominately multiplicity one events. For those events that resulted in a multiplicity greater than one, the decay was isolated to the pixel that registered the largest energy loss. Once a 39 decay pixel was identified, it was tagged with an absolute time stamp and correlated with a previously identified implant (i:l:1) within the same pixel. Lifetime curves were generated by taking the difference between the absolute time of fragment implants and subsequent beta decays. Neighboring i:l:1 pixels with the same time difference were zeroed as they were set in the same implant array. The decay curve for 57V, shown in Fig. 4.3a. was obtained by gating the total lifetime (a) 300 1 1 1 ‘ (b) 80 1 ' ‘ 268 250 ~ r 60 — 7 .2 m C H 3 340‘ ' U U 20 _ 689 - l 473 1239 O T I I I O _ p— 0 1000 2000 3000 4000 5000 0 500 1000 1500 2000 Time (ms) Energy (keV) Figure 4.3: (a)The 57'V half-life curve following the correlation of 57V implants and their subsequent beta decays. (b)Beta delayed gamma ray spectrum obtained by gating the total gamma ray spectrum on beta. correlated 57V implants. spectrum on the 57V contour in the correlated-AB versus TOF spectrum (see Fig. 4.1b). The data was fit using a two-component exponential, one component for 57V and the other for the background, in PHYSICA, a mathematical analysis and data visualization software. Using the FIT command in PHYSICA, the fit parameters were varied to minimize the least—squares residual between the equation and the dependent variable [31]. From this least-squares fit, a half-life of Tia/2 = 358(62) ms was extracted. This half-life is consistent with the previous measurements of Sorlin et al. [29], T1/2 = 323(30) ms, and Ameil et al. [30], T1/2 = 340(80) ms. A beta-delayed gamma ray spectrum was also extracted following the decay of 57V. A total gamma ray spectrum was generated by adding the energy spectrum of one of the five Ge detectors (Ge 120%, Ge 80% and any of the three clover detectors) that observed a gamma trigger above threshold on an event-by-event basis. Figure 4.3b was produced by gating the total gamma. ray spectrum on the same 57V contour discussed 40 above. An intense gamma ray peak was observed at 268.1(1) keV. In addition, several small gamma ray peaks were observed at 473, 689 and 1239 keV. The smaller peaks are the result of a random background generated by the decay of the other radionuclides implanted within the DSSD. For instance, the 473 keV and 689 keV gamma rays are populated by the beta decay of 59Mn and the 1239 keV gamma. ray is fed by the beta decay of 59Cr. Background peaks. in addition to true ,3-delayed '7 peaks, have been observed in the beta-delayed gamma ray spectra for the other eight implanted radionuclides. Typically, the most intense gamma. ray peak(s) observed in the beta-delayed gamma ray spectrum corresponds to a true beta-delayed gamma ray transition in the nuclide of interest. Thus, the intensity of the 268 keV peak suggests that this peak is indeed the result of a 13-delayed y-ray transition in 57Cr and is not a random background peak. Considering the area of this peak, the (,3 value listed in Table 4.1 and the 6., determined in Appendix B, a beta decay branching ratio from the ground state of 57V to the 268 keV state in 57Cr may be extracted. To ensure that this branching ratio is correct, a nuclide with a. known branching ratio produced in this study was first analyzed. An 18(3)% beta branch has been determined for the ground state feeding of 61Min to the 629 keV state in 61Fe [32]. A 3-delayed gamma ray spectrum for 61Fe was produced in a similar manner as the spectrum for 57'Cr. 52:3 counts were observed in the 629 keV peak. Considering the beta efficiency for 61Mn (see Table 4.1), the gamma efficiency (0.0605) and the total number of 61Mn implants (493(1) x 105), a beta decay branch was determined as follows: Tcounts (629) 6); =1: c, 6111171 implants BR = = 0.374(524)% (4.1) This branching ratio is a factor of 21 smaller than the value reported by Runte et al. [32], suggesting that (,5 =1: e, is a factor of 21 too large. During the experimental run, a number of single-sided events satisfying a beta condition were observed. These single—sided events were originally assumed to arise 4’1 Table 4.2: Comparison of the number of experimental and simulated single-sided beta events. E 126 771 Erpe 1‘7 771 e nt 37172111017071 Single-Sided Front 1.97 x 105 3.25 x 104 Single-Sided Back 3.80 x 105 7.32 x 104 Neither Front nor Back 1.65 x 103 3.37 x 103 from the presence of dead strips or strips with high threshold settings on one side of the DSSD. To test this theory. a FORTRAN code was written to count the number of single-sided events expected for each side of the strip detector when a given number of beta particles were emitted into the detector. The user was required to enter the central position and F W'HM of the extended source each time the code was executed, and the position of the emitted beta. particle was varied such that by programs end, the source had a Gaussian distribution in both the x and y plane. Events identified in strips that were not working properly or set with high energy thresholds in the exper- iment were not counted. Table 4.2 lists the number of single-sided events observed in the simulation and experimentally when a 908r source run was performed. 7.69 x 105 beta particles were observed at an energy below z 6 MeV in the DSSD during the source run, thus, 7.69 x 105 beta particles were considered in the simulation. Although the ratio of the single-sided front to single-sided back events are comparable (52% from experiment and 44% from simulation), there are clearly more single-sided events observed experimentally. The reason for this discrepancy is unknown, however, it may explain the enhancement of Cg by at least a factor of 6. A significant portion of the enhanced 65*6, is believed to arise from improperly set gates on the ADC’s processing the germanium signals. “True” beta events were identified in software as double-sided DSSD events. The number of observed beta— delayed gamma rays may have been reduced because the ADC gates may not have overlapped with the actual coincident 7-ray energy signals from the Ge amplifiers. When the gamma ray spectra were examined without requiring a software beta coin- cidence, there were far more gamma rays observed because the master gate was set 42 by any event above threshold in the strip detector. Since there was a. large number of single—sided DSSD events, the gamma ray gate was almost always open, allowing one to see almost all the beta delayed gamma. rays within the limits of the Ge detection efficiency. However, the later gamma. ray spectra were uncorrelated. In an attempt to extract a beta decay branch from the ground state of 57V to the 268 keV state in 57Cr, the 57V branching ratio was normalized to the known branching ratio of 6‘ M 11, ')",~0,,,,,,(57l/') 6,3(61111 72) 6111172 imp. 6,.(611’1177) 72011711331111?!) 673(57V) 57V imp. (7(57V) 'i I) = 83(6111‘171) (4.2) Using Eq. 4.2 the enhancement of (fit, may be factored out. Based on this equation, a beta branch of 3623,76 was determined following the beta decay of the ground state of 57V to the 268 keV state in 57Cr. A i22% error was determined by propagating the statistical error due to the 57V related terms (:tl%) and the systematic error from the 6an related terms (i21%). In addition, an upper limit -4% error was determined for a possible 1% gamma ray intensity feeding into the 268 keV state in 5TV from a higher-lying state. In the absence of an additional gamma ray in the beta-delayed gamma ray spectrum for 57V, the intensity of such a gamma ray would be on the order of 1%. Considering this branching ratio, the extracted half-life and Eq. 2.6—2.7, a log ft range of 4.43 3 log ft 3 5.35 was determined, suggesting that the 268 keV state is populated by an allowed beta transition. To enhance the observed 7-ray spectrum, a second beta-delayed gamma ray spec- trum was obtained by accepting gamma rays observed within a 200 ms time window following the implantation of 57V nuclide (see Fig. 4.4a). To correct for random back- ground, the intensity of two non-57Cr peaks in the 57V-gamma spectrum, 726 keV and 1239 keV, were compared with the intensity of these peaks in the total gamma ray spectrum (shown in Fig. 4.4b). The 726 keV gamma ray is populated by the beta decay of 59Mn and the 1239 keV gamma ray is populated by the decay of 59Cr. The gamma ray peaks were fit to Gaussians using the Oak Ridge Display, Analysis and Manipulation Module, DAMM. A background correction factor of 0.859 was calcu- 43 lated by taking the average ratio of the area of the 726 keV and 1239 keV y-ray peaks in the 57V spectrum to the area of the same peaks in the total y-ray spectrum. By multiplying the total gamma spectrum by this correction factor and subtract- ing the resulting spectrum from the 57V-gamma spectrum, a. background subtracted 57Cr spectrum was obtained, see Fig. 4.4c. A single gamma-ray peak was observed at 268.1(1) keV. 3000 l l l 1 1 1 l 3000 l u_ 1 1 L 1 L 268 (a) 268 (b) 2500 4 - 2500 - . 2000 - - 2000 ~ _ .9 .3 c ,_ c _, _ {:33 1500 a 1239 8 1500 1239 Q 726 1000 - 725 '- 1000 - b 500 - — 500 4 c O I I I I I I I 0 I I I I I I I i 0 200 400 600 800 1000 1200 1400 0 200 400 600 800 1000 1200 1400 Energy (keV) Energy (keV) l l L l l l 1 14° ‘ 268 (C) ’ 120 r r 100 -‘ ' U) ‘5 80 ~ _ 3 o o 60 n _ 40 ~ — 20 i l. 0.4 0 200 400 600 800 1000 1200 1400 Energy (keV) Figure 4.4: (a)The Beta-delayed gamma ray spectrum following the beta decay of 57V, (b)the total gamma ray spectrum and (c)the background subtracted 3—delayed gamma-ray spectrum following the decay of 57V. Figure 4.5 depicts the [3-delayed gamma ray spectrum observed by Sorlin et al. [29] following the fl-decay of 57'V. The spectrum was obtained using bismuth germanate (BGO) inorganic scintillator detectors, which have a higher counting efficiency but poor energy resolution as compared to HPGe detectors. The authors identified three y—rays in Fig. 4.5 at 300(50), 700(50) and 900(50) keV. The authors also identified 44 5 1 tee-i LA '- -'__-,- l 200-- i-Hmm--- 150 F 100 I- 2 iii . Counts o i 1 1 Bug o 500 1000 1500 2000 2500 Energy (keV) Figure 4.5: Beta-delayed gamma ray spectrum observed by Sorlin et al. [29] following the decay of 57V. a 267(4) keV gamma ray in their 3—gated Ge spectrum, in the absence of the two higher-energy gamma rays, which is consistent with the current measurement. Sorlin et al. [29] extracted a 45(5)% beta branch to the 300(50) keV state following the beta decay of 57V, suggesting that the beta branch to the 268 keV state is indeed the result of an allowed beta transition. In an attempt to explore the low-energy level structure of 57Cr, a 268-7 coincidence spectrum was generated. This spectrum was obtained by recording y-ray transitions observed in one of the Ge detectors when another detected a 268 keV transition. Coincident gamma rays are observed if a transition overlaps within the resolving time of the spectrometer with the 268-keV gamma ray. The resulting 268-y spectrum is shown in Fig. 4.6. No coincident gamma rays were observed. 4.0.4 J 7' discussion 57V has 23 protons and 34 neutrons. In its ground state, the odd, 23rd proton resides in the 1f7/2 single-particle orbital, suggesting a J1r value of 7/2‘. The National Nuclear Data Center [33] has tentatively assigned the ground state spin and parity of 57V 45 20 1 l l 15- - 10* - Counts |l|| ll 1 0 500 1000 1500 2000 Energy (keV) Figure 4.6: 268-7 coincidence spectrum. as 7/2' based on the systematics of the odd-A vanadium isotopes. The extracted 4.43 S log ft 3 5.35 following the ground state beta decay of 57V to the 268-keV state in 57Cr suggests that this state is populated via an allowed beta transition. With this J " assignment, allowed beta transitions would populate states in 57Cr with a spin and parity of 5/2‘, 7/2‘ and 9/2' (see Table 2.1). Thus, the spin and parity of the 268 keV state in 57Cr should be 5/2', 7/2‘ or 9/2‘. The ground state of 5"'Cr has been assigned a J1r ranging from 3/2‘ to 7/2‘ [33]. Davids et al. [34] have assigned this state a spin and parity of 3/2", however, this J1r value was not directly measured following their 48Ca(“B,pn) study. The spin and parity were deduced by considering the decay scheme of 57Mn. Allowed 3—branches to the ground and 1835 keV states have been observed in 57Mn. Both states have a J’r of 5/2‘, thus, the possible J’r values for the ground state of 57'Cr are again 3/2‘, 5/2“ and 7/2'. In addition, Davids ct al. considered a state at 2188-keV that was assigned a spin of 1/2 by Aniol et al. [35]. Davids et al. identified a state at 2186—keV that was populated following an allowed beta branch from 57Cr. For the ground state of 57Cr to decay to the 5/2” and 1/2’ states in 57Mn via an allowed beta transition, the ground state of 57Cr is expected to be 3/2‘ [34]. However, this assignment relies heavily on the 1/2(_) identity of the 2188 keV state in 57Mn [35]. In the absence of 46 a. J7r confirmation, the ground state spin and parity of 57Cr can only be limited to 3/2", 5/2‘ or 7/2‘. In the event that the ground state .17r of 57Cr is either 5/2‘ or 7/2’, one would expect a strong ground state to ground state beta. branch from 57V to 57Cr. 4.0.5 Summary The decay properties of 57Cr have been examined following its production via. the beta decay of 57V. The goal of this study was to compare experimentally extracted properties with the previously published results to ensure that the new DSSD beta detection system was working properly. Utilizing this new beta detection system, a beta decay half-life of 358(62) ms was extracted, which compares well with Sorlin 61 al. [29] and Ameil ct al. [30] measurements. In addition, a beta-delayed gamma ray was observed at 268.1(1) keV, which is consistent with the 267 keV peak observed in the fi—gated Ge spectrum of Sorlin et al. [29]. A 36‘33‘0 branching ratio to the 268 keV state in 57'Cr was determined through a normalization to the 61Mn-628 keV beta branch. A range of log ft values of 4.43 S log ft 3 5.35 was determined, suggesting the beta decay of the ground state of 57V to the 268 keV state in 57'Cr is the result of an allowed beta transition. Based on the systematics of odd-A vanadium isotopes, the ground state spin and parity of 57V is expected to be 7/2', suggesting the J” of the observed 268 keV state in 57Cr is 5/2“, 7/2‘ or 9/2‘. An allowed fl-branch to the ground state of 57Cr may also be possible if its spin and parity is 5/2‘ or 7/2‘. 47 Chapter 5 Experimental Results & Interpretation 5.1 Subshell Gaps and Neutron-Rich Nuclei To predict the decay properties of nuclei away from stability, an understanding of nuclear structure is essential. To date, most of the information regarding the structure of extremely neutron—rich nuclides has been attained through the extrapolation of experimentally derived measurements of stable nuclei. However, if the magic numbers weaken or subshell closures (minor shell gaps) develop away from stability, this will have a profound impact on such predictions. For this study, the existence of the N = 40 subshell was investigated by examining the properties of 33M.“ and its beta decay daughter, 33cm. If N = 40 is a good subshell closure, then the low energy level structure of 69N i and 69Cu may be described as a neutron and a proton, respectively, coupled to the excited states in the underlying even-even 68N i core. In addition, it was of interest to extend the study of N = 40 to lighter mass systems. If N = 40 is indeed a good subshell closure, then collectivity should be maximum at midshell. However, following the beta decay study of 58V, new empirical evidence for an N = 32 subshell was observed. Comparing the first. excited 2+ state of 33Cr30 and the new measurement for 3§Cr34, a clear rise in E (27) was observed for 3§Cr32 relative to its N i 2 neighbors. This peak in E (27) for 56Cr suggests the existence of a significant subshell gap at N = 32. 48 0% ’ttt _..._4 5.1.1 Neutron-Rich Nickel Near N = 40 One region that. has attracted a. good deal of attention are nuclei within the vicinity of N = 40. Broda (I al. [I] suggested the existence of a subshell closure at N = 40, Z : 28 finding that the first excited 2+ state in 68M lies at an energy of 2.033 MeV. As compared to the E(2T) values of its even—even neighbors. see Fig. 5.1a, apeak in the first excited 2+ state energy is observed for 68M. This peak in E(2f) is believed to be an indication of a significant subshell closure at N : 40. Further support for an N = 40 subshell can be found in the recently measured first excited 4+ state of 68Ni. Ishii ef al. [37] observed the 4]" state of 68Ni at an energy of 3147 keV. The ratio of the first excited 4+ state to the first excited 2+ state is approximately 1.5, suggesting this nucleus is spherical in nature (see Sec. 1.4.2). Figure 5.1b depicts the E(4T)/E(2]") ratios for nickel isotopes ranging from N = 28 — 42. As neutrons are added to the 56Ni core, this ratio begins to increase, suggesting that collective interactions ensue. In the middle of the N = 28 — 40 subshell, the E(4f)/E(2']') ratio is maximum at a: 2, indicating that midshell nuclei are vibrationally deformed. However, by 68Ni, the E (41+) / .E (2?) ratio has decreased and is shell model in character. Raman et al. [36] have recently reported the reduced transition probability, B (E2), for 68Ni as 260(60) ezfm“. This value was provided by D. Guillemaud-Mueller and O. Sorlin in a private communication. The reduced transition probability is another experimental probe that may be used to determine the extent of quadrupole collec- tivity associated with a given nuclei. The reduced transition probability is related to quadrupole deformation as follows, 477 = 326R2(/B(E2;0T —> 2:) (3.1) ('32 where Z6 is the charge of the nucleus of interest and R0 z 1.25 fm 241/3. This equation suggests a small degree of quadrupole deformation (32 z 0.1) for 68Ni. As compared with the B(E2) values of other nickel isotopes in this region (see Fig. 5.1c) a reduction in quadrupole deformation is observed for 56Ni and 68Ni. 49 3000 1 1 1 1 1 1 1 1 a 2500-" ( ) '- g 2000 -‘ _- x V A 1500 -‘ - + P1 N 1000-1 [- v LLI 500 - l. O I I I I I I I I 26 28 30 32 34 .36 38 4O 42 44 2.5 l 1 l 1 l l l l A + v-1 2 0 Ci 15-4 r///. _ UJ \ A + v-i 1.0 ~ ~ <1- v “J 0.5 — — 0.0 I I n I I I I I 26 28 :50 .32 34 :56 38 4O 42 44 1000 1 1 1 1 4 1 L l I i (C) 2 4 m 0 O 1 —0—4 I B(EZ) (e fm ) 3 0 0 0 o o L l 200 — i ,_ O I I 1 I I I I I 26 28 30 :52 34 .35 38 40 42 44 Neutron Number Figure 5.1: (a)The first excited 2+ energies, (b)E(4f)/E(2T) and (c)the reduced transition probabilities for nickel isotopes in the region 28 g N g 40 [1,9,16,36,37]. Magicity was also suggested for 68Ni by Bernas et al. [38] following their spin assignment of 0+ to the first excited state of ggNiw. This J" assignment was made following an angular distribution measurement around 00 for the 7OZn(”C,“50) reac- tion. The authors based their hypothesis on the inversion of the 2? and 0'; states, which has also been observed in 513608., ‘2‘8Ca20, ggGem, 332F503 38Zr56 and flak/{056 [39]. The lowering of the 0'; state below the 2? state in 68Ni has been attributed to a two- particle excitation to the V1g9/2 orbital, resulting in a strong two—neutron coupling in this shell [38]. However, based on the 2? and 0'; spin inversion argument, their suggestion of magicity for 68N i was premature at best. The collective dynamics of 68Ni have been investigated by calculating its potential energy as a function of quadrupole deformation based on Hartree—Fock-Bogoliubov theory [39]. Two minima have been predicted, an absolute minimum at E = 0 MeV with ,8 z 0, and a local minimum at E z 3 MeV with fl z 0.4. The absolute minimum suggests that the ground state of 68Ni is spherical, whereas the local minimum is indicative of a deformed 02+ state. For this study, the existence of an N = 40 subshell was investigated by examining the properties of ggNi“ and its beta decay daughter, 33Cu40. If N = 40 is indeed a good subshell closure then the excitations in the A - 1 and A + 1 nuclei should consist of single-hole or -particle states coupled to excited states in the underlying even-even 68N i core [40]. In light of this argument, the low-energy structure of 69Cu will be discussed. Recently, several new microsecond isomeric states have been identified in the neutron-rich nuclides near 68Ni, including a 0.439(3) [18 state at 2.70 MeV in 69Ni [41]. The depopulation of this isomeric state in 69Ni follows mainly a three 7-ray cascade to the ground state (see Fig. 5.2a). Two weak 'y—ray cascades were also observed from this isomer, one terminating at a previously unidentified level at 321 keV in 69Ni. The authors proposed the 321—keV state as a second isomer in 69Ni with J7r = 1/2‘ (based on an assumed spin-parity of J7r = 17/2" for the 2.70 MeV isomeric state and a cascade of four stretched E2 transitions). They estimated a half-life, based on the 51 ’3 9L “"eisskopf estimate, of 2: 14 days for an M4 transition from the proposed 32l—keV isomeric state to the 9/2+ ground state of 69Ni. The more probable decay path for this isomeric state, as pointed out in Ref. [41], is :5 decay to the J7r = 3/2‘ ground state of 69Cu. Assuming a log ft value similar to that observed for the decay of the J’r = 1/2" ground state of 67Ni to the J7r = 3/2‘ ground state of 67Cu (log ft : 4.7 [32]), a 3 decay half-life of z 3 s was predicted [41]. Mueller et al. [42] studied the ,3 decay of 69Co and its subsequent daughters. The parent nuclei were produced by proton induced fission of 238U, and the Ion Guide Laser Ion Source [43] at the Leuven Isotope Separator On-Line was used to selectively ionize and efficiently extract the Co isotopes from the production target. They observed a 594—keV fl-delayed “pray transition, which they attributed to the decay of 69Co, and a 1298-keV transition assigned as a fi-delayed 7 ray following the decay of a 3.5(5) s isomeric state in 69Ni. This beta-delayed gamma ray was previously identified at 1296 keV [44]. The proposed sequence for the 69Co [3 decay is shown in Fig. 5.2b, along with the states observed following the decay of the 0.439 ,us isomer in ”M. (17/2-) 2701 439a: 0.22: o ' (1312-) 2552 “Go (1312+) — 2241 (I) (9I2-)- —- 1959 0’) (5I2-)— '- 915 915 (1,29 321 3 5 s 321 (912+)..1.___L 0 ”m 2.85 min 0 69c“ Figure 5.2: (a) The 69Ni levels identified by Grzywacz et al. [‘11] and (b) the 69Co - 69Ni B decay sequence proposed by Mueller et al. [42] Q1 [0 The recent improvement in the intensities of metal primary beams at the Na- tional Superconducting Cyclotron Laboratory (NSCL) at Michigan State University has allowed access to new regions of the chart of the nuclides for nuclear structure measurements. For example, the production of the 34(7) 5 isomeric state in 69Ni via projectile fragmentation was detailed in Section 3.2.1. A portion of the fl-delayed y-spectrum collected when the A1200 was set for the peak production of 69Ni from 76Ge is shown in Fig. 5.3a. The rotating collection wheel setup described in Sec. 3.2.1 was used for this measurement. All major transitions in the fi-delayed 7 spectrum could be attributed to known y rays from the decay of 69Ni or from the decays of 67Co, 68Ni, 70‘“Cu, and 7'ZZn (the major beam contaminants) except for a peak at 1297-keV. To investigate the origins of this beta-delayed gamma ray, the corresponding beta decay half-life was extracted. The half—life curve was gen— erated by gating a 16-bit clock in software with coincident beta particles observed in either of the two plastic scintillators incorporated within the setup (see Sec. 3.2.1) and 1297-keV gamma rays observed in the Ge detectors. The half—life curve for the 1297-keV transition is shown as an inset in Fig. 5.3a. The decay portion of the half— life curve was fit using PHYSICA with an exponential plus a constant background, and revealed a half-life of z 4 s, inconsistent with the known half-lives of the six constituents of the beam. For comparison, the half-life curve for the 1297-keV transi- tion is shown in Fig. 5.4 along with the half-life curves for the major 'y-ray transitions from four of the six radioactive nuclides comprising the secondary beams. In addition, the full—width at half-maximum (FWHM) of the 1297—keV peak in the fi-gated ’y-ray spectrum was found to be m 50% larger when compared to the FWHM of other peaks in this energy region, suggesting this peak is a doublet. To investigate the origin of the components of the 1297-keV doublet, the tune of the A1200 fragment analyzer was changed to implant a different subset of nuclei from the 76Ge fragmentation reaction. This second tune was set for the peak production of 7“Cu. In addition to this isotope, the secondary beam contained the radioactive nuclides 68Co, 69”Ni, 72Cu, and 73Zn. A portion of the fl—delayed y-spectrum for 200 _ 1296 keV (a) h I I T1/z = 3.4(7) S 150 " I = 100 ~ I F I 100 ~ ”N,“ 7°Cu o . I. I =-= 1 20 40 Time (s) 50 * 69Nim+7lcu 59Nil 0 .. I 1.1/2 = 19(3) 3 300 ~ I ~ = 100r I I I s I I I 200 '- 71Cu 1 1 20 40 "Cu Time (s) 71 73211 71 as .11: "Cu C C + N 100 - 11 “Ni‘ u 1 ”Ni‘ "Cu ”Zn Vicu 1200 1400 1600 Energy (keV) Figure 5.3: fl—delayed 7-ray spectrum obtained when the A1200 separator was tuned for peak production of (a) 69Ni and (b) 7“Cu. Known 7-ray transitions are labeled. The half-life curve shown as an inset in each spectrum corresponds to the 1297-keV doublet. the A1200 tune set for peak production of “Cu is shown in Fig. 5.3b. A 1297-keV doublet peak was also present in this fl-delayed y-spectrum; however, the relative ratio of the two components of the doublet have changed significantly (see Fig. 5.6). The half-life curve obtained for the 1297-keV transition during the second tune of the A1200 is shown as an inset in Fig. 5.3b. A single component fit (exponential plus background) to this half-life curve revealed a half-life of z 19 3, consistent with the adopted half-life of 71Cu (Tl/2 = 19.5 s). In addition, the 1298.1(4) keV transition, not previously assigned to the B decay of “Cu, is observed to be coincident with the known 489—keV transition in 7“Zn (see Fig. 5.5). Based on the half—life measurement 54 902 keV 680 keV 1000 E 70Cum E “Nig 500E T1)2 42(7) 3 ; TU2 = 11.7(6) s l l 100 50_ B 10 L 4 1 1 1 1 1 1 1 .L g 1296 keV 675 keV 694 keV 8 100 E ”Nim E “Cu E ”Co . Fl 0 10 20 30 O 10 20 30 O 1 2 3 Time (s) Figure 5.4: Decay time curves for selected 7-ray transitions identified during implantation of 67Co, 68’69Ni, 70'71Cu, 72Zn. The two nuclides denoted with a superscript of ‘m’ represent metastable/ isomeric forms of the indicated nuclide [45]. and 7-7 coincidence data, the higher-energy member of the 1297-keV doublet was assigned to the decay of 71Cu. The decay portion of the half-life curve for the 1297-keV doublet obtained during the first tune of the A1200 (Fig. 5.4) was fit taking into account a contribution from the 1298-keV transition now assigned to the ,8 decay of 7“Cu (Tl/2 = 19.5 s). A two—component fit , y(T) = A(69Ni) * arm-0.693 * T/ leg) + A(71Cu) * e.rp(—0.693 * T/19.5 s) (5.2) where T1/2 is the half-life of the beta-decaying isomer and A(69Ni), A(7‘Cu) are the corresponding activities of 69Ni and 71Cu at the beginning of the beam off cycle, (0) n 1 1 1 1 J 1 1 81 489 keV ‘ o 5‘ "' ‘E 5 4. - 2‘ .. , ILlLlllllLILlllLlfiLllLLJ 1, mum ,111 III, III 11, O 200 400 600 800 1000 1200 1400 1600 Energy (keV) (b) w l I L l l l l 8" 489 keV .. o 6" " ‘E 5 4. - 2'- .. 0‘ . l 0 200 400 600 800 ‘DOO 1200 1400 1600 Energy (keV) Figure 5.5: 1298-7 coincidence spectra for the (a) 80 and (b) 120% Ge detectors. The newly identified 1298-keV transition is observed in coincidence with the known 489~keV transition in “Zn. resulted in a deduced half-life of 3.4(7) s for the low-energy member of the l‘297-keV doublet. The short half-life of this 1296.1(2)-keV *y-ray cannot be attributed to the ground state decay of any species implanted when the A1200 was tuned for peak production of 69Ni. Although the half-life for the l‘296-keV transition is only slightly outside the 10 value of the measured half-life for 70Cug, the [3 decay of this nucleus is known [9] to feed only the ground and first excited (885 keV) states of 70Zn. There was no evidence of a 1296-885 coincidence in the 7-7 data, and the relative peak intensities of these transitions would imply a direct [3 feeding of > 10% if the 1‘296-keV transition directly populated the ground state of 70Zn. Since the 1296-keV transition was observed in the fi—delayed ”yr—ray spectra for both A1200 tunes, it may be attributed to a. [3-decaying isomer in either 69Ni or 71Cu, 56 l l l l L 140 — _ 120 — — 100 - — U) 'E 80-‘ — :3 O 0 60 - _ 4o — — 20 — — O l l l l l 1240 1260 1280 1300 1320 1340 1360 Energy (keV) Figure 5.6: A portion of the fi—delayed gamma ray spectrum when the A1200 was tuned for the peak production of 69Ni (black line) and the peak production of 71Cu (red line). which were the only two nuclei present in both radioactive beam implantations. From the difference in the production intensities of 69Ni and 71Cu and the change in the 1296-1298 7—ray intensities (see Fig. 5.6), the 1296-keV activity is correlated with the production of 69Ni. This suggests that the 1‘296—keV i3-delayed Array transition originates from a 3.4(7) s isomer in 69Ni. This transition is consistent with Mueller et al. [42], see Fig. 5.2b. To determine if other gamma ray transitions having a similar half-life to the 1296 transition were present, the gamma ray intensities during the beam on and beam off cycles were examined. By taking the ratio of the beam on to beam off intensity, a comparison of the half—lives of the beta-delayed gamma ray transitions observed in the Ge detectors were made. Nuclides with short fl-decay half—lives would result in a. larger beam on/off ratio relative to longer-lived species. Figure 5.7 depicts the ratio of the on /off intensities for the main fi—delayed gamma ray transitions. These data was generated by examining the fl-delayed 7-ray spectra gated on the beam—011 and beam-off cycles. The gamma ray peaks were fit to Gaussians and their areas were 57 J 32 T €15 + l g1 Qi iii 1 { § {i f 5 30.5 i %+ i. . o 1 . . T . . . i o 200 400 600 800 1000 1200 1400 1600 1800 2000 Energy (keV) Figure 5.7: The ratio of gamma ray intensities during beam on and beam off cycles as a function of energy. The green diamonds correspond to gamma ray transitions following the beta decay of 69Ni, the pink squares 71Cu, the blue circles 70Cu and the black triangles correspond to transitions of unknown origin. Note that no other transition is observed with an equivalent half-life to the 1296 keV gamma-ray. extracted using DAMM. No evidence for other transitions having a similar half-life to the 1296-keV gamma ray were observed. This implies that the 1296-keV state in 69Cu is the only excited state significantly populated following the beta decay of 69Ni“. Branching ratios following the beta decay of the 1/2‘ isomer in 69Ni to the 1296- keV and the ground state of 69Cu were extracted. To perform this measurement, it was necessary to calculate the total number of 69Ni nuclides implanted within the collection foil. A particle identification spectrum taken when the fragment analyzer was set for the peak production of 69Ni is shown in Fig. 5.8a. Yellow ovals have been drawn around each of the radionuclides implanted within the collection foil. Assuming the counting efficiency of the upstream Si PIN detector (see Sec. 3.2.1) was a: l, a one-to—one correlation could be made between the total number of 69N i observed in the Si PIN detector and the number of 69Ni nuclides implanted within the collection foil. As one may note, however, there is an overlap between the 67'Co and 69Ni nuclides €58 a x . c l _ =3 1 l _ S . ( V 67 l ” ||l C04; < y/. 2 i _ f x l ,4 - .37 \f- 2io 22'0 230 25.0 250 2:0 TimeofFlight(Arb. Units) AE (Arb. Units) Figure 5.8: (a)Si PIN energy-loss as a function of time of flight. This particle identification spectrum was taken when the A1200 was set for the peak production of “9X6. The yellow ovals have been drawn around the individual radionuclides implanted within the collection foil. (b)Bnergy-loss in the Si PIN detector gated on the 69Ni implants. The black circles represent the data, the red line is the fit to GTCO, the green line is the fit. to 69N1 and the blue line is the summed Gaussian fits. (see Fig. 5.8a). To determine the total number of 69Ni implants, a gate was drawn around 69Ni in the PIN AE versus radiofrequency spectrum and projected onto the PIN energy loss spectrum. As shown in Fig. 5.8b. this condition produced a doublet peak in the PIN AE spectrum, consisting of a 67Go and 69Ni component. To resolve the 69Ni peak, this doublet was fit with two Gaussian curves. The individual and summed Gaussians are shown in Fig. 5.8b. From the Gaussian fit, a. total number of T.23(26) x 105 69Ni implants were identified. Assuming that for each 69Ni isotope implanted there is a. corresponding beta decay, 2.8908) x 105 beta particles should be observed, based on a 40(2)% 1’? efficiency. Details on the beta efficiency calculation are provided in Appendix A. To determine the number of beta particles emitted following the decay of the 1/2' isomeric state. it was first necessary to determine the total beta particles emitted from the ground state decay of 69Ni, as N,,(69Ni) = N3(g.s.) + A130 /2-) (5.3) This was accomplished by applying a Gaussian fit to the 1871-keV gamma ray of 69Cu, a known fl-delayed gamma ray transition originating from the ground state of 59 69Ni. Factoring in the beta. efficiency. the gamma. ray peak efficiency, 1.29%, and the relative gamma ray intensity, 0.41 [9], the total betais attributed to the ground state decay of 69Ni was determined to be 269(8) x 105. A description of the gamma-ray peak efficiency calculations are provided in Appendix B. Based on Eq. 5.3, the total number of betas emitted following the decay of the 1/2‘ isomeric state is 207(194) x 104. This consists of the number of betas decaying to the 3/2; 1296-keV excited state and the 3/21‘ ground state of 69Cu (see Fig. 5.2). A total of 2.54(31) x 104 beta particles were calculated to feed the 3/22' state in 69Cu. This value was deduced by considering the intensity of the 1296-keV transition in the ,B-delayed gamma ray spectrum, 3.73(46) x 102, corrected for the 1296 peak efficiency, 1.47%. Based on the errors of this calculation, an upper limit of 36% was extracted for the fl-branch of the 69Ni 1/2' isomer proceeding to the ground state of 69Cu. Considering the measured half-life, the beta branches and Eq. 2.7, the partial half-lives for the beta decay to the 3/21' and 3/22- states in 69Cu were determined to be 9.44 8 (lower limit) and 5.31 8 (upper limit), respectively. In addition, taking Eq. 2.6 into account, where Q3 was taken from Ref. [9], log ft values of 4.54 (upper limit) and 5.23 (lower limit) to the 3/2; and 3/21- states in 69Cu, respectively, have been deduced. 5.1.1.1 Configuration mixing in 69Cu From the experimental data for 69Ni’"1 decay, we can conclude that the ,8 decay of the 1/2' isomer in 69Ni mainly proceeds through the excited 3/2" state at 1296 keV in 69Cu. No other excited state in 69Cu has been observed in the isomer 8 decay, neither in the present study nor in the data of Mueller et a1. [42]. The allowed character of the Gamow—Teller transition from the 1/2“ isomer in 69Ni to the excited 3/2' in 69Cu can be understood schematically assuming the pure configurations indicated in Fig. 5.9. Taking the ground state of 68Ni as the reference state, the initial 1/2’ configuration in 69Ni can be written as: [1/2_> = [VQPf/lz (”196/2)0+> (5-4) 60 -1 2 1/2- vz9112("199/2 ’o+ 32 keV / 69 m log ft > 5'23 1'2":a/2("z"iz/2"1992/2 10+ < 4.54 Figure 5.9: Schematic of the 1'3 decay of 69Ni depicting the configurations discussed in the text [45]. and the final 3/2‘ configurations in 69Cu are: ]3/22_> : [71'2p3/2 (V2157) u1g3/2)0+) (5.5) and [3/2éns> = [n2p3/2>. (5.6) We can rewrite the configurations given in Eqs. 5.4—5.6 describing all the excita- tions in terms of particles instead of particles and holes. This reduces to using the ground state of 66Ni as a reference state. The expressions become: [1/2-> = [V2P1/2(V19 (5-7) for the 1/2‘ state in 69Ni and [3/2;) = [7T2p3/2 (mg/2),”) (5.8) and [3/2és.> = [n2p3/2 (VZPf/2)o+> (5.9) for the excited 3/2' state and the ground state of the daughter nucleus 69Cu. It is a good approximation to assume that the pair of 199/2 neutrons, present in the wave function of the parent 1/2" state, plays no role in the [3’ decay process. The matrix elements for the Gamow-Teller decay then reduce to (3/‘22‘IT(GT)Ill/2‘> = (w2p3/2IIT(GT)|II/‘2p1/2) (5.10) <3 2g.s.IIT(GT)II1/2'> 2 0. (5.11) Therefore, assuming the wave functions of the parent and daughter states can be described by pure configurations, the L3 decay of the 1/2‘ isomer of 69Ni should proceed only to the excited 3/2‘ state at 1296 keV in 69Cu. Some configuration mixing, resulting in a fragment of the 7r2p3/2 <32:- z/(Igg/22pl722) configuration in the ground state of 69Cu, can produce branching to the ground state from the decay of 69Ni"”. The upper limit of 4.54 for the log ft value for the decay of the 1/2’ isomer in 69Ni to the 3/22“ state in 69Cu compares rather well with the value log ft 2 4.7 obtained for the decay of 67Ni 1/2‘ ground state (Tl/2 = 21(1) 5) to the 3/2‘ ground state of 67Cu [32]. This agreement is only qualitative, since the variation of the reduced transition probability B(GT) is roughly a factor of 1.7 for the log f t—values quoted above. The configuration mixing in the 1/2‘ and 3/2‘ states connected by the GT transition seems to decrease when going from A = 67 to A = 69. The two particle- two hole (2p-2h) configuration involved in the structure of the 3/2; state in 69Cu is expected to be mainly concentrated in this state, and some fragmentation is needed to account for branching to the ground state. Using the upper limit of 36% obtained for the fl—branching to the ground state of 69Cu in the decay of 69Niml, the amount of 2p—2h configuration mixing in the ground-state was determined to be < 15%. This value was deduced by relating the ft values for the isomeric beta decay to the ground and excited 3/2‘ states in 69Cu to the probabilities of observing these states with a 7r2p3/2 63) V(lg§/22pl')‘iz), (12, and a pure 7r2p3/2, ()2, configuration, ft(3/27) _ a2 ft(3/22‘) ” b2 assuming that 69Ni’"l would beta decay to only one of these two states (a2 + b2 = 1). A similar 2p—2h admixture was calculated for the ground-state of 67Co, using a QRPA approach, in a recent fl—decay study of the 67Co —+ 67Ni by Weissman et al. [46]. In that case, the neutron 2p—2h admixture in the 7/2" ground state of 6"'Co can produce a fl—branch to a state with mainly a Mfg/12 C?) Wig/22.121722) configuration via the allowed 1/1f5/2 —> 7r1f7/2 GT transition, see Fig. 5.10. Experimental evidence 62 was found for the population ofa second 5/ 2 state at2 .1 MeV with log f=t 5.5. The interpretation in terms of the above configuration is only tentative. Particle-vibration coupling can give rise to fragmentation of the single—particle strength in nuclei around closed shells (see for example, the study of 57Cu —> 57Ni by Trache et al. [47]), and a non-negligible fragment of the hole-state ft): in a state with mainly a 2+(68Ni) 1‘3 p172 structure can be expected around the energy of 2.1 MeV. 11,2: 425(20) ms Qfl= 8422 keV lap/0) log ft 5 5(2) 5.5 2155 (v1 512)“ 21(“ND 91.5(3.5) 4.7 (Sn-i 594 1 v(19912291121512) (UN 0 -1 57 NI V2512 Figure 5.10: The low-energy level scheme of 67N1 following the beta decay of 67'C-0. The configurations for the excited and ground states of the parent and daughter nuclide have been labelled as discussed in Ref. [46]. The < 15% 2p-2h mixing deduced for the ground state of 69Cu is only an upper limit, derived from the upper limit of 36% on the fl—branching from the 69Ni 1/2‘ isomer to the 69Cu ground state. Taking the 13 branch for this decay as zero, which would translate to no 2p-2h mixing in the ground state of 69Cu, the log ft value for the 3/22 state in 69Cu becomes 4. 3. It should be noted that if the branch for the 691\1iml decay to the ground state of 69Cu is near the established upper limit, its origin can be readily explained by the configuration mixing arguments presented above. In fact, 63 the 2p—2h configuration is the only low-lying configuration expected to be populated in the allowed GT transition from the 2p-1h 1/2‘ isomer. Another higher—energy GT transition l/lfs/Q -—> 7r1f5/2 can lead to the 7r1f5/2 <13} (V2pf/121f'ilzlgg/2) configuration. This has some overlap with the particle—vibration configuration 7r1f5/2 G1) 2+(68Ni) and can give a small admixture in the 3/29‘5. The quadrupole matrix element for f5)? - 113/2 is small, due to the spin—flip involved. The resulting admixture would result in a. (3— branch with a relatively large log ft value. The degree of 2p-2h correlations in the ground state of 68Ni, evident from the configuration mixing derived experimentally in 69Cu, can provide a measure of the validity of the N = 40 subshell closure. Assuming the u(2p,—/22193/2) mixing in the ground state of 68Ni is similar to that deduced for 67Co and 69Cu, such a small value (< 15%) suggests “double—magic” (proton shell closure and neutron subshell closure) character of this nucleus. A reduced mixing is also consistent with the predicted deformed character of the 03’ state in 68Ni [39]. However, with limited mass measure- ments of Ni isotopes in this region, this interpretation cannot be substantiated by the present data available (experimental and extrapolated) for two—neutron separation energies [5]. 5.1.1.2 Summary A 3.4(7) s isomeric state has been directly populated in 69Ni following fragmentation of a 76Ge beam at 70 MeV/nucleon in a Be target. This state, proposed to have a configuration V(p1'/lzg§/2), was observed to populate a single excited 3/2’ state at 1296.1(2) keV in the daughter 69Cu with an allowed GT transition (log ft 3 4.54). A 6 branch to the 3/2‘ ground state of 69Cu in the H decay of the 69Ni 1/2" isomer can result from a neutron two particle - two hole admixture in the ground state of 69Cu. Based on an upper limit of 36% for this 6 branch, an upper limit of < 15% was deduced for the configuration mixing, similar to that deduced for 67Co [46]. This small 2p-2h admixture in the ground state of 69Cu suggests that this nucleus exhibits single-particle character and can be described as a proton coupled to a 68Ni core. The 64 dominance of a. 68Ni core in the excited states of 69Cu provides a strong case for the N = 40 subshell. 5.1.2 Neutron-Rich Nuclides Near N = 32 To determine the robustness of the N = 40 subshell, it was of interest to pursue increasingly neutron-rich nuclei in the vicinity of N = 40. If N = 40 is a good subshell closure for 68N i. then it may develop into a real shell closure for lighter mass systems [40]. Thus, in an attempt to characterize N = 40, nuclei in the midshell region of N = 28 — 40 were examined. One would expect the collective nature of these nuclei to be maximum at midshell. However, systematics for Ca isotopes in this region suggest the existence of a new subshell at N = 32. Such a subshell would diminish the extent of quadrupole collectivity associated with nuclei in this midshell region. Based on self-consistent energy density calculations, Tondeur [48] proposed N = 32 as a new magic number for neutron-rich nuclides. Following the beta decay of 52K, Huck et al. [2] assigned the 2.56 MeV state in ggCagg a spin and parity of 2+ at a sig— nificantly higher energy compared to the first excited 2+ level in 50Ca. Based on this finding, Huck et al. [2] suggested the rise at N = 32 was due to the V2p3/2 subshell closure, indicating that N = 32 was semi-magic. This assertion was consistent with Tondeur’s theoretical prediction [48]. Following a mass measurement of 52Ca [49], an increase in binding was also noted at N = 32. However, when considering the rise in E(2f) for 52Ca, one must bear in mind the uncertainty associated with the spin and parity assignment of this state. In addition, in the absence of mass measurements for 54Ca and more neutron-rich calcium isotopes, the systematic variations of pairing energy and two—neutron separations are inconclusive. Using a shell-model calculation, Richter et al. [50] predicted the first excited 2+ state of 52Ca will lie at 1.85 MeV. Recalculating the single-particle energies of this nuclide based on a shell-model plus Hartree—Fock approximation [51], the 2:" state was predicted at 1.91 MeV. Both of these theoretical values are significantly lower than the suggested experimental value 65 of 2.56 MeV. Based on this finding, the authors [50,51] attributed the rise in E(2T) to the filling of the V2p3/2 subshell, suggesting N = 32 is a good subshell closure for calcium. The motivation for the present. study was to explore the mass region A = 50 — 60 to confirm the N = 32 subshell closure for neutron—rich nuclides. For this work, the properties of neutron-rich Cr isotopes were examined. 5.1.2.1 Beta decay of 58V .56 Similar to the case of ggCag-z, the first 2+ state of 24Cr32 lies higher in energy relative to its N —— 2 neighbor, 54Crgo. However, unlike 52Cagg, the spin and parity assignment of the 2+ level for 56Cr32 was deduced from the shape of proton angular distribution curves following its production via the (t,p) reaction [52]. A second (t,p) study con- firmed the spin-parity assignments for a number of states, including the first excited 2+ state at 1007 keV [53]. The authors also reported that shell model calculations reproduced the energy of the first excited 2+ state. To determine whether the first excited 2+ energies continued to rise or peaked at N = 32, it was necessary to mea- sure E(2'1+) beyond N = 32. Thus, for this study, the low-lying levels of 58Cr34 were investigated. Ameil et al. [30] recently measured the fl-decay half—lives of several neutron— rich isotopes of Ti to Ni following their production via the fragmentation of a 500 MeV/ nucleon 86Kr beam in a thick Be target at GSI. One of the nuclides produced during this reaction was 58V. Following its beta decay, a half-life of 200(20) ms was extracted. Sorlin et al. [29] have also investigated the beta decay properties of neutron- rich nuclides in this region of the chart of the nuclides. Following the fragmentation of a 64.5 MeV/ nucleon 65Cu beam in a 9Be target, neutron-rich Sc and V isotopes were produced at GANIL. During this study, a 205(20) ms beta decay half-life was mea- sured following the decay of 58V. In addition, a beta-delayed gamma ray spectrum was acquired, see Fig. 5.11. Sorlin et al. observed a broad peak at 900(100) keV in BGO scintillator detectors following the beta—delayed gamma emission of 58V. This 900- 66 I I I I 40 I- u 35 )- .1 30 )- - a 2»- a . g 20 1— " -l U ,’ ‘ 15 I- 1 d ‘0“. “ 1o 3 "~. E o J l l 0 500 1000 1500 2000 2500 Energy (keV) Figure 5.11: Beta—delayed gamma ray spectrum following the decay of 58V observed by Sorlin et al. [29]. keV transition had a FWHM approximately twice that of other transitions observed in their BGO detectors. The authors proposed this peak as a doublet, which may contain the 4+ —> 2+ —-> 0+ cascade. Assuming E(2l+) = 800 keV and E(4f’) = 1800, their E(41+)/E(2]l) = 2.25, suggesting that 58Cr was predominately governed by vi- brational collective motion and that rotational collectivity near the middle of the N = 28 — 40 subshell was modest at best. In addition, Sorlin ct al. extracted an 80(10)% beta branch to the 900(100) keV state following the ground state beta decay of 58V. To study the low-energy properties of 58Cr, the decay of its parent nuclide, 58V, was monitored using the DSSD experimental setup discussed in Sec. 3.2.2. Figure 4.1b shows the correlated fragment implant-decay events for all nine radionuclides . produced during this experiment. By defining a gate in the correlated energy loss versus TOF spectrum, the decay properties of 58V were deduced similar to the method discussed in Sec. 4.0.3. A half-life curve was obtained (see Fig. 5.12a) by taking the difference between the absolute time of fragment implant and subsequent beta decay. 67 A Tif/z = 180(36) ms was extracted by fitting the data in Fig. 5.12a with a, two component exponential, one component for 58V and the other for the background, in PHYSICA. A lifetime curve was also obtained by correlating 58V fragments with beta-delayed gamma rays of energy 880 keV within a 400 ms time window following implantation (see discussion below). Considering this half-life, T’s—.2] = 218(30) ms, along with Til/2, an adopted half-life of 202(36) ms was obtained for the decay of 58V. This half-life is consistent with previous I‘neasurements performed by Sorlin 6! al. [29] and Ameil et al. [30]. A beta-delayed gamma ray spectrum was obtained by accepting gamma rays ob- served within a 200 ms time window following the implantation of 58V nuclides. This spectrum was corrected for random background as discussed in Chapter 4, with a background correction factor of 0.184. By multiplying the total gamma spectrum by this correction factor and subtracting the resulting spectrum from the 58V-gamma spectrum, a background subtracted 58Cr spectrum was obtained, see Fig. 5.12b. A single gamma-ray peak was observed at 879.9(2) keV in the background corrected beta-delayed gamma ray spectrum below 1.5 MeV (see Fig. 5.12b). This result is in general agreement with the work of Sorlin et al. [29] who observed a broad peak at 900(100) keV following the beta-delayed gamma emission of 58V. Although the authors proposed this peak as a doublet, no evidence for a second transition in the range 800 - 1000 keV, with similar intensity to the 880—keV gamma ray, was observed in the present study. In an attempt to extract a beta decay branch from the ground state of 58V to the 880 keV state in 58Cr, a second beta-delayed gamma ray spectrum was generated by gating the the total gamma ray spectrum on the 58V contour discussed above. A peak at 880 keV was observed with 8i3 counts. Considering Eq. 4.2 and the number of 58V implants (295(1) x 105), a 541.33% beta decay branch from the ground state of 58V to the 880 keV state in 58Cr was determined. From this branching ratio and the half-life of 58V, a log ft range of 4.12 3 log ft S 6.01 was extracted, suggesting that the 880 keV state is populated following an allowed beta transition. 68 60., (b) 880 keV 4O 0 Counts 20 .. . . . . H l .1 . 1 . _. I T T f O 0 200 400 600 800 0 250 500 750 1000 Time (ms) Energy (keV) Figure 5.12: (a) Extracted 58V life-time curve following the correlation of 58V implants and subsequent beta decays. (b) fi-delayed gamma-ray spectrum following the decay of 58V. In general, the depopulation of excited states in even—even nuclei is characterized by a significant portion of the gamma ray intensity passing through the first excited 2+ state. Thus the 2] —> OT transition should be the most intense. One exception, in some even-even nuclei, is the presence of a 3' state at similar energy to the 2? state. However, the systematics of the lighter Cr isotopes do not support a low-energy 31' state in this mass region. Therefore, the 880—keV fl-delayed gamma ray observed in the present study is proposed as the 2f —) 0] transition in 58Cr. The absence of a second beta-delayed gamma ray transition feeding the first excited 4Jr state in 58Cr may be an indication of a low spin ground state for 58V. Considering the j j-coupling model for odd—odd nuclei [54], the ground state spin of 58V is predicted to be 1, which would result in strong beta feeding to the first excited 2+ state and minimal feeding to the first excited 4+ state. This ground-state spin-parity assignment for 58V is also in agreement with an allowed beta transition feeding a 2+ state in 58Cr. The low-energy level structures of the neutron-rich chromium isotopes in the range N = 28 — 36 are shown in Fig. 5.13, where the data were obtained from Ref. [9,55—57]. As compared to 54Crgo and the new measurement for 58Cr34, there is a clear rise in E(2f) for 56Cr32. This peak in the E(ZT) value for 56Cr32 provides empirical evidence for a significant subshell gap at N = 32. 69 4* 2682 4+ 2370 . (4+) 2076 °‘-.4+ 1824 2+ 1434 .2+ 1007. "-._2+ 5 (2+) 880., °"-..(2+) 646 52Cr28 “Cr,o “Cr” ”Cr“ ”Cr“ Figure 5.13: Low-energy level scheme for neutron—rich chromium isotopes in the range 28 g N g 36. The E(2fl values were obtained from Ref. [9,-55~57]. Tu 6! al. [49] attributed the increase in binding at N = 32 for 52Ca to the Z = 20 shell closure. However, based on the present measurement, a peak in E(2f) is now seen for 56Cr32, which resides in the middle of the Z = 20 — 28 shell. In addition, although E(2f) values increased at N = 32 for the calcium isotopes, this behavior is not observed for nickel (see Fig. 5.14, data taken from Ref. [9,19,55,56]), which has a closed proton shell. If the strength of N = 32 were reinforced by a proton shell closure, a similar peak in E(2l+) would be expected for 60Ni. An alternative explanation for the appearance of the N = 32 subshell for neutron- rich systems is to consider a change in the proton—neutron monopole interaction strength. Nickel has a closed proton shell at Z = 28. According to Federman and Pittel [58], the proton-neutron interaction is strongest when the orbitals they occupy strongly overlap. To illustrate this point, consider the following interaction between two particles at r] and 7‘2 [10]: lr'i(|-r1.r2|) = ZVA-("ls1‘2)Pk(('0-50121 ( k=U g! H [Ca V which is summed over all multipoles. k. P1.(c05012) is a Legendre polynomial. The term 1/1.(r1, r2) may be reduced to: 21: + 1 6(1‘1 — r2) 4 7r 1,», (5.13) VA-(I'l , 7‘2) z where (S(rl — r2) is a zero—range interaction. Reducing this expansion to its first term, the monopole term. gives: 1 _)3/2 6("1 — 7'2) ‘1 71" 7‘17'2 1’i11(|7'1~"2|) = ( (5-14) The overlap between the proton and neutron orbitals is maximum when in z [p [.58]. This results in a shift in the single-particle orbitals [59]: C21,, 2 5],, + Z V1211 (515) j1r where V?" is the proton occupation probability. When Z = 28, the 1f7/2 orbital is filled and the 7r1f7/2 - V1f5/2 interaction should be strong, depressing the energy of the V1f5/2 orbital [60]. The 1f5/2 neutrons would act to stabilize the 1f7/2 pro— ton configuration [61]. As protons are removed from the 1f7/2 orbital, the 7r1f7/2 - l/1f5/2 interaction weakens. When Z = 20, no protons occupy the 1f7/2 orbital in the ground state, thus the 7r1f7/2 - V1f5/2 interaction should be diminished. This reduced monopole interaction, and the significant 2p1/2 — 2123/2 spin-orbit. energy splitting, results in the emergence of the N = 32 subshell. To probe the proton-neutron monopole interaction, ideally, the single-particle en- ergies for the 2p3/2, 2171/2 and the 1f5/2 orbitals should be measured. These energies may be deduced for the odd—A, N = 29 isotones using spectroscopic factors extracted from the analysis of transfer reactions. In an attempt to extract the single-particle energies for the N = 29 isotones, the spectroscopic factors for the known 3/2‘ , 1/2', 5/2‘ and 7/2‘ states were tabulated (see Table 5.1, complete data for N = 29 iso- tones are provided in Appendix D). However, the experimental information is limited. 71 3.0 " — ”Ni 2.0“ —" 10: 7 -.- _g_ 15- 3- _ 0.0 4 _ 26Fe 0 1'0] ; £ '5- '“- 3 9 0.0 Q « _ “Cf V 1'03 .i & 1r- 0 o n 1 _ 5 M . m _ o 22T1 l 0 100"4 A. O o O 0.0 ‘00: — zoca ' 30° '1 “ '5' 2.0: o 1.0- -“- ° ° 0,0 . . . . f 4 . f 25 21130 32343533404244 Neutron Number Figure 5.14: E(2IL) systematics for neutron—rich nuclides between 20 3 Z 3 28. The experimental values are denoted by dashes, where the data were obtained from Ref. [9, 19,55,56]. The open circles represent E(2l+) values obtained from truncated shell-model calculations. See text for details. Not all of the states have been assigned a spectroscopic factor, thus the single—particle energies cannot be correctly calculated. An additional complication may arise from the misassignment of spins. An example of such complications may be found in 53Cr. A large spectroscopic factor has been extracted for a high-energy state at 3.63 MeV [62]. However, there is some uncertainty pertaining to the spin of this 5 = 1 state [62,63], which seriously impacts the ordering of the single—particle orbitals. Due to the difficulty in extracting single-particle energies from experimental data for the N = 29 isotones, several authors have calculated these values. The single— 72 Table 5.1: Calculated single-particle energies (s.p. E(keV)) for the N = '29 isotones in the region 20 3 Z s 28 [9,64-68]. Nuclide Neutron Single-Particle Ol‘bim/s .S'ing/r-Pm'lic/e Energy (keV) 49C?! 2113/2 95.2 2p1/2 2059.3 lf5/2 3986.1 SITI 2p3/2 83.2 2p1/2 1671.0 lf5/2 2136.0 53Cr 2p3/2 366.6 2])1/2 1287.0 lfs/2 1009.0 1f7/2 1302.3 55Fe 2])3/2 215.4 2})1/2 482.8 lf5/2 997.2 1f?)2 1334.0 57Ni 2113/2 30.0 2p1/2 1113.0 lf7/2 3547.7 particle energies for 2123/2, 2121/2 and 1f5/2 orbitals in the N = 3 shell for 57N129 have been calculated by Trache et al. [47] and Duflo and Zuker [69]. Considering a ground state spin of 3/2 for 57Ni [68], the lowest orbital in this shell would be 2123/2. The 1f5/2 state was calculated at z 1 MeV above 2p3/2, followed by 2121/2. As protons are removed from 1f7/2, the single-particle energies for the 2p3/2, 2p1/2 and 1f5/2 orbitals shift. By 49Ca29, the 1/1f5/2 and the V2p1/2 orbitals have inverted [69]. For this study, shell-model calculations1 in the region N = 28—40 and Z = 20—28 were carried out in a pf-shell model space with an FPD6 effective interaction [55,70]. For the Ca isotopes the full basis calculation is feasible. The calculated energies of the lowest 2+ states in the Ca isotopes are (in MeV) 3.66 (48Ca), 1.33 (50Ca), 2.75 (52Ca), 1.47 (54Ca), 1.37 (56Ca) and 1.30 (58Ca). The agreement with the experimental values in 48Ca, 50Ca and 52Ca is good. The high energy of the 2+ state in 48Ca is due to a 1Shell model calculations were performed by B.A. Brown. rather good .lf7/2 shell closure, and the relatively high energy for the 2+ state in 52Ca is due to a partial shell closure for the 2113/2 shell. Beyond 52Ca the effective single- particle energies of the 2p”; and lf,—,/2 orbits are close and there are no other shell effects until the 60Ca closed shell. In nuclides around 60Ca the 1g9/2 orbit may become important, but. this is not included in the model space and there is no experimental information available. For nuclei with larger values of Z, the shell-model calculation in the full pf shell quickly becomes intractable because of the large dimensions. In a few cases such as 56Ni, the Monte-Carlo shell-model has been used [71] (for which the FPD6 interaction still gives a good spectrum). However, the good closure of the 1f7/2 shell at 48Ca means the nuclei beyond N = 28 may be treated as neutrons in the (2113/2, 2})1/2, 1f5/2) model space (to a. good approximation). When this truncation is made for the Ca isotopes the energies of the 2+ states (see Fig. 5.14) and their wave functions remain similar to those obtained with the full space, which includes 1f7/2. (These truncated calculations use as inputs the single-particle levels in 49Ca as obtained from FPD6 which are close to the experimental values.) For higher Z there is clear evidence of the dominance of the 1f7/2 shell for protons in the 01’, 2+, 4+, 6+ spectra of 50Ti, 5"iCr and 54Fe. 56Ni shows a partial 1f7/2 shell closure (e.g. the relatively high 2+ energy). Thus for protons, the model space is truncated to the pure 1f7/2 shell with the proton two-body interaction taken as a function of Z to match exactly the 0+, 2+, 4+, 6+ spectra of 50Ti, 52Cr and 54Fe. The neutron single—particle energies are linearly interpolated between 49Ca and 57'N i such that the spectrum of single-particle states in 57Ni is reproduced. This defines the input to the shell-model interpretation of the 2+ energies. Figure 5.15 depicts the low-energy level structure for the odd A, N = 29 isotones within the vicinity 20 S Z 3 28, where data was taken from Ref. [9]. For comparison, the levels predicted via shell-model calculations for 49Ca and 57Ni are also shown. The energies of the 3/2‘, 1/2‘ and 5/2' states follow the general behavior of the V2p3/2, 1/2p1/2 and 1/1f5/2 orbitals, respectively (see Table 5.1). At Z = 20, a substantial 74 1 4 1 _iLl' A a ——. z . V 3- . ' . I a _112. g: l. 2 ——fi : ' C \ : I O \i l '4'.- \fi—'——\ ,- g 1- ‘——‘,___i 1—1-L2-—13' "—4 _ _ a \\ 1,. 5(2 _ELZ . —l . 3(2' 3(2' 3! ' SM Exp. 2211 “CT 25 Fe SM EXP. zoca ”Ni Figure 5.15: Low-energy states for the odd—A N = 29 isotones in the range 20 S Z S 28 [9]. Shell-model results for 49Ca and 57Ni are also depicted. gap is observed between the V(2p1/2 — lfs/Q) and the V(2p3/2 — 2121/2) orbitals. The existence of these gaps suggests an N = 32 and possibly an N = 34 subshell for calcium isotopes. As protons begin to fill the 1f7/2 orbital, the 5/2' state is lowered. By Ni, the 7rlf7/2 — V1f5/2 interaction is maximum and draws the l/lf5/2 orbital below 1/2p1/2, which eliminates N = 32 subshell closure. For chromium isotopes beyond N = 32, in addition to the present measurement, Sorlin et al. [56] observed the 2? —> 0: transition of 60Cr at 646 keV following the beta decay of 60V. Considering the new E(2f) measurement for 58Cr at 880 keV and Sorlin’s measurement [56], a considerable decrease in E(2f) is observed beyond N = 32 for Cr (see Fig. 5.13). The overall E(2f) trends in neutron—rich chromium isotopes imply that as neutrons fill the 1f5/2 orbital, the 7rlf7/2-1/1f5/2 quadrupole interaction strengthens, inducing nuclear deformation [.58]. Such effects have been previously noted in, for example, the Mo isotopes, where a strong 5199/2 - V1977; proton—neutron interaction produces deformed ground state structures beginning at 100Mo [72]. The relatively low energy of the first excited 2+ state of Cr, as compared with Fe, Zn and 75 Ge isotopes (see Fig. 5.14), has been suggested as evidence of oblate-prolate shape coexistence predicted in this region [56]. As a result of the monopole proton-neutron interaction, shape coexistence may be rationalized as follows. As neutrons are added to a 56Cr32 core, the 7r(1f7/2)—1/(1f5/2) interaction strengthens and may draw a pair of 1(13/2 protons into the 1f7/2 orbital. The energy required to promote the d3/2 protons through the Z = 20 shell closure would be recovered from the monopole energy. Toward N = 40, the monopole proton-neutron interaction will become increasingly strong and may result in a new proton configuration, possibly leading to an oblate—- prolate shape coexistence for Cr isotopes in this region. However, based on shell model calculations for chromium isotopes (see Fig. 5.14) the 21+ energy level is predicted to remain fairly constant for 34 S N S 38. 5.1.2.2 Summary The decay properties of 58Cr have been studied following the beta decay of 58V. A beta-delayed gamma ray was observed at 879.9(2) keV and has been assigned to the 2? —> 0? transition in 58Cr. A beta decay branching ratio of 54133% has been extracted for the ground state beta decay of 58V to the 880 keV state in 58Cr. A log ft range of 4.12 S log ft S 6.01 has been determined, which suggests that the 880 keV state is populated by an allowed beta transition from the ground state of 57V. Considering that the 880 keV state is fed by an allowed beta transition and the jj-coupling model for odd-odd nuclei [54], the ground state spin and parity of 58V is predicted to be 1+. The even-even systematics of the neutron-rich chromium isotopes indicate an in- crease in E (2]) at N = 32. Following the present measurement, E(2‘1I) for chromium isotopes were found to peak at N = 32. This rise in E(2f) is consistent with the in- crease observed at N = 32 for calcium isotopes. Although this trend does not continue beyond Z = 24, this may be due to the lowering of the V1f5/2 orbital as a result of a strong 7rIf7/2 - 1/1f5/2 proton-neutron monopole interaction. The data is in agreement with shell-model calculations, which also show enhanced binding at N : 32 for goCa, 22Ti and 24 Cr. “J "J Chapter 6 Summary Two experiments have been performed to study the evolution of subshell gaps at N = 32 and N : 40 for neutron-rich nuclides within the N = 28 — 50 shell. In the first experiment. a conventional beta. detection system. was used to study the beta. decay of neutron-rich nuclides near N = 40. During this study, a 34(7) 5 isomeric state in 69Ni was directly produced following the fragmentation of a 76Ge beam at 70 MeV/nucleon in a Be target. The identification of this isomeric state was based on a newly discovered 1296 keV beta-delayed gamma ray. The decay of the 1/2‘ isomer in 69Ni was observed to proceed mainly through the excited 3/2‘ state at 1296 keV in 69Cu. No other excited states in 69Cu have been observed to be fed following the /3 decay of this isomer. By comparing the total number of 69Ni nuclei implanted within a Si PIN detector with the intensities of the beta-delayed ’7 rays following the decay of the 1/2' isomeric state and the ground state of 69Ni, a 36% upper limit has been extracted for the 13 branch from the isomeric state in 69Ni to the ground state in 69Cu. Based on this branching ratio, a small (< 15%) 2p—2h mixing into the ground state of 69Cu may be deduced. This small 2p—2h admixture in the ground state of 69Cu suggests that this nucleus is predominately single-particle in character and may be described as a proton coupled to a 6‘BNi core. The dominance of the 68Ni core in the excited states of 69Cu supports the case for an N = 40 subshell. In the second experiment, a new beta detection system was employed to study the decay properties ofne1.1tron-rich nuclides in the midshell region N = 28 — 40. A 78 985 pm double—sided silicon strip detector (DSSD) was utilized to correlate implanted nuclei with subsequent beta particles on an event-by-event basis. For this study, the N = 32 subshell was investigated. An N = 32 subshell gap was first suggested following the measurement. of the high—lying 21+ state of 52Gag-2 [2]. Although extending the E(2T) systematics to heavier calcium isotopes would be of value, such nuclei were difficult to produce with sufficient statistics during the time of this experiment. Thus, in this work, the low-energy properties of 58Cr were studied following the beta. decay of 58V. A beta decay half-life of 202(36) ms was extracted which was consistent with Sorlin it al. [29] and Ameil et al. [30] measurements. In addition, a beta-delayed gamma ray was observed at. 879.9(2) keV and has been assigned to the 2:" —> 0? transition in 58Cr. Based on a beta decay branch of 54fii(o, a range of log ft values of 4.12 S log ft S 6.01 have been extracted, suggesting the 880 keV state in 58Cr is populated by an allowed beta transition from the ground state of 58V. Considering the E (2?) value for 54Cr30 and the present measurement for 58Cr34, a clear peak in E(21+) is apparent at N = 32. This rise in E(2T) is consistent with the calcium systematics. However, this trend does not seem to continue beyond Z = 24. The presence of a substantial N = 32 subshell gap has been attributed to the lowering of the l/If5/2 orbital as a result of a strong 7r1f7/2 - V1f5/2 proton-neutron monopole interaction. The systematics of even—even, neutron-rich chromium isotopes indicate a gradual increase in E(2f) toward N = 40, see Fig. 5.15. This evolution suggests a slow onset of collectivity in the midshell region N = 28 — 50. However, this is in contrast to the shell model predictions shown in Fig. 5.14. Based on shell model calculations, E(21+) values for neutron-rich nuclides between 20 S Z S 28 increase toward N = 40, in support of an N = 40 subshell. Discrepancies such as those observed between the experimental systematics and the shell model predictions toward N = 40 illustrate the need for continued experimental studies of exotic nuclear systems. It would be of interest to extend the study of the N = 28 — 40 midshell and the N : 40 subshell to lighter mass systems. A 69 0 69 - — Proton Number, 2 58 58 — — 23V35 —>,,, CrM+B +v Neutron Number, N Figure 6.1: A table of the isotopes with the magic neutron (labelled with blue numbers) and magic proton (labelled with pink numbers) shell closures indicated. The N = 40 and N = 32 subshells have also been included. The blue squares that run nearly along the diagonal represent stable nuclei. In summary, two subshell gaps within the N = 28 — 50 shell have been explored. As a result of the 69Ni"” beta—decay study, further support for an N = 40 subshell has been provided. However, based on this study, this subshell can only be confined to the nickel isotopes (see Fig. 6.1). Following the beta decay study of 58V, new empirical evidence for an N = 32 subshell has been established. This subshell has been attributed to a proton—neutron monopole interaction and is believed to extend from calcium to chromium (see Fig. 6.1). To validate this hypothesis it would be of interest to measure the E (2?) values for neutron—rich Ca and Ti isotopes, in particular 52,54Ca and 54‘56Ti. 80 6.0.3 Outlook 5‘~58V measurement was the first exper- The beta detection system discussed for the iment of its kind run at the NSCL utilizing a double-sided strip detector to directly correlate fragments of interest with subsequent beta decays during continuous beam implantation. As such, there were several shortcomings that were encountered. For instance, using single high gain electronics to process energy signals from the DSSD allowed us to isolate a beta event to a given pixel, however, in terms of an implant, one could only isolate such an event to a 6 x 6 strip area. An implant pixel was identified as the most central strip in x and y in this 36 pixel array. In addition, i:l:1 strips were also labelled as possible implant pixels. As a result of this limitation, shortly after this experiment, 160 channels of integrated pre—amplifier and amplifier electronics to outfit one 40 x 40 DSSD with dual (high and low) gain electronics were purchased. At present, three experiments have been performed with the DSSD beta detection system and the new electronics. As a result of efficiency related problems, prior to these experiments, a 207'Bi source run was performed. 207Bi is an electron and gamma ray emitter, thus by using this source the ADC gates for the Ge detectors could be properly set for an e17 coincidence, a serious problem that may have effected the efficiency calculations for the present study. Using this new system, implant events have been characterized as predominately multiplicity one events and may be easily correlated with subsequent beta particles identified within the same pixel. In addition, by properly setting the gates on the ADC’s for the Ge detectors, the (fie, efficiency has vastly improved. 81 Appendix A Beta Efficiency Calculations A.0.4 Experimental Efficiency for Exp. 97 004 To determine the total beta efficiency for the rotating target wheel setup detailed in Sec. 3.2.1, the intensities of the gamma ray singles and the beta-delayed gamma ray peaks were compared. The prominent gamma ray peaks were fit to Gaussians using the program DAMM. The area of the background subtracted peaks in gamma ray singles, N7, and the beta—delayed gamma ray data, N723, were determined. The beta efficiency was extracted by taking the ratio of 1’V,_,3/N.,, ./V,,_,v3 _ Inf-“76.13 (Al) N, [~57 where I, is the intensity of the gamma ray transition, 6., is the peak gamma ray efficiency and (13 is the beta efficiency. The beta efficiency reported in Ref. [45,73] was 40.0(24)%. In an attempt to repro- duce this measurement, the N, and N,__3 values for the prominent gamma ray transi— tions were extracted. Table A.1 provides a list of calculated N.“ N,_,3 and efficiencies. Taking the weighted average of these values, a total beta efficiency of 32.0(5)% has been determined, which is close, but does not match the quoted value. Any additional factors considered in the earlier beta efficiency calculation are unknown. A.0.5 Simulated Beta Efficiency for Exp. 98020 In an attempt to simulate the beta efficiency for Exp. 98020, GEANT was utilized. To determine whether the simulation was working properly. the results were compared to F.) lv‘ Table A.1: Calculated beta efficiency for Exp. 97004. The errors are listed in the paren- theses for N.“ r\l,_,3 and ()3. E (keV) N, N,_,. a). ((7.2) 1430 290(5) x 104 608(58) 21.0(20) 156.0 254(4) x 104 842(65) 33.1(26) 175.0 4.01(160)x103 239(44) 59.7(261) 193.0 7.33(184)x103 3.49(48) 47.6(136) 4100 902(31) x 103 246(9) 27.3(13) 432.0 178(4) x 104 685(12) 38.5(10) 450.0 124(3) x 104 5.10(11) 41.2(13) 5960 354(12) x 104 8.94(24) 25.2 11 ) 620.0 575(82) x 103 1.06(11) 18.4(32) 628.0 627(83) x 103 2.06( 13) 32.9(49) the experimental beta efficiency for a 908r source placed 26.7 cm upstream from the strip detector. The source was mounted at the center of a 7 cm x 7 cm, 1458 mg/cm2 Al degrader. The chamber was placed under vacuum and data were collected for 30 minutes. Based on the certificate of calibration, the 903r source was produced on March 1, 1997 with an activity of 41.0(1.3) kBq. As 90Sr decays, a secular equilibrium is established with 90Y, thus A(QOSr) z A(90Y). At the time of the measurement, the calculated activity of 908r was 36.8(1.2) kBq and a total of 1.41 x 108 beta particles were emitted by the source from 90Sr and 9CY combined. During this 30 minute mea- surement, 4.12(1) x 105 beta particles were observed in the strip detector. This value has been corrected for the computer dead time, however, the electronics dead time has not been considered. Taking this dead time correction into account, a lower limit experimental beta efficiency of 0.291(9)% was calculated at this source-to—detector distance. A geometrical efficiency, (geomsz/Mr, of 0.175% was calculated considering the solid angle of a rectangular detector [74], (r2 - 4tp)(y‘2 - yp) 2p\/(I‘2 - asp)? + (y2 - .7417)2 + 2:22 (—:vio)(y2 - yp) ~2'10\/(--:l‘-P)2 + (y2 — WV + 3P2 Q = arctan[ — arctan[ 83 (.1'2 — .1'p)(—yp) :p\/(.r2 — .rp)2 + (—yp)2 + :1)? (- 0, then HMAT contains the proportion by weights of each basic material in the mixture. If NLMAT < 0, then HMAT contains the number of atoms of a given kind in the compound. *********** call gsmixt(matpla,’mylar’,AMYL,ZMYL,DMYL,-3,WMYL) call gsmixt(matSt,’steel’,ASTE,ZSTE,DSTE,-3,WSTE) * print out material parameters call gpmate(0) * set up user media & tracking parameters * tracking medium number. medVac = 1 medAir = 2 medAl = 3 medGe = 4 medSi = 5 93 medpla = 6 medSt = 7 *--Tracking medium parameters. Default values used when values a: *************** of < 1 are entered. dmaxms = -1. !Maximum step size permitted (cm) deemax = -1. !Maximum Fractional E loss in one step epsil = 1e-14 !Boundary crossing precision (cm) stmin = -1. !Minimum step size (cm) CALL GSTMED(ITMED,NATMED,NMAT,ISVOL,IFIELD,FIELDM, TMAXFD,DMAXMS,DEEMAX,EPSIL,STMIN,UBUF,NWBUF) ITMED - tracking medium number. NATMED - tracking medium name. NMAT - material number corresponding to ITMED. ISVOL - =0 if not a sensitive volume (not a detector). IFIELD = 0 no magnetic field. other options detailed in CONS2OO FIELDM - maximum field value (kG) TMAXFD - maximum angle due to field permitted in one step. DMAXMS - maximum step size. DEEMAX - maximum fractional energy loss in one step. EPSIL - tracking precision. STMIN - minimum step size. UBUF - array of NHBUF additional parameters. call gstmed(medVac,’vacuum$’,matVac,0,0,0.0,0.0,dmaxms, + deemax,epsi1,stmin,0,0) call gstmed(medAir,’air$’,matAir,0,0,0.0,0.0,dmaxms, + deemax,epsi1,stmin,0,0) * dmaxms for detectors and degrading material calculated as 1/3 of * the thickness of the given medium. a: call gstmedeedAl,’al$’,matAl,0,0,0.0,0.0,0.08, + deemax,epsi1,stmin,0,0) call gstmed(medGe,’ge$’,matGe,1,0,0.0,0.0,dmaxms, + deemax,epsil,stmin,0,0) call gstmed(medSi,’si$’,matSi,1,0,0.0,0.0,0.02, 3 0.8,epsil,stmin,0,0) call gstmed(medpla,’mylar$’,matpla,0,0,0.0,0.0,2e-4, + O.8,epsil,stmin,0,0) call gstmedeedSt,’steel$’,matSt,0,0,0.0,0.0,0.005, + O.8,epsi1,stmin,0,0) print the tracking medium parameters call gptmed(0) 94 RETURN END ************************t*********************************** * dssd_geom *********************#**************#*********************** * Detector types and geometries are defined here. ************************************************************ SUBROUTINE UGEOM * GEANT common blocks INCLUDE ’nsc1_bnmr:[prisc.geant.beta.ginc]gcbank.ins’ INCLUDE ’nscl_bnmr:[prisc.geant.beta.ginc]gcflag.ins’ INCLUDE ’nsc1_bnmr:[prisc.geant.beta.ginc]gctmed.ins’ * USER defined common blocks INCLUDE ’nscl_bnmr:[prisc.geant.beta.uinc]umaterials.ins’ integer testset,testdet,slot,strip real dssdpos character eloss*4,num*4,name*4 * A few of the overall parameters are defined here. real HRLD(3) real FLGEC3), CHMBCS), VACC(5), VAC2(3), BEAMCS) real PLAS(3), RINGCS), DISK(3), DEGR(3) real PIN2(3), PIN3(3), DSSD(3). PIXI(3) *--Definition of volume shape. Here are several shapes that may * be defined and the information necessary to create such a volume. ’BOX ’ - the x, y and 2 half lengths must be provided. ’TUBE’ - inner radius, outer radius and half length in z. ’CONE’ - half length in z, inner and outer radii at low 2 and inner and outer radii at high 2 limit. **** * Outside world, ’BOX ’. DATA WRLD/70.,70.,70./ * Vacuum chamber, ’TUBE’. DATA ELSE/0.0, 8.35, 0.65/ DATA CHMB/12.15, 5.0, 5.35, 8.0, 8.35/ DATA VACC/12.15, 0.0, 5.0, 0.0, 8.0/ * Source holder, ’TUBE’. DATA PLAS/0.0, 1.19, 3.22E-4/ DATA RING/1.19, 1.27, 0.159/ DATA DISK/0.0, 1.19, 0.0127/ * The source was mounted on an A1 degrader, ’BOX ’. DATA DEGR/3.5, 3.5, 0.27/ * Beam line and vacuum, ’TUBE’. DATA BEAM/5.0, 5.35, 12.15/ DATA VAC2/0.0, 5.0, 12.15/ * Create a detector, ’BOX ’. DATA PIN2/2.5, 2.5, 0.02515/ DATA PIN3/2.5, 2.5, 0.01545/ DATA DSSD/2.0, 2.0, 0.04925/ DATA PIXI/0.05, 0.05, 0.04925/ *--Creates mother volume or master system CALL GSVOLU(NAME,SHAPE,NMED,PAR,NPAR,IVOLU*) NAME - unique four character name. SHAPE - 4 character name of system shape, see GEOMOSO. NMED - tracking medium number. PAR - array containing shape parameter. NPAR - number of such parameters. IVOLU - number returned by subroutine as system volume number. ******* CALL GSVOLUC’WRLD’,’BDX ’,medAir,WRLD,3,ibox) CALL GSVOLU(’FLGE’,’TUBE’,medAl,FLGE,3,ibox) CALL GSVDLUC’CHMB’,’CONE’,medA1,CHMB,5,ibox) CALL GSVOLU(’VACC’,’CONE’,medVac,VACC,5,ibox) CALL GSVOLU(’VAC2’,’TUBE’,medVaC,VAC2,3,ibox) CALL GSVOLU(’BEAM’,’TUBE’,medAl,BEAM,3,ibOX) c Call gsvolu(’PIN2’,’BOX ’,medSi,PIN2,3,ibox) c call gsvolu(’PIN3’,’BOX ’,medSi,PIN3,3,ibox) call gsvoluC’DSSD’,’BOX ’,medVac,DSSD,3,ibox) CALL GSVOLUC’PLAS’,’TUBE’,medpla,PLAS,3,ibox) CALL GSVOLU(’RING’,’TUBE’,medAl,RING,3,ibOX) CALL GSVOLUC’DISK’,’TUBE’,medSt,DISK,3,ibOX) CALL GSVOLUC’DEGR’,’BOX ’,medAl,DEGR,3,ibox) * Creating the individual pixel volumes for DSSD. do i = 1, 1600, 1 * Converts integer value to character notation, 0001 - 1600. encode(4,17,num) i c print *, ’num = ’,num call gsvolu(num,’BOX ’,medSi,PIXI,3,ibox) enddo *--Prints the volume parameters. c call gpvoluCO) *--Creates a rotation matrix * CALL GSROTM(IROT,THETA1,PHII,THETA2,PHI2,THETA3,PHI3) * IROT - rotation matrix number. * THETAI - polar angle for axis x’. 96 PHIl - azimuthal angle for axis x’. THETA2 - polar angle for axis y’. PHI2 - azimuthal angle for axis y’. THETA3 - polar angle for axis 2’. PHIB - azimuthal angle for axis 2’. ***** PIN2 is orientated such that the distance from the top of the PIN to the flange is 8.2 cm and the distance from the bottom of the PIN to the flange is 8.7 cm. Thus, there is a 4.1 degree angle with respect to theta_z. CALL GSROTM(1,90.0,0.0,85.9,90.0,4.1,270.0) **** *--Positioning volume inside its mother. CALL GSPOS(NAME,NR,MOTHER,X,Y,Z,IROT,KONLY) NAME - four character volume name. NR - copy number of volume. MOTHER - four character name of volume in which this volume is placed. X,Y,Z - position of volume in reference to the mother volume. Position is defined as the center of volume relative to the center of the mother volume. IROT - rotation matrix number describing orientation of volume relative to the mother volume. KONLY - flag indicating if a point found in this volume may also be in other volumes. ************ * VACC and HRLD have been shifted such that they are centered * at the position of the DSSD. dssdpos = 5.83075 CALL GSPOS(’VACC’,1,’HRLD’,0.0,0.0,-dssdpos,0,’ONLY’) CALL GSPOS(’CHMB’,1,’HRLD’,0.0,0.0,-dssdpos,0,’ONLY’) CALL GSPOSC’FLGE’,1,’HRLD’,0.0,0.0,12.8-dssdpos,0,’ONLY’) CALL GSPOS(’VAC2’,1,’HRLD’,0.0,0.0,-24.3-dssdpos,0,’ONLY’) CALL GSPOS(’BEAM’,1,’HRLD’,0.0,0.0,-24.3-dssdpos,0,’ONLY’) * Distance of detectors relative to center of chamber. c CALL GSPOS(’PIN2’,1,’VACC’,0.0,0.0,3.72487,1,’ONLY’) CALL GSPOSC’DSSD’,1,’VACC’,0.0,0.0,dssdpos,0,’ONLY’) c CALL GSPOS(’PIN3’,1,’VACC’,0.0,0.0,7.63455,0,’ONLY’) * Source distance for 33Mg run. Note position is relative to VAC2. CALL GSPOSC’RING’,1,’VAC2’,0.0,0.0,24.3-20.9,0,’ONLY’) CALL GSPOSC’DISK’,1,’VAC2’,0.0,0.0,24.3-20.875988,0,’ONLY’) CALL GSPOSC’PLAS’,1,’VAC2’,0.0,0.0,24.3-20.862966,0,’ONLY’) CALL GSPOS(’PLAS’,2,’VAC2’,0.0,0.0,24.3-20.862322,0,’ONLY’) CALL GSPOSC’DEGR’,1,’VAC2’,0.0,0.0,24.3-21.32,0,’ONLY’) * Source distance for 33Al run. Note position is relative to VACC. 97 c CALL GSPOS(’RING’,1,’VACC’,0.0,0.0,-7.309,0,’ONLY’) c CALL GSPOSC’DISK’,1,’VACC’,0.0,0.0,-7.284988,0,’ONLY’) c CALL GSPOSC’PLAS’,1,’VACC’,0.0,0.0,-7.271966,0,’ONLY’) C CALL GSPOS(’PLAS’,2,’VACC’,0.0,0.0,-7.271322,0,’ONLY’) * Positioning individual pixels within DSSD mother volume. do y = 1,40, 1 do x= 1,40,1 * Each pixel will be labelled 0001 - 1600. slot = x+40*(y-1) * Converts integer value to character notation, 0001-1600. encode(4,17,name) slot c print *, name * Positioning individual pixels starting at lower lefthand corner. call gspos(name,1,’DSSD’,(-2.05+O.1*x), 1 (-2.05+0.1*y),0.0,0,’ONLY’) enddo enddo *--Dec1aring active detector volumes. * CALL GSDETV(CHSET,CHDET,IDTYP,NHHI,NHDI,ISET,IDET) * CHSET - four character set identifier * CHDET - four character detector identifier, has to be the * name of an existing volume * IDTYP - detector type. * NHHI - initial size of HITS banks. * NHDI - initial size of DIGI banks. * ISET - position of set in back JSET. * IDET - position of detector in back JS=LQ(JSET-ISET) * Declaring PIN2 an active detector volume. c CALL GSDETV(’DEP2’,’PIN2’,medSi,100,100,testset,testdet) * Declaring individual pixel volumes as active detectors. do j = 1, 1600, 1 * Converts integer value to character notation, 0001 - 1600. encode(4,17,name) j c print *,name * Active detector pixels labelled from 1001 - 2600. encode(4,17,eloss) j+1000 c print *,eloss CALL GSDETVCeloss,name,medSi,100,100,testset,testdet) enddo * Declaring PIN3 an active detector volume. c CALL GSDETV(’DEP3’,’PIN3’,medSi,100,100,testset,testdet) 98 17 format(i4.4) *--This routine should be called after all volumes and positions * have been defined. CALL GGCLOS return end ************************************************************ * dssd_kine t*********************************************************** * Emission of particles with defined E and angle. ************************************************************ subroutine gukine * GEANT common blocks INCLUDE ’nscl-bnmr:[prisc.geant.beta.ginc]gcflag.ins’ INCLUDE ’nsc1_bnmr:[prisc.geant.beta.ginc]gconst.ins’ * User common blocks INCLUDE ’nscl_bnmr:[prisc.geant.beta.uinc]ukine.ins’ INCLUDE ’nscl_bnmr:[prisc.geant.beta.uinc]uedep.ins’ real vert(3),RNDM(2),plab(3),dssd_z 4: real eTheta,ePhi,eEnergy integer iloop,counter,evnts,tab-evnts character*1 respon * Determine where the particle will be emitted IEVENT is a trigger counter. It counts from 1 to NEVENT (total particles emitted). Counter is a variable used to count from 1 to inputted trigger. This variable needs to be initialized the first time through the program. **** O if(IEVENT.eq.1) counter = 1 c if(counter.eq.1) then c respon = ’y’ * EVNTS is the total number of particles in a given trigger, * whereas tab_evnts is an evnts counter. c evnts = NEVENT - tab_evnts c endif * Position of the source. vert(1) = 0.0 !x position 99 vert(2) = 0.0 !y position Considering a gaussian distribution of implantation depth. Sigma and avg are read in from user.inp file. Print *,’I am bombing here I’ call Gaussian(std,avg,evnts,dssd_z,respon) vert(3) = dssd_z !z position 0001's} * Source distance for 33Mg run. vert(3) = -26.693394 !z position * Source distance for 33A1 run. c vert(3) = ~13.102394 !2 position c Print *,’x=’,vert(1),’y=’,vert(2),’z=’,vert(3) c counter = counter + 1 c if(counter.eq.(evnts+1)) then c counter = 1 c tab_evnts = evnts + tab_evnts c endif stepct = 0 *--Storing/retrieving vertex and track parameters. * CALL GSVERT(VERT,NTBEAM,NTTARG,UBUF,NUBUF,NVTX) * VERT - array of (x,y,z) position of the vertex. * NTBEAM - beam track number origin of vertex, =0 if * none exists. * NTTARG - target track number origin of vertex. * UBUF - user array of NUBUF floating point numbers. * NVTX - new vertex number. call gsvert(vert,0,0,0,0,Nvert) if(Nvert .eq. 0) then write(6,1000) stop endif 1000 format(’ error in gukine calling gsvert’) * Prints vertex parameters. c call gpvert(0) * Prints initial track parameters. c call gpkine (0) * Determine the angle of the emitted event if (KineOpt.eq.0) then * emit 4pi Call GRNDM(RNDM,2) 100 eTheta=ACOS(-1. + 2. * RNDM(1)) ePhi=TWOPI*RNDM(2) else if (KineOpt.eq.1) then * emit in cone of (ThetaMax Call GRNDMCRNDM,2) eTheta=ACOS(-1. + 0.01111111*ThetaMax*RNDM(1)) ePhi=THOPI*RNDM(2) else * emit at fixed angle eTheta = ThetaMax*0.017453293 ePhi = PhiMax*0.017453293 endif * Calculate modified energies here. if (Particle.eq.2.or.Particle.eq.3) then if (BetaOpt.eq.0) then eEnergy = BetaMom(Energy,MaxBeta,Particle,Znumber) else eEnergy = Energy endif else eEnergy = Energy endif eBeta = eEnergy c print *,eBeta * Convert Energy and angles into x, y and z momenta plab(1)=0.000001*eEnergy*SIN(eTheta)*COSCePhi) plab(2)=0.000001*eEnergy*SIN(eTheta)*SIN(ePhi) plab(3)=0.000001*eEnergy*COS(eTheta) Create the event write(*,*) ’Particle =’,Particle write(*,*) ’eEnergy =’,eEnergy write(*,*) ’eTheta =’,eTheta write(*,*) ’ePhi =’,ePhi 0000* CALL GSKINECPLAB,IPART,NV,UBUF,NUBUF,NT) PLAB - components of momentum. IPART - type of particle. NV - vertex number origin of track. UBUF - array of NUBUF floating point user parameters. NT - track number. *I-‘I-I'I-‘I' CALL GSKINE(p1ab,Particle,Nvert,0,0,NT) 101 return end ************************************************************ * FINDMAX: This subroutine determines the maximum value of * the beta energy function, which is necessary for the * beta energy simulation. ***************************************t******************** subroutine FindMax(BetaQ,BetaMax,particle,Z) real BetaQ,BetaMax real rtemp,OldTestVa1,TestVal integer iloop,particle,Z rtemp=1.0 iloop=0 OldTestVal = BetaEnergy(betaQ,rtemp,1.0,particle,Z) do while (iloop.ne.1) rtemp = rtemp + 0.00001*beta0 TestVal = BetaEnergy(betaQ,rtemp,1.0,particle,Z) if (TestVa1.lt.OldTestVal) then iloop=1 TestVal = OldTestVal else if (rtemp.gt.beta0) then iloop=1 write(*,*) ’Improper initialization of BetaMax’ endif OldTestVal = TestVal enddo BetaMax = 1/TestVal return end t*********************************************************** BETAMOH (function): This subroutine determines the beta Energy and emits a Beta Particle * * a: * This is a basic monte carlo routine that samples a simulated * beta spectrum (defined by BetaEnergy) to randomly determine * the emitted beta energy. * a: t The accepted beta energy is in variable BetaEner and in units of MeV! ****#***tt************************************************** real function BetaMom(BetaQ,BetaMax,particle,Z) real BetaQ,BetaMax,BetaEner,NTe real RNDM(2) end integer particle,iloop,Z iloop = 0 do while (iloop.ne.1) CALL GRNDMCRNDM,2) BetaEner = BetaQ*RNDM(1) NTe = BetaEnergy(BetaQ,BetaEner,BetaMax,particle,Z) if ( RNDM(2).le.NTe ) then iloop = 1 endif enddo betaMom = sqrt(BetaEner*BetaEner + 2*BetaEner*510.99906) return *****************************************************tt#*t#s * BETAENERGY (function): This function is used to simulate 1: ******* the energy distribution of beta decays. Note: This is Eq. 9.25 from ”Introductory Nuclear Physics" by Krane and corrected with the fermi correction function F(Z,E) Because the function becomes too large when the values are in keV, we use them in MeV. ************************************************************ real function BetaEnergy(BetaQ,Test,MaxFactor,particle,Z) integer particle,Z real BetaQ,Test,Q,Te,MaxFactor,nom,denom Te=Test*0.001 Q=BetaQ*0.001 if (particle.eq.3) then nom = MaxFactor*Z*(Q-Te)*(Q-Te)*(Te+0.51099906) *(Te+0.51099906) denom = 1-exp(-2*3.1415*Z*(Te+0.51099906)/ (137*sqrt(Te*Te+2*Te*O.51099906))) BetaEnergy=nom/denom else if (particle.eq.2) then if (Te.1t.0.003) then BetaEnergy=0. else nom = MaxFactor*Z*(Q-Te)*(Q-Te)*(Te+0.51099906) *(Te+0.51099906) 103 denom = 1-exp(2*3.1415*Z*(Te+0.51099906)/ + (137*sqrt(Te*Te+2*Te*0.51099906))) BetaEnergy=nom/(-denom) end if else type*,’particle should be 2 or 3’ end if return end ************************************************************ Subroutine Gaussian(sig,aver,totevt,z,resp) Real H_mod(986),Prob(986),H(986),Tot_Prob,z,y,sig integer Height(986),depth,hit(986),aver,totevt,fwhm logical first character*1 resp parameter (pi = 3.141592654) c print *,’gaussian subroutine’ * Initialize parameters. if(resp.eq.’y’) then do j = 1,985,1 Prob(j) = 0.0 H_mod(j) = 0.0 w(j) = 0.0 Heighth) = 0 hit(j) = o H_mod(j) = enddo Tot_Prob = 0.0 depth = 0 z 0.0 y = 0. 0.0 O" resp = ’n’ * Probability that ion implanted z um within a 985 um DSSD. Sig = FWHM/2.354. See equation 3-30 and 4-12 in Krane’s "Radiation Detection and Measurement." ** c Print *,’I am bombing here 11’ c fwhm = nint(sig*2.354) do j=1,985,1 Prob(j) = ((2.0*pi*(sig)**2)**(-0.5))tExp(-((j- 1 aver)**2.0)/(2.0*(sig)**2)) Tot_Prob = Tot_Prob + Prob(j) enddo 104 c Print *,’I am bombing here III’ do j=1,985,1 Prob(j) = Prob(j)/Tot_Prob !Normalized Prob. H(j) = Prob(j)*totevt !Height * When triggering 1 - 6 beta events, calculated probabilities * were all below acceptable limits. Needed to artificially * adjust this to prevent the program from getting trapped in * this section. if(totevt.ge.1.and.totevt.le.6)then w(j) = H(j)*6 endif H-mod(j) = AMODCHCj),1.0) if(H(j).ge.0.2.and.H(j).lt.0.5) then H(j) = 0.5 endif weight(j) = nint(H(j)) if(weight(j).ge.1) then Print *,j endif enddo endif * Determine the number of times an implant will occur at z. x = 5 20 Call Random(x) depth = nint(985.0*x) if(weight(depth).ge.1) then Height(depth) = Height(depth) - 1 else goto 20 endif y = rea1(depth) c PRINT *,Y y = y/10000 O z = -0.04925 + y !penetration w/in DSSD c Print *,z return end ********#****************************#*********************t Subroutine Random(Rannum) Integer N, Consti Real Rannum, Const2 Parameter (Constl = 2147483647, Const2 = 1./Const1) Save Data N /0/ If(N.eq.0) N = Int(Rannum) N = N * 65539 If(N.lt.0) N = (N + 1) + Constl Engineers and Scientists” by Larry Nyhoff and Sanford Leestma, The values Constl and Const2 have been arrived at Rannum = N * Const2 RETURN end * The subroutine Random has been taken from ”FORTRAN77 for 4: * page 420. * by using the following equations 2**M - 1 and 1/(2**M -1), * respectively. M respresents the number of * bit memory words of the computer, in this case M = 32. ************************************************************ * dssd_step #***********#*********************************************** * Step size and energy loss is determined here. ************************************************************ subroutine GUSTEP 1: * GEANT common blocks INCLUDE INCLUDE INCLUDE INCLUDE INCLUDE INCLUDE INCLUDE ’nsc1_bnmr: ’nscl_bnmr: ’nscl_bnmr: ’nsc1_bnmr: ’nscl_bnmr: ’nscl_bnmr: ’nscl_bnmr: * User common blocks INCLUDE ’nscl_bnmr: character set*4,det*4 integer name,eloss * store secondary particles call gsking(0) *--Prints the tracking and physics parameters after the current * step. c call gpcxyz * if (ISHIT(1).eq.1) then *--Stores current space point. call gsxyz * endif [prisc [prisc [prisc [prisc [prisc [prisc [prisc [prisc .geant .geant .geant .geant .geant .geant .geant .geant 106 .beta. .beta. .beta. .beta. .beta .beta. .beta. .beta. ginc]gcsets. ginc]gctrak. ginc]gckine. ginc]gcflag. .ginc]gconst. ginc]gcvolu. ginc]gctmed. ins’ ins’ ins’ ins’ ins’ ins’ ins’ uinc]uedep.ins’ C write(*,*) ’t##flflflflfiflfltfifl3886888883688##8##88####3#####66’ c write(*,*) ’IPART=’,ipart,’ NSTEP=’,nstep,’ ISTAK=’,istak c write(*,*) ’ X=’,vect(1),’ Y=’,vect(2),’ Z=’,vect(3) c write(*,*) ’NMEC=’,nmec c do iiii = 1,nmec c write(*,1492) namec(lmec(iiii)),lmec(iiii) 1492 format(5x,A4,i10) c enddo c write(*,*) ’destep=’,destep c write(*,*) ’istop=’,istop c write(*,*) ’kcase=’,kcase,’ ngkine=’,ngkine c write(*,*) ’ihset=’,ihset c write(*,*) ’ihdet=’,ihdet c do 70 j=1,42,1 c write(*,*) ’ numbv(’,j,’) ’,numbv(j) c70 continue c write(*,*) ’The total number of elements in numbv is ’,nvname if (IHSET.eq.’DEP2’) then if (IHDET.eq.’PIN2’) then write(*,*) ’Energy deposited’ Multiply destep by 10‘6 so that energy is in terms of keV. EnP2 = EnP2 + destep*1000000 write(*,*) ’EnP2,destep =’,EnP2,destep endif endif 0000*00‘l-0-I' if (IHSET.eq.’DEP3’) then if (IHDET.eq.’PIN3’) then write(*,*) ’Energy deposited’ EnP3 = EnP3 + destep*1000000 write(*,*) ’EnP3,destep =’,EnP3,destep endif endif 0000000 * If active detector volume isn’t DEP2 or DEPB, then... if(IHSET.gt.0.and.IHSET.ne.’DEP2’.and.IHSET.ne.’DEP3’) then * Converts the integer IHSET to its internal character form. encode(4,17,set) IHSET c print *, ’set =’,set * Converts the character set to the equivalent integer. decode(4,21,set) eloss c print *, ’eloss =’,eloss 107 IHSET is an integer. Comparing IHSET to the integer value of ’DEP2’. IHDET is an integer. Comparing IHDET to the integer value of ’PIN2’. * If not within PIN2 or PIN3, then... if(IHDET.gt.0.and.IHDET.ne.’PIN2’.and.IHDET.ne.’PIN3’)then Converts the integer IHSET to its internal character form. encode(4,17,det) IHDET * Converts the character set to the equivalent integer. decode(4,21,det) name print *, ’IHDET’,name * c write(*,*) ’Energy deposited’ Ener(name) = Ener(name) + destep*1000000 c write(*,*) ’En ’,name,’ destep =’,ener(name),destep endif endif if (NSTEP.eq.oldSTEP) then return endif oldSTEP = NSTEP 17 format(A4) 21 format(i4.4) return and ************************************************************ * dssd_out **************ass******************************************s * The output of tracking information is performed here. st*********************************************************s subroutine GUOUT * GEANT common blocks INCLUDE ’nscl_bnmr:[prisc.geant.beta.ginc]gcflag.ins’ INCLUDE ’nscl_bnmr:[prisc.geant.beta.ginc]gctmed.ins’ * User common blocks INCLUDE ’nsc1_bnmr:[prisc.geant.beta.uinc]uedep.ins’ INCLUDE ’nscl_bnmr:[prisc.geant.beta.uinc]uresol.ins’ INCLUDE ’nscl_bnmr:[prisc.geant.beta.uinc]uoutput.ins’ INCLUDE ’nscl_bnmr:[prisc.geant.beta.uinc]ukine.ins’ real Sigma logical thres_DS integer mult_DSSD * initialize threshold thres-DS = .false. * initialize multiplicity 108 mult_DSSD = 0 * draw the particle tracks c if (ISHIT(1).eq.1) then call gdxyzCO) c endif * Prints particle name and track. c call gdpart(0,11,0.25) * Draws hit points in sensitive detectors. c call gdhits(0,0,0,0,0.25) * Fill Histogram * HFILL( id, xValue(REAL), yValue(REAL), Weight ) CALL HFILL(1,EnP2,0,1.0) CALL HFILL(2,EnP3,0,1.0) * Check threshold on each of the pixels on the strip detector. do j = 1,1600,1 if(ener(j).gt.thres_pixi(j))then thres_DS = .true. EnDs = ener(j) + EnDs mult_DSSD = mult_DSSD + 1 endif enddo if(Thres_DS.eq..true.) then CALL HFILL(3,EnDs,O,1.0) CALL HFILL(4,EnP2+EnP3+EnDS,0,1.0) endif CALL HFILL(5,eBeta,O,1.0) Checking beta efficiency for PIN2. if(EnP2.gt.0.and.Thres_DS.eq..true.) then CALL HFILL(11,eBeta,O,1.0) CtP2 = CtP2 + 1 EffP2 real(CtP2)/real(IDEVT) ErrP2 EffP2*Sqrt((1.0/rea1(CtP2))*(1.0/ 1 real(IDEVT))) print *, ’EffP2’,EffPZ,’+/-’,ErrP2 00000001! CALL HOPERACIDI,CHOPER,ID2,ID3,C1,C2) ID3 = C1*ID1 (OPERATION) C2*ID2 ID1,ID2 operand histogram identifiers CHOPER identifies the operation, +,-,*,/ along will the **** 109 * computed errors * ’B’ computes binomial errors * ’E’ computes errors on resulting hist. assuming ID1 * and ID2 are indep * ID3 identifier for the hist containing operation * C1,C2 multiplicative constants c CALL HOPERA(11,’/E’,5,6,1.0,1.0) c endif * Checking beta efficiency for PIN3. if(EnP3.gt.0.and.Thres_DS.eq..true.)then CALL HFILL(12,eBeta,0,1.0) CtP3 = CtP3 + 1 EffP3 = rea1(CtP3)/real(IDEVT) ErrP3 = EffP3*Sqrt((1.0/rea1(CtP3))+(1.0/ 1 real(IDEVT))) c print *, ’EffP3’,EffP3,’+/-’,ErrP3 CALL HOPERA(12,’/E’,5,7,1.0,1.0) endif * Checking beta efficiency for DSSD. c if(Thres_DS.eq..true..and.mult_DSSD.eq.1) then if(Thres_DS.eq..true.) then c print *,’Above threshold’ CALL HFILL(13,eBeta,O,1.0) CtDSSD = CtDSSD + 1 EffDSSD = rea1(CtDSSD)/real(IDEVT) EerSSD = EffDSSD*Sqrt((1.0/rea1(CtDSSD))+ 1 (1.0/real(IDEVT))) CALL HOPERA(13,’/E’,5,8,1.0,1.0) endif EnP2 = 0.0 EnP3 = 0.0 EnDs = 0.0 do j = 1,1600,1 ener(j) = 0.0 enddo * don’t write spectra until number of events is a factor of * ’output’ IF (MOD(IDEVT,output).EQ.O) then CALL HistOut endif c print *,’stuck in jp-outii’ 110 return end ************************************************************ * HistOut: Write the Histograms to disk ******#****tt*********************************************** subroutine HistOut * GEANT common blocks INCLUDE ’nscl_bnmr:[prisc.geant.beta.ginc]gcf1ag.ins’ INCLUDE ’nscl_bnmr:[prisc.geant.beta.ginc]gctmed.ins’ * User common blocks INCLUDE ’nscl_bnmr:[prisc.geant.beta.uinc]uoutput.ins’ INCLUDE ’nscl_bnmr:[prisc.geant.beta.uinc]uedep.ins’ write(*,*) ’On Event #’,IDEVT c write(*,*) ’EffP2 = ’,EffP2,’+/-’,ErrP2 write(*,*) ’EffP3 = ’,EffP3,’+/-’,ErrP3 write(*,*) ’EffDSSD’,EffDSSD,’+/-’,EerSSD write(*,*) ’Counts DSSD’,CtDSSD if (Begin.eq.1) then CALL HROPENCZO,’JIP’,FileOut,’N’,1024,ISTAT) CALL HROUT(0,VersNum,’ ’) CALL HREND(’JIP’) close(20) Begin = 0 else OPEN(20,File=FileOut,STATUS=’OLD’) close(20,STATUS=’DELETE’) CALL HROPEN(20,’JIP’,FileOut,’N’,1024,ISTAT) CALL HROUT(0,VersNum,’ ’) CALL HREND(’JIP’) close(20) endif return end *******************************ss**************t*t********** * GAUSSRAN (function): Generate a random gaussian distribution **************#*******************#**************#********** real function GAUSSRAN(mu,sigma) real mu,sigma,rndm(12),sum call grndm(rndm,12) :nzm=0. do i=1,12 sum=sum+rndm(i) 111 and do gaussran=mu+(sum-6)*sigma return and *stt:s**t*ssstssss#***************************************** * dssd_last ***************************#******************************** * This is the main body code for initiating and nicely ending * GEANT simulation runs. ************************************************************ subroutine UGLAST * GEANT common blocks INCLUDE ’nscl_bnmr:[prisc.geant.beta.ginc]gcflag.ins’ * User common blocks INCLUDE ’nscl_bnmr:[prisc.geant.beta.uinc]uoutput.ins’ INCLUDE ’nsc1_bnmr:[prisc.geant.beta.uinc]uedep.ins’ print *,’in jp_last’ IF (MODCIDEVT,output).NE.O) then print *,’before histout call’ type*,’On Event t’,idevt * output all histograms into the hbook file. call HistOut print *,’after histout call’ endif print *,’before glast call’ *--Call standard GEANT termination routine. call glast return end A.0.5.2 Sample Input File The following is a sample input file used to calculate the beta. efficiency of 908T ((2,; = 546 keV). RNDM 5126527 35277282 !Initial random numbers RUNG 1 1 !User run number AUTO 0 !=0 reads user defined tracking parameters !=1 uses default tracking parameters TRIG 25 !Number of events to process CUTS 0.000010 0.00001 0.000010 !Low energy cuts for particles 0.000010 0.000010 0.000010 !(see BASE040) 0.000010 1.64 1.e4 112 0.000010 1.910 0. 0. 0. O. 0. MUNU 0 HADR 0 DRAY 0 DEBU 0 TIME 100000 1 ERAN 1.8-6 EVTPRT 1000 KINEOPT 0 BETOPT 0 PARTICLE 3 Z 38 AVER_DEPTH 691 STD 6.28 ENERGY 546 OUTPUT 1000 !Muon nuclear interaction flag !Hadronic process flag !Delta-ray flag 0 0 !1st event to debug, last, print freq. 10000000 !Time left after initialization, !time required for termination, !test every itime events 0.01 90 ! !Obsolete, used to print details of this event !=0 emits particle w/ ENERGY in 4pi !=1 emits particle w/ ENERGY from O-theta !=2 emits particle w/ ENERGY at theta & phi !=O emits beta particle w/ realistic beta !spectrum w/ Qbeta = ENERGY !=1 emits beta with ENERGY !Type of particle to emit [CONSBOO] !Proton number of emitting nucleus !Aver. implantation depth (um) for !given nuclide !Sigma=FHHM/2.354 for AVER_DEPTH !Energy of the particle (in keV) !After OUTPUT number of evnts triggered, !HistOut subroutine triggered !(see dssd_out) A.0.5.3 Running the GEANT simulation Before the GEANT simulation can be run, the FORTRAN program shown in Sec. A.0.5.1 needs to be compiled. To compile the program, the following command file shouhilxaexecuted: 3 define cernlib DISK$SYS-LIB:[ALPHA.NSCL.CERNV5.97A.lib] $ for dssd-geant $ link/exe=dssd_geant.exe - dssd_geant, - CERNLIB:czdummy.obj, - CERNLIB:ctldummy.obj, - CERNLIB:gethostname.obj, - CERNLIB:geant321/1ib, - CERNLIszawlib/lib, - CERNLIB:graflib/lib, - CERNLIB:grafxli/lib, - CERNLIszacklib/lib, - CERNLIB:mathlib/lib, - 113 CERNLIszernlib/lib, - grafmotif/opt 3 exit Running this command file will generate an executable named dssd_geant,.exe. To run this program in V MS, sin'lply type: run dssd_geant This action will load the GEANT program. resulting in the GEANT prompt and a graphics window showing the detector setup (see Fig. A.1). To produce a given number of beta particles, N(beta), emitted from the source, type: trigger N(beta). As the program is currently set. up, the calculated 13 efficiency from the simulation will be printed after every 1000 beta events. This may be modified by changing the OUTPUT number in the input file. Further instructions for using GEANT may be obtained from the GEANT online manual [75]. 114 Figure A.1: GEANT simulated DSSD setup. 115 Appendix B Gamma-ray Efficiency Calculations B.0.6 Experimental Efficiency for Exp. 97 004 To extract a peak gamma. ray efficiency for the rotating target wheel experiment, a mixed gamma ray source consisting of 1258b and 154'155Eu and a 228Th source were utilized. The mixed source was produced at noon eastern standard time on September 1, 1988. The source consisted of 2.277 pCi 154Eu, 0.7527 ,uCi 155Eu and 1.630 pCi 125Sb. The activity of each component of this mixed source has been determined from the tabulated emission rates for the gamma ray transitions associated with each of the radionuclides as provided by N IST. The activity of the 228Th source was determined to be 0.5 pCi shortly after the measurement by Reg Ronningen. A 30 minute gamma ray singles spectrum was acquired for each source at the same source-to—detector distance used during the experiment (15 mm for the 80% HPGe detector and 45 mm for the 120% detector). The prominent gamma ray peaks were fit to Gaussians using DAMM, providing the area of each fit, the error and the F WHM. An emission rate was calculated for each peak by dividing the area of the fit by the duration of measurement, 30 minutes. To correct for the computer and electronic dead time of the system, a pulser signal was transported through the test input of the Ge detectors. The ratio of the number of counts in the pulser peak to the number of counts emitted by the pulser provided a dead time correction factor of 0.252. Theoretical emission rates were calculated using Eq. 2.1 and an elapsed time of 3392.9 days from the time the source was 116 F1 Table 3.1: Sources used for total efficiency measurement. Source ActivityflL) (pCi) To E, (keV) 5706 6.00 March 30. 1079 122, 136 6OCo 9.992 November 15, 1997 1173, 1332 137Cs 10.11 November 1, 1988 667 2”Th 13.91 October 1, 1988 583, 2615 manufactured. By taking the ratio of the experimental to the theoretical emission rates, peak efficiencies were determined for the prominent gamma ray peaks. The data was fit. with a fifth order polynomial of the form: log (pm), 2 3.689 (log E)5 -—- 48.068 (log E)4 + 249.69 (log E)3 —616.47 (log E)2 + 833.87 16g E — 429.83. (13.1) To correct the peak efficiency data for summing effects, it was necessary to extract a total efficiency curve for the Ge detectors. For this measurement, four sources were used, 57’60Co, 137Cs and 228Th, see Table B.1. To determine the total gamma ray efficiency for each of the sources listed in Table B.1, a gamma ray singles spectrum was acquired for 30 minutes. After the collection period, the gamma ray spectrum was summed from above a low energy threshold to a channel just below the pulser peak. A dead time correction factor was calculated similar to the method discussed above. The spectrum area was divided by the dead time correction factor, yielding a corrected spectrum area. To obtain the total efficiency, the corrected spectrum area was divided by the number of counts expected from the source (the theoretical activity of the source multiplied by the run time). To calculate the total efficiency for the 57Co source, several additional factors were taken into consideration. 57Co emits two low-energy gamma rays of energy 122 keV and 136 keV in parallel. Thus, for each beta particle emitted by the source, one of the two gamma ray transitions is observed. The calculated total efficiency was calculated for the average of the two energies, 129 keV. In addition, since the two emitted 117 photons are low in energy, one must also consider a competing nuclear de—excitation mode, internal conversion. In this process, the excitation energy is transferred to an orbital electron within the atom, and the electron is emitted with an energy equal to the excitation energy minus the binding energy of the electron [76]. Thus, the total activity of the source is: A = A, + A6- = A,(1 + 07’) where A, is the activity due to the emission of gamma radiation, .46- is the activity due to the conversion electron process and 017 is the total conversion coefficient, zip/AT To correct for this process, the calculated ('1‘ was multiplied by (1 + 01‘), 1.17 [77], where or was the average cm for the 122 keV and 136 keV transitions. K] W ten calculating the total efficiency for 60Co, one needs to consider that for each emitted beta particle, two gamma rays, 1173 keV and 1332 keV, are emitted in series. Thus, the calculated total efficiency was divided by two. In addition, the total efficiency was calculated for the average of the two energies, 1253 keV. In the case of 228Th, the three prominent gamma rays emitted by the source are 269 keV, 583 keV and 2615 keV. To determine the total efficiency at an energy of 2615 keV, the gamma ray spectrum was summed from above 586 keV. To account for the Compton scattered gamma rays below 586 keV, a background line extending to the beginning of the spectrum was drawn. The area encompassed by this box was extracted and added to area of the spectrum above 586 keV. To determine the total efficiency at 2614 keV, the number of counts in the pulser peak was deducted from the calculated value. To correct for dead time, this value was divided by the dead time correction factor. The total efficiency was determined by dividing the corrected spectrum area by the number of counts expected from the source (the theoretical number of counts). Figure B.1 depicts the total efficiency for the four sources detailed above. The data was fit with a second order polynomial of the form: (Tom, 2 1x10-8 15:2 — 5x10-5 E + 0097 (B2) 118 00°. 00°: 0.06 a Total Efficiency 9 2 0.03 * 0.02 1 0.01 ~ 0 500 1000 1500 2000 2500 3000 Energy (keV) Figure 3.1: Total efficiency for the 120% Ge detector at a source—to—detector distance of 45 mm. The solid line is a second order polynomial fit to the data. Using the fits to the uncorrected peak and total efficiency data, the summing correction factors listed in Table B.2 were calculated (see discussion in Appendix C). Sum corrected peak efficiencies were determined by dividing the uncorrected peak efficiencies by the correction factors. To extend the peak efficiency data to higher energies, a 228Th source was utilized. 228Th emits three prominent gamma rays of energy 269 keV, 583 keV and 2614 keV. The peak efficiencies for the 583 keV and 2615 keV gamma rays were calculated in a similar manner discussed for the mixed source. The correction factors for the 583 and 2615 keV peaks were deduced from Eq. C5. p, was calculated by multiplying the relative intensity of the photon of interest by 0.9916 [9]. Table B.3 lists gamma rays coincident with the 583 keV and 2615 keV transitions, and the calculated coefficients (Ia/p.583 and p7/p2515) for the summing corrections. Neglecting terms with coefficients less than 0.01, the summing corrections 119 Table 3.2: Summing corrections for the prominent gamma rays emitted by the mixed gamma ray source as documented by NIST. {E} is the uncorrected peak efficiency for a gamma ray emitted with energy E and [E] is the total efficiency at energy E. To get the correction factor in the same form as discussed in Appendix C, take the inverse of the correction term. E (keV) Correction 86.6 1.0 105.3 1.0 123.1 (1.0-0.072[248.0]-0.055[591.7]-0.019[692.4]-0.120[723.3] -0.049[756.9]-0.130[873.2]-0.201[1004.8]-0.010[1246.2] -0.401[1274.4]-0.021[1596.5]) 176.4 (1.0—0.035[204.11-0.057[3210]) 248.0 (1.0-0.287[42.8]-0.455[123.1]-0.072[444.4]-0.022[582.0] -0.134[591.7]-0.015[612.2]-0.043[625.2]-0.022[676.6] -0.039[723.3]-0.613[756.9]-0.059[892.7]-0.022[904.1] —0.130[1246.2] 380.5 (1.0+0.157{176.4}{204.l}/{380.5})*(1.0-0.010[‘27.4] -0.190[116.9]) 427.9 (100.598[2741—0059(355]) 463.4 (10+0.169{35.5}{427.9}/{463.4}) 591.7 (1.0—0.297[42.8]-0.455[123.1]-0.178[‘248.0]-0.196[756.9] -0.800[1004.8]) 600.6 (1.0+0.010{427.9}{172.6}/{600.6})*(1.0—0.597[27.4] -0.059[35.5]) 635.9 (1.0+0.012{427.9}{208.0}/{635.9})*(1.0—0.597[27.4] -0.059[35.5]) 723.3 (1.0—0.154[42.8]-0.243[123.1]-0.013[248.0]—0.014[625.2] -0.518[873.2]-0.465[996.4]) 873.2 (1.0+0.024{248.0}{625.2}/{873.2})*(1.0-0.282[42.8] -0.455[123.1]-0.894[723.3]) 996.4 (1.0+0.507{123.1}{873.2}/{996.4})*(1.0-0.894[723.3]) 1004.8 (1.0+0.221{248.0}{756.9}/{1004.8})*(1.0—0.282[42.8] 0455(123.1]—0.217[591.7]) 1274.4 (1.0+0.014{692.4}{582.0}/{1274.4})*(1.0-O.‘281[4‘2.8] -0.455[123.1]) 1596.5 (1.0+0.275{692.4}{904.1}/{1596.5}+5.568{873.2} *{723.3}/{1596.5}+2.094{1004.8}{591.7}/{1596.5} +0.052{1118.5}{478.3}/{1596.5})*(1.0-0.281[42.8] —0.455[123.1]) Table 3.3: Summing correction coefficients for the 583 keV and 2615 keV gamma rays emitted following the decay of 208T1, a member of 228Th decay chain. E (keV) Rel. Intensity p, Coeflicient(583) 277.4 6.36 x 10‘2 6.31 x 10'2 7.46 x 10'2 510.8 2.28 x 10’1 2.26 x 10"1 2.68 x 10'1 722.0 2.03 x 10"3 2.03 x 10"3 2.38 x 10'3 748.7 4.30 x 10‘4 4.26 x 10'4 5.05 x 10"4 763.1 1.83 x 10"2 1.81 x 10’2 2.15 x 1072 927.6 1.32 x 10'3 1.31 x 10‘3 1.55 x 10-3 982.7 2.05 x 10"3 2.03 x 10'3 2.41 x 10"3 1160.8 1.10 x 10‘4 1.09 x 10’4 1.29 x 10’4 1185.1 1.70 x 10“4 1.69 x 10’4 2.00 x 10‘4 1282.8 5.20 x 10‘4 5.16 x 10"4 6.10 x 10-4 2614.5 1.00 0.9916 1.17 E (keV) Rel. Intensity p, Coefiicient(2615) 583.1 8.52 x 10"1 8.45 x 10’1 8.52 x 10-1 860.6 1.25 x 10'1 1.24 x 10"1 1.25 x 10'1 1093.9 4.00 x 10"3 3.97 x 10’4 4.00 x 10‘4 1381.1 7.00 x 10‘5 6.94 X 10'5 7.00 x 10"5 1744.0 2.00 x 10’5 1.98 X 10"5 2.00 x 10'5 have been calculated as follows: 1 C583 : (1 — 0.0746(27 C2615 = 1 7.4] — 0.268[510.8] - 0.0215[763.1] — 0.992[2614.5]) (1 — 0.852[583.1] — 0.125[860.6]) To incorporate these data points into the corrected peak efficiency plot determined for the mixed source, these value were first normalized. A linear regression of the peak efficiencies at energies 463 keV and 592 keV, scaled the 583 keV efficiency from 1.48% to 2.31%. To properly adjust the peak efficiency for the 2615 keV gamma ray, the calculated peak efficiency was multiplied by a scaling factor, Normalized epk(583) Calculated cpk(583) ' ScalingFactor 2 Figure B.2 depicts the peak efficiency data points for the mixed source and the 228Th source. Table B.4 provides a list of the energies, calculated peak efficiencies and errors shown in Fig. B.2. To determine the peak efficiency at an unknown energy, the data 121 log Peak Efflcloncy 3 1.4 1.9 2.4 2.9 3.4 3.9 '09 Emmy (keV) Figure B.2: Sum corrected peak efficiency for the 120% Ge detector at a source-to—detector distance of 45 mm. The solid line represents a fifth order polynomial fit to the data. was fit to a fifth order polynomial of the form: log (pmk(120%)= 1.5093 (log E)5 — 20.79 (log E)4 + 114.2 (log E)3 — 312.65 (log E)? + 426.02 log E — 232.16. (B5) The peak efficiency for the 80% detector at a source-to—detector distance of 15 mm was determined in a similar manner as the 120% HPGe. Table B.4 provides a list of the energies, peak efficiencies and errors calculated for this second Ge detector. The data was fit to a fifth order polynomial of the form: 10 c 5,0),(80‘76) = —1.2848 (lo E '5 + 16.499 log E 4 — 82.019 log E 3 g p g + 194.97 (log E)? — 217.38 (log E) + 86.276. (8.6) In the orientation discussed above for the 80% and the 120% Ce detectors, a peak y-ray efficiency of 4.5% at 1.274 MeV was attained. Table B.4: Peak efficiency data for the 120% and 80% Ge detector used in Exp. 97004. E (keV) Ge 120% Ge 80% (peak (%) Error (peak (%) Error 86.6 2.65 0.13 0.708 0.11 105.3 3.83 0.18 1.43 0.16 123.1 4.03 0.06 3.10 0.06 176.4 4.07 0.45 3.34 0.53 248.0 3.63 0.03 8.83 0.12 427.9 2.75 0.03 6.64 0.08 463.4 2.48 0.05 5.36 0.11 583.1 2.31 0.01 5.01 0.01 591.7 2.30 0.03 4.98 0.09 600.6 2.27 0.04 5.14 0.13 635.9 2.26 0.04 4.80 0.12 723.3 1.98 0.02 4.21 0.07 873.2 1.86 0.02 3.80 0.06 996.4 1.64 0.02 3.38 0.08 1004.8 1.72 0.02 3.52 0.06 1274.4 1.48 0.01 2.98 0.03 1596.5 1.39 0.03 3.13 0.05 2614.5 1.35 0.03 2.47 0.01 123 Table 3.5: Peak efficiency data for the 120% and 80% Ge detectors used in Exp. 98020. E (keV) Ge 120% CC 80% cpeak (%) Error Cpeak (%) Error 123.1 0.755 0.015 0.753 0.029 248.0 1.020 0.110 0.940 0.067 427.9 0.825 0.073 0.826 0.077 463.4 0.849 0.138 0.705 0.156 591.7 0.885 0.085 0.622 0.051 600.6 0.369 0.186 0.691 0.094 635.9 0.577 0.151 0.596 0.130 723.3 0.713 0.021 0.567 0.031 873.2 0.672 0.022 0.560 0.021 996.4 0.635 0.031 0.529 0.031 1004.8 0.676 0.021 0.506 0.022 1274.4 0.590 0.009 0.432 0.009 1596.5 0.588 0.033 0.380 0.026 B.0.7 Experimental Efficiency for Exp. 98020 To determine the peak gamma ray efficiency for the DSSD experiment, the mixed gamma ray source was used. The peak efficiencies were calculated using the same method discussed above. The calculated efficiencies for the 120% and the 80% Ge detectors were corrected for summing. However, since the clover detector consisted of smaller crystals (four 25% crystals), and were further removed from the source, summing corrections were not performed on the clover detectors. To determine the peak efficiencies for each of the clover detectors, the gamma ray spectra for each crystal within a given clover were summed on an event-by-event basis. A dead time correction factor was obtained for each detector by taking the ratio of the number of counts in the master gate live sealer to the master gate scaler. The peak efficiencies for the prominent gamma ray transitions are listed in Tables B.5—B.6, however, note that these efficiencies were determined for a point source. B.0.7.1 Computer Simulation In the DSSD experiment, the secondary beam was defocussed to illuminate z 2/ 3 of the active area of the strip detector. To determine the peak efficiency for an extended 124 Table 3.6: Peak efficiency data for the Ge clover detectors used in Exp. 98020. E (keV) GeCl GeCé’? GeC3 (pm), ((71) Error (mat (%) Error 6pm].- f (71‘) Error 86.6 1.56 0.28 1.48 0.22 1.54 0.26 105.3 2.18 0.38 2.02 0.30 2.60 0.38 123.1 2.15 0.09 2.24 0.08 2.48 0.09 248.0 1.93 0.08 2.03 0.09 2.25 0.13 427.9 1.58 0.11 1.62 0.11 1.7... 0.13 463.4 1.64 0.21 1.27 0.20 1.66 0.25 591.7 1.28 0.08 1.23 0.07 1.37 0.07 600.6 1.13 0.13 1.34 0.13 1.47 0.13 635.9 1.21 0.17 1.26 0.16 1.32 0.17 723.3 1.20 0.04 1.17 0.02 1.28 0.04 73.2 1.01 0.02 1.02 0.03 1.14 0.05 996.4 0.978 0.035 1.01 0.04 1.10 0.07 1004.8 1.01 0.03 0.993 0.031 1.09 0.05 1274.4 0.875 0.022 0.852 0.040 0.953 0.045 1596.5 0.849 0.049 0.854 0.054 0.964 0.039 gamma. ray source, MCNP, a general Monte Carlo N-particle transport code, was utilized. To perform the simulation, it was necessary to enter the dimensions and the ge— ometries of the Ge detectors within the MCNP input file. The Ge crystal in the 120% detector is 105.8 mm in length, and 80.8 mm in diameter. The distance from the endcap to the crystal is 4 mm. The closed—ended coaxial detector has a hole 8 mm in diameter and 92 mm deep running through the core of the crystal. The core of the detector was removed to provide an electrical contact. A second contact was produced by placing an electrode on the outer surface of the Ge crystal. A 0.7 mm layer of inactive Ge runs along the outer perimeter of the crystal. The crystal in the 80% detector is 92.0 mm in length and 75.5 mm in diameter. There is a 4 mm distance between the crystal and the endcap of the detector. This coaxial detector has a hole 8 mm in diameter and 78 mm in length through its core. Similar to the 120% Ge detector, a 0.7 mm layer of inactive Ge runs along the outer w'w- (a) //\\ (b) //TT\\\ . \ / \ ‘\. / Clover 9 // Clover 17 / U 120% Go \ 7’] 120% Go ] . \\ °'°"°' 3U . \ 30% Gem / ‘ \\\ // .\ / (c) fi\ if- / / Clover 17 Clover 8 Clover 9 Figure 3.3: The simulated Ge detector orientations in the (a)x-y plane, (b)x-z plane and (c)y-z plane. perimeter the 80% crystal. The crystals in the clover detectors are 80 mm in length and 45 mm wide. The inner edges of the crystals have been shaved to configure four crystals in clover geometry. There is a 0.2 mm gap between each pair of crystals. In addition, the distance from the crystal to the endcap of the detector is 10 mm. Once the dimensions and the geometries of the Ge detectors were entered into MCNP (see Fig. B.3), a simulation was performed to compare the experimental peak efficiencies of the detectors with the simulated efficiencies. To make this comparison, a point source was simulated using the energies listed in Tables B.5—B.6. The simulated and experimental measurements were in good agreement for the 80% and 120% Ce 126 ~l\ _ 0.013 .________ -, - - “MK 0.000 E 0.00 ~ 0.000 . 0.000 ~ .2: 0.004 .. 0 004 ~ 2 0.002 . 1 2 0.002 . . 0 1000 2000 0 1000 2000 Energy (keV) Energy (keV) (a) (b) § 0-034 “*—— — ——- — 0.034 0.034 1 ,, 0.024 , i. 0.024 . 0.024 8 0.0147 0.014 f 0.014 1 . 8 0-004 . i 0.004 . 1 0.004 . 1 , o 1000 2000 0 1000 0 1000 2000 Enemy (keV) Enemy (keV) Enemy (keV) (e) (d) (a) Figure BA: The experimental and simulated peak efficiencies for a point source for (a) the 120% Ge detector, (b) the 80% detector, (c) clover 8, (d) clover 17 and (e) clover 9. The energy spectra for each crystal within a given clover has been summed yielding a total energy spectrum for the clover. The solid line represents the MCNP simulation. Note that a dead layer was not considered in the MCNP simulation for the clover detectors. detector when a 4.5 mm dead layer was considered (see Fig. B4). The inactive Ge layer in both the 80% and 120% Ge detectors were extended from the manufacturer’s quoted value to better match the experimental peak efficiencies at low energy. One would expect a larger dead layer on these detectors because both crystals are p-type. In p-type detectors, the high voltage contact is placed on the outside of the crystal, thereby increasing the inactive layer of germanium. The clover detectors, on the other hand, are n-type crystals. In n-type detectors, the high voltage contact is along the core of the crystal. Thus, one would expect a much smaller inactive Ge layer in n-type detectors. To determine the peak efficiency for the DSSD setup, an extended gamma source was simulated in MCNP. An extended source 2.5 cm in diameter and offset by 4 mm up and 4 mm to the right of the center of the DSSD was considered to mimic the beam profile shown in Fig. 3.7. A 1 mm dead layer on the face and outer perimeter of the clover detectors was considered to improve the agreement between the experimental a r— l 4.5 4.5 -- ~ -1 v I: -1.7 . t: -1.7 « -1-2 1 34.1% “-1.91 54"“ -1,‘ l 2414 141* i-Lr -u 4 .13 4 .2 -4 3 -2.5 3 ~25 3 -12 . -2.7 e % -2.7 . 1 -2.4 . 4 1.7 2.7 3.7 1.7 2.7 3.7 1.7 2.7 3.7 [ log Energy log Enemy log Energy (a) (b) (C) a, -. 22“”? - -1.2 '1 2 .M . E 4.4 « E 4.4 « 5 3 4.6 ~ I 4.0 4 2:: 49 < u“ 4 . '10. "‘ ‘ 'u 4 \ 1 .1 . .2 ~ 0 i 3 4.21 3 -2.2 « 3 4" ; ~24 . . -2.4 . 4 -24 . . 1.1 2.7 3.7 1.7 2.1 3.7 1,1 2,7 37 be My I00 Enemy log m (d) (e) (0 Figure B.5: The simulated peak efficiencies for an extended source for (a) the 120% Ge detector, (b) the 80% detector, (c) clover 8, (d) clover 17, (e) clover 9 and (f) the Ge array. The solid line is a fifth order polynomial fit to the simulated efficiency data. and simulated peak efficiencies. Figure B.5 shows the simulated peak efficiencies for the extended source and Table B.7 lists the fit parameters. To ensure that the MCNP simulation was treating the extended source properly, several experimental runs were performed with a 22Na source. The location of the point source was varied for each run. Thirty minute measurements were made with the source placed at the center and four corners of the DSSD position. The area of the 511 keV peak was extracted for each source position and normalized by dividing the area by the real time of the measurement. To compare the results with the simulation, a ratio of the corrected area of the 511 keV peak when the source was placed on each corner was divided by the area of the 511 when the source was located at the center position. Table 38 lists the experimental and simulated 511 keV ratios. The values are in good agreement, suggesting that the simulation was indeed treating the extended Table source for 3.7: A the Ge detectors fit. to t he used simulated in peak efficiency Exp. 98020. The fit. for an extended is in the form: log (mat : A*(log E)5 + B*(log E)4 + C *(log E)3 + D*(log E)2 + E*log E + F. Detector A B C D E F 80% Ge 1.351 -19.566 112.71 -322.88 459.43 -261.39 120% Ge 0.9035 -13.621 81.452 -241.54 354.79 -208.18 Clover 8 0.3931 -5.8652 34.639 -101.27 146.05 -84.348 Clover 9 0.1868 -2.9707 18.603 —57.42 86.865 -52.884 Clover 17 0.4849 —7.0859 41.124 -118.48 168.85 -96.395 Ce Array 0.4982 -7.3746 43.324 -l26.29 182.16 -104.66 Table 3.8: Comparison of the experimental and simulated ratios of the 511 keV peak area for the 22Na at the four corners of the DSSD position to its central position. The positions are designated as UR (upper right), UL (upper left), LR (lower right), LL (lower left) and CC (center). Ratio G6 1.20% Ge 80% Exp. (MCNP Exp. MCNP UR/CC 0.797(14) 0.833 0.683(33) 0.615 UL/CC 0.810(13) 0.830 0.647(31) 0.599 LR/CC 0.888(13) 0.836 1.660(76) 1.438 LL/CC 0.870(17) 0.828 1.196(58) 1.443 source properly. However, it should be noted that the peak efficiencies calculated for an extended source did not differ greatly from the peak efficiencies calculated for a point source (cpeafiextended) = 0.33% and (peak(point) = 0.43% at 1.27 MeV for the 80% HPGe). B.0.7.2 Sample Input File The following is a sample input file. It specifies the dimensions and geometries of the 80%, the 120% and the three clover Ge detectors. In addition, an extended source has been simulated. In this simulation, 500000 photons of energy 900 keV were emitted by the source. c 98020 experiment with extended source 1 0 1 $outside world 2 2 -0.00114 -1 #3 #4 #5 #6 87 #8 #9 #10 #11 #12 #(30 -31 -20) #(44 -45 -34) #(47 -49 50 -51 52 -57> Table B.9: Continued:Comparison of the experimental and simulated ratios of the 511 keV peak area for the 22Na at the four corners of the DSSD position to its central position. The positions are designated as UR (upper right), UL (upper left), LR (lower right), LL (lower left.) and CC (center). Each crystal of the clover detectors is labelled as A, B, C and D. In addition, the MCNP simulation is listed as A, B, C and D. Ratio Clover 8 Exp. A A Erp. B B Exp. C C Exp. D D UR/CC 1.20(13) 1.28 132(8) 1.22 1.73(19) 1.82 1.93(11) 1.72 UL/CC 065(7) 0.61 067(4) 0.62 071(8) 0.66 068(4) 0.68 LR/CC 1.80(20) 1.75 2.00(11) 1.82 1.26(14) 1.22 1.38(9) 1.17 LL/CC 074(8) 0.67 075(4) 0.72 064(7) 0.57 067(4) 0.59 Ratio Clover 17 Exp. A A Exp. B B Esp. C C Exp. D D UR/CC 1.75(16) 1.79 2.08(20) 1.74 1.31(14) 1.21 1.41(16) 1.24 UL/CC 1.22(11) 1.20 1.38(14) 1.23 1.75(19) 1.80 1.85(21) 1.80 LR/CC 065(6) 0.71 068(7) 0.65 058(7) 0.57 062(7) 0.60 LL/CC 059(6) 0.60 064(7) 0.58 068(7) 0.69 066(8) 0.66 Ratio Clover 9 Exp. A A Exp. B B Exp. C C Exp. D D UR/CC 058(5) 0.56 055(6) 0.62 062(8) 0.71 063(7) 0.73 UL/CC 1.10(9) 1.29 1.03(11) 1.09 1.72(22) 1.89 1.52(16) 1.49 LR/CC 061(5) 0.66 066(7) 0.71 060(8) 0.56 056(6) 0.61 LL/CC 1.72(14) 1.82 1.69(18) 1.52 1.29(16) 1.31 1.24(13) 1.08 130 32 33 34 35 36 37 38 39 40 41 42 43 0(76 ~78 79 ~80 81 ~86) 0(105 ~107 108 ~80 81 ~115) $inside world 3 ~2 22 ~5 ~5 29 ~2 36 OHHHHHHHHonHoonHoooowwwwww 48 .71 ~2 3 ~4 .71 .71 .71 .71 .71 .71 ~11 ~9 ~15 ~13 18 .71 .32 .32 .32 .32 .32 .32 .32 .32 7 ~3 ~4 6 8 ~7 ~4 6 ~5 6 ~8 9 ~9 11 ~12 13 ~13 15 ~14 16 18 ~16 15 ~17 ~3 9 13 ~20 ~23 .32 24 ~25 ~26 ~28 013 .32 19 ~20 ~21 ~27 013 014 ~32 ~20 015 014 013 .71 30 ~31 ~20 016 015 014 ~34 ~37 .32 38 ~39 ~40 ~42 018 .32 33 ~34 ~35 ~41 018 019 ~46 ~34 020 019 018 44 ~45 ~34 021 020 67 ~69 70 67 ~69 ~71 67 68 70 67 ~71 66 60 66 ~61 66 60 66 ~61 ~53 54 ~55 56 027 019 023 024 025 026 028 013 018 $i30160 backplate $is0160 oring $180160 flange $chamber wall 1 $chamber wall 2 $chamber wall 3 $isoIOO flange $chamber vacuum 1 $chamber vacuum 2 $chamber vacuum 3 center contact active area crystal vacuum region $Ge080 cryostat $06080 $GeO80 $Ge080 $Ge080 $Ge120 center contact $Ge120 active area $09120 crystal $Ge120 vacuum region cryostat $Gel20 $clover $clover $clover $clover $clover $clover $clover $clover 029 030 3 ~2.71 027 028 .32 .32 .32 .32 .32 .32 .32 .32 OHHHHHHHH l 01 77 040 033 ~82 023 47 ~49 50 ~51 52 ~57 031 024 025 026 $clover cryostat 029 030 ~101 96 ~102 96 ~103 96 ~104 96 95 95 95 95 83 ~84 034 035 023 ~98 ~98 97 97 ~88 ~88 87 87 99 ~100 99 ~100 89 ~90 89 ~90 033 034 035 036 85 ~86 037 038 039 036 $clover vacuum region 3 ~2.71 76 ~78 79 ~80 81 ~86 041 037 038 039 040 033 034 035 036 $clover cryostat 1 -5.32 ~130 125 ~115 -127 99 131 Sclover Sclover $clover $clover $clover $clover $clover $clover Ge Ge Ge Ge Ge Ge Ge Ge 024 025 026 $clover vaccum region Ge Ge Ge Ge Ge Ge Ge Ge area red area green active area blue active area black crystal red crystal green crystal blue crystal black active active active area blue active area red active area black active area green crystal blue crystal red crystal black crystal green $clover Ge active area blue 44 45 46 47 48 49 50 51 52 (OCDVOSU'lv-hOOMD-t wwwwwwwwwwwwwwwwm»HHHHHHHH mmpwwuommflmmhwwpomonsioacnwswrol-a OHHHHHHH 106 ~111 112 ~84 85 ~115 5.32 5.32 5.32 5.32 5.32 5.32 5.32 ~131 ~132 ~133 ~12O ~121 ~122 ~123 125 125 125 124 124 124 124 ~115 ~115 ~115 ~115 ~115 ~115 ~115 ~127 ~100 $clover Ge active area red 126 99 $clover Ge active area black 126 ~100 $clover Ge active area green ~117 89 043 $clover Ge crystal blue ~117 ~90 044 $clover Ge crystal red 116 89 045 $clover Ge crystal black 116 ~90 046 $clover Ge crystal green 047 048 049 050 043 044 045 046 $clover vaccum region 3 ~2.71 105 ~107 108 ~80 81 ~115 051 047 048 049 050 043 044 045 046 $clover cryostat so 40 px px cx cx cx px px px kx kx px cx cx px cx H HHHHHHHHHHHHHH’O "OO'U'U NNNX 7 OohCfl‘l‘ltOO) .50 .30 .00 .70 .40 .90 .70 .70 $world ~41.668 .0305 1 ~43.386 .0305 1 ~13.90 5.15 4.85 ~16.90 6.50 ~18.10 px 9.00 px 18.20 cx 3.775 px 10.40 ex 0.4 px 9.45 cx 3.325 px 17.75 kx 5.70 1 kx 6.35 1 px 8.6 px 8.5 cx 4.75 cx 4.65 8.6 19.18 4.04 9.98 $chamber $chamber $chamber $chamber $chamber $chamber $chamber $chamber $chamber $chamber $chamber $chamber $chamber $chamber $chamber $chamber $66080 $Ge080 $66080 $Ge080 $66080 $Ge080 $Ge080 $66080 $Ge080 $66080 $66080 $66080 $Ge080 $66080 backplate backplate backplate od is0160 end id 180160 end isoi60 o~ring isol60 flange transition i80160 end transition id transition od transition isoiOO and 0d isolOO end id isolOO end isolOO flange od isoIOO flange end front crystal back crystal crystal od central contact crystal id front active area active area od back active area bullet crystal bullet active area inner face cryostat outer face cryostat od cryostat id cryostat od $Ge120 front crystal $09120 back crystal $Ge120 crystal od $Ge120 central contact 37 38 39 4o 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 7o 71 72 73 74 75 76 77 78 79 80 81 82 83 cx px cx px kx kx px px 0 N 5000000101 0 >4 wwwwwwwwwwm5316701616wmmmwmwmwwmmmwmwwmwww 0.4 9.05 3.59 18.73 H1000 HP .75 .65 px 8.1 px 8.3 PY PY pz pz PY PY pz pz px PY PY pz pz 5.05 ~5.05 5.05 ~5.05 4.85 ~4.85 4.85 ~4.85 17.1 0.01 ~0.01 0.01 ~0.01 c/x ~1.7777 1.7777 2.5 c/x ~1.7777 ~1.7777 2.5 c/x 1.7777 1.7777 2.5 c/x 1.7777 ~1.7777 2.5 px 9.1 px 9.2 py 0.02 py ~0.02 pz 0.02 pz ~0.02 c/x ~1.7777 1.7777 2.4 c/x ~1.7777 ~1.7777 2.4 c/x 1.7777 1.7777 2.4 c/x 1.7777 ~1.7777 2.4 px 8.1 px 8.3 py 5.05 py ~5.05 pz 5.05 pz ~5.05 py 4.85 py ~4.85 $66120 $Ge120 $Ge120 $Ge120 $09120 $Ge120 $Ge120 $Ge120 $Gel20 $Ge120 crystal id front active area active area od back active area bullet crystal bullet active area inner face cryostat outer face cryostat od cryostat id cryostat $clover outer face cryostat $clover inner face cryostat $clover $clover $clover $clover $clover $clover $clover $clover $clover $clover Sclover $clover $clover left cryostat outer wall right cryostat outer wall top cryostat outer wall bottom cryostat outer wall left cryostat inner wall right cryostat inner wall top cryostat inner wall bottom cryostate inner wall back crystal spacing +y spacing ~y spacing +z spacing ~z $clover Ge crystal red $clover Ge crystal green $clover Ge crystal blue $clover Ge crystal black $clover front crystal $clover front active area $clover active spacing +y $clover active spacing ~y $clover active spacing +z $clover active spacing ~z $clover Ge active area red $clover Ge active area green $clover Ge active area blue $clover Ge active area black $clover $clover $clover $clover $clover $clover $clover $clover 133 outer face cryostat inner face cryostat left cryostat outer wall right cryostat outer wall top cryostat outer wall bottom cryostat outer wall left cryostat inner wall right cryostat inner wall 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 111 112 115 116 117 120 121 122 123 124 125 126 127 130 wwwwwwwwwwwwwwww .basépwoowww 109 H H “>90 113 114 rhubh HH HH coco hubrb-fitkhphrh 128 129 4.85 -4.85 17.1 0.01 -0.01 pz 0.01 pz -0.01 c/x -1.7777 1.7777 2.5 c/x -1.7777 -1.7777 2.5 c/x 1.7777 1.7777 2.5 CI: 1.7777 -1.7777 2.5 px 9.1 px 9.2 py 0.02 py -0.02 pz 0.02 pz -0.02 c/x -1.7777 1.7777 2.4 c/x -1.7777 -1.7777 2.4 c/x 1.7777 1.7777 2.4 c/x 1.7777 -1.7777 2.4 pz pz px PY PY 0001-t 8. px 8. 5. 5 -5.05 4 pz 5.05 4 pz -5.05 4.85 -4.85 4 pz 4.85 4 pz -4.85 17.1 0.01 -0.01 4 pz 0.01 4 pz -0.01 PY PY px PY PY c/x -1.7777 1.7777 2.5 c/x -1.7777 -1.7777 2.5 c/x 1.7777 1.7777 2.5 c/x 1.7777 -1.7777 2.5 px 9.1 px 9.2 py 0.02 py -0.02 4 pz 0.02 4 pz -0.02 c/x -1.7777 1.7777 2.4 $clover $clover $clover $clover $clover $clover $clover $clover $clover $clover $clover $clover $clover $clover $clover $clover top cryostat inner wall bottom cryostate inner wall back crystal spacing +y spacing -y spacing +z spacing -2 Ge crystal blue Ge crystal red Ge crystal black Ge crystal green front crystal front active area active spacing +y active spacing -y active spacing +z $clover $clover $clover $clover $clover $clover $clover $clover $clover active spacing -2 Ge active area blue Ge active area red Ge active area black Ge active area green outer face cryostat inner face cryostat left cryostat outer wall right cryostat outer wall $clover top cryostat outer wall $clover bottom cryostat outer wall $clover $clover left cryostat inner wall right cryostat inner wall $clover top cryostat inner wall $clover bottom cryostate inner wall $clover back crystal $clover $clover spacing +y spacing -y $clover spacing +z $clover spacing -z $clover $clover $clover $clover $clover $clover $clover $clover Ge crystal blue Ge crystal red Ge crystal black Ge crystal green front crystal front active area active spacing +y active spacing -y $clover active spacing +z $clover active spacing -z $clover Ge active area blue 134 131 132 133 *trl *tr2 *tr3 *tr4 mode impzp sdef sp1 sil sp2 si2 cutzp m1 m2 m3 e8 f8:p nps 4 c/x -1.7777 -1.7777 2.4 $clover Ge active area red 4 c/x 1.7777 1.7777 2.4 $clover Ge active area black 4 c/x 1.7777 -1.7777 2.4 $clover Ge active area green 0 0 0 -104 90 -166 90 0 90 -194 90 -284 0 0 O 94 90 4 9O 0 90 184 90 94 0 0 0 -94 -184 90 -184 86 9O 90 90 0 -2.0 0 0 94 4 90 184 94 90 9O 90 0 P 0 1 50B par=2 pos=0 -O.4 0.4 axs=1 0 O rad=D1 ext=D2 erg=2.900 -21 0 1.25 -21 0 0.05 1j 0.001 0 32000 1 8016 0.25 7014 0.75 13000 1 0. 1e-05 2.880 2.920 14 19 23 24 25 26 33 34 35 36 43 44 45 46 (23 24 25 26) (33 34 35 36) (43 44 45 46) (14 19 23 24 25 26 33 34 35 36 43 44 45 46) 500000 135 Appendix C Gamma ray Summing Corrections When two or more gamma rays are emitted by a radionuclide within the resolving time of a Ge detector, any two of them may sum and deposit their energy in a composite peak. Each count that results from coincidence summing will result in losses in the full energy peaks, Eq., of each of the individual emitted gamma rays. During this process, each of the photons may deposit their full energy or a fraction of their energy. The sum of the pulses will result in a peak whose energy is less than or equal to E1 + E2. If a third gamma ray with energy E3 = E1 + E2 were also a member of this decay scheme, then in the event of coincident summing its photopeak would gain counts. The probability of coincidence summing increases with decreasing source-to—detector distance. To correct for summing effects, it is necessary to calculate the appropriate correction factors for the photopeaks of interest. Debertin and Schéitzig [78] have derived the summing correction factors for the case of a simple, two photon cascade. Fig. C.1 illustrates a simple decay scheme involving three photons. Assuming that the emitted beta particles are absorbed in the endcap of the detector and neglecting bremsstrahlung (electromagnetic radiation emitted when an electron is accelerated in the 5' field of the nucleus [23]), then the rate of the observed pulses depositing their full energy in the Ge detector may be calculated as: JV] 2 2419161 (C.1) AIQ 2‘— .‘lpgfg 136 B- A Zx N 73 lyl 72 v A Z+1YN-1 Figure C.1: Simple two photon decay scheme used to illustrate summing corrections cal- culation. 1V3 Z .41.);3 f 3 where A is the activity of the source, p1,. is the probability '71 will be emitted by the source and 6.1. is the peak efficiency for a 7-ray with energy Er. However, due to summing, the actual pulse rate will differ from N1, N2 and N3. The observed pulse rate for 71, Ni, will be smaller than N1 due to summing out effects. 71 will always be followed by 72. As a result, the probability that the full energy of 7'1 will be absorbed and sum with ’72 is 12161672, where (T2 is the total efficiency of detecting 72. Thus, the sum corrected rate of 71 is: AI; = 1V1 — A P161673 (0.2) The summing correction factor for '71 is: NI 1 C — —_ — 0.3 I IV], 1 — 6 T2 ( ) The correction factor for peak 2 is calculated differently than peak 1, because 72 is not always preceded by 71. In this case, the probability that '72 will deposit its full energy and sum with '71 is [2162671. The sum corrected rate of 72 is: IV; 2 AL) — .4 plf2f-Tl (0.4) and the calculated summing correction factor is: 1 C : C5 2 1 —' (Pl/P'zlle ( ) 137 In the case of peak 3. rather than losing counts within its full energy peak, it will gain counts as a result of summing in effects. To correct: for this gain in photopeak intensity, the corrected pulse rate must take into account the probability that both ’71 and 72 deposit their full energy within the detectors resolving time, plus-z. The sum corrected rate for peak 3 is: [VI/5 Z XVI; + A [)16162 (C.6) and the summing correction factor for this peak is: 1 C 2 C.7 3 1 + 1216162/(1’353) ( ) The correction factors for complex decay schemes have been derived in Ref. [79— 82]. A summary of these corrections have been provided by the National Institute of Standards and Technology (NIST). For summing in gains, the correction factor is calculated as follows: 1 C = C.“ 1 + E[[\'(a,-,bi,c)cp(a.,-)cp(b,-)/cp(c)] ( b) where l\'(a,-,b,-,c) is the probability that ya and ’7}, will be emitted in coincidence relative to the emission probability of 76, and cpl. is the peak efficiency for a 'y-ray with energy Er. For summing out losses, the correction factor is: . _ 1 ‘ C — 1 — E[I\'(sJ-,r)cT(sJ-)] (C.9) where I\'(sj, r) is the probability for the emission of two gamma rays in cascade and €T(8j) is the total efficiency of observing radiation 3 (for summing losses, the energy of the coincidence gamma rays may range from a fraction to their total energy) summing with the peak area of radiation r. To correct for summing losses and gains, the experimental emission rates for a number of prominent gamma ray transitions were multiplied by the appropriate cor- rection factors. 138 Appendix D Single-Particle Calculations for N = 29 Isotones To extract. the energies of the ‘21)3/2, ‘21)1/2, 1f5/2 and 1f7/2 single-particle orbitals, the known spectroscopic factors were compiled. Tables D.1—D.5 provide a list of estimated single—particle energies for the N = ‘29 isotones in the region ‘20 S Z s 28. The sp<.>(.‘t.roscopic factors have been normalized and a weight, W, for each state assigned with the same J’r was calculated as the square of the normalized spectroscopic factor. The single—particle energies for each of the states were calculated as, 2;, E,( keV) >1: ll".- 2:1:1 Til/vi (D.1) However, experimental data is limited. The correct single-particle energies cannot be calculated with the present information. Thus, the values tabulated below should only be considered as estimates to the single—particle energies. 139 Table D.1: Calculated single-particle energies (s.p. E(keV)) for 49Ca [9,64]. J7T E (keV) C725 Normalized C25 Weight s.p. E (keV) 3/2“ 0.0 0.840 0.866 0.750 4069.0 0.130 0.134 0.018 5539.5 —— —— — 6492.0 — — —— 95.2 1/2‘ 2021.0 0.910 0.883 0.781 4261.0 0.120 0.117 0.014 4272.0 — —— — 5443.9 — — —- 5568.0 — —— — 5587.7 —— — — 2059.3 5/2‘ 3586.0 0.110 0.116 0.013 3993.0 0.840 0.884 0.782 3986.1 Table D.2: Calculated single-particle energies (s.p. E(keV)) for 51Ti [9,65]. J7r E (keV) C25 Normalized C25 Weight s.p. E (keV) 3/2‘ 0.0 2.500 0.804 0.646 2189.0 0.260 0.084 0.007 3164.0 0.350 0.113 0.013 83.2 1/2‘ 1160.0 0.960 0.608 0.369 2896.0 0.620 0.392 0.154 1671.0 5/2’ 2136.0 2.000 1.000 1.000 2136.0 7/2‘ 1437.3 — — — 2691.4 — —— —— 140 Table D.3: Calculated single-particle energies (s.p. E(keV)) for 53Cr [9,66]. J7r E (keV) 3 Normalized 5 Weight s.p. E (keV) 3/2- 0.0 2.220 0.698 0.487 2327.0 0.960 0.302 0.091 2708.5 — — — 7940.2 — —— — 366.6 1/2‘ 565.0 0.710 0.589 0.347 2676.0 0.110 0.091 0.008 3629.0 0.385 0.320 0.102 1287.0 5/2‘ 1009.0 1.000 1.000 1.000 1968.0 — —-— — 1009.0 7/2' 1281.0 0.430 0.768 0.590 1535.0 0.130 0.232 0.054 3381.7 —— —— — 10650.0 — -— — 1302.3 141 Table D.4: Calculated single-particle energies (s.p. E(keV)) for 55Fe [9,67]. E (keV) 5' Normalized 5 Weight s.p. E (keV) 0.0 3.100 0.658 0.433 2058.0 0.350 0.074 0.006 2478.0 0.680 0.144 0.021 3035.0 0.100 0.021 4e‘4 3800.6 — — -— 3906.7 -— — — 215.4 413.0 1.200 0.805 0.649 1925.0 0.200 0.134 0.018 3599.0 -— — — 3790.0 — — —— 4495.1 — —— — 5775.0 0.090 0.060 0.004 482.8 933.0 3.900 0.809 0.655 2151.0 0.920 0.191 0.036 2577.4 — —— — 997.2 1322.0 0.360 0.720 0.518 1413.0 0.140 0.280 0.078 2938.9 — — — 7780.0 — — — 1334.0 Table D.5: Calculated single-particle energies (s.p. E(keV)) for 57Ni [9.68]. J1T E (keV) C25 Normalized C25 l'l""eight 5.1). E (keV) 3/2‘ 0.0 1.040 0.832 0.692 3007.1 —— —— —— 3840.0 —— —- — 4932.0 0.030 0.024 0.001 5089.0 0.030 0.024 0.001 5190.0 0.020 0.016 0.0003 5668.0 0.030 0.024 0.001 6230.0 0.010 0.008 0.0001 6550.0 0.030 0.024 0.001 6592.0 0.030 0.024 0.001 6695.0 0.010 0.008 0.0001 7042.0 0.020 0.016 0.0003 30.0 l/2‘ 1113.0 0.210 1.000 1.000 1113.0 5/2‘ 769.0 1.050 1.000 1.000 2443.3 —- — — 769.0 7/2' 2570.0 3.100 0.381 0.145 3232.0 0.580 0.071 0.005 1 3362.0 0.160 0.020 0.0004 4220.0 0.320 0.320 0.002 4572.0 0.250 0.031 0.001 4892.0 0.020 0.002 4e’6 5132.0 0.110 0.014 0.0002 5235.0 2.050 0.252 0.064 5367.0 0.240 0.030 0.001 5710.0 0.050 0.006 4e—5 5795.0 0.060 0.007 5e“5 5850.0 0.090 0.011 0.0001 6115.0 0.050 0.006 4e-5 6280.0 0.020 0.002 4e-6 6427.0 0.020 0.002 4e—6 6520.0 0.040 0.005 3e‘5 6845.0 0.070 0.009 8e"5 6880.0 0.040 0.005 36'5 7130.0 0.760 0.093 0.009 7580.0 0.060 0.007 5e"5 7985.0 0.040 0.005 3e—5 3547.7 143 Bibliography [ll [7] [8] [9] [101 [11] [1‘3] R. Broda, B. Fornal, W. 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