mwfid, if 1.} .42 u t 1 finfiufizfifiy 31.3..- .I3« .11.“! I! In!!! ‘1 u 4.. . . $3.11 7 ,_ .. fiéfiéfi M _ _. ., _‘ .7 , .. _ , 2g... THESIS 2.00“) This is to certify that the dissertation entitled ,B-Decay Half-Life of the rp-Process Waiting-Point Nuclide 84Mo presented by Joshua Bradshaw Stoker has been accepted towards fulfillment of the requirements for the degree In Chemistry Wat/CM "/ M‘ajor Professor’s Signature 2. ( i ‘i I 2.0 0‘} Date MSU is an Affirmative Action/Equal Opportunity Employer «--3-.-.-.-.-3-0-0-0-0-0-0-0-0-0-o-0-1-9-n—oan--. fl-DECAY HALF-LIFE OF THE rp—PROCESS WAITING-POINT NUCLIDE 84M0 By Joshua Bradshaw Stoker A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Chemistry 2009 ABSTRACT p—DECAY HALF-LIFE OF THE rp-PROCESS WAITING-POINT NUCLIDE 84M0 By Joshua Bradshaw Stoker 84M0 is an even-even N = Z nucleus lying on the proton drip line that is thought to be created during explosive hydrogen burning in Type I X—ray bursts in the as- tr0physical rapid proton capture (rp) process. 84M0 is an important waiting point in the rp-process reaction sequence, determining mass abundance at and procession beyond A = 84 for stable isotopes on the proton-rich side of the valley of stability [1]. A previous experiment established the half-life of 84Mo to be 3.71%}; s [2]. How- ever, treatment of the decay-chain parameters and the poor statistics accumulated during that study left questions about the statistical and systematic errors in the measurement. The half-life of 84Mo has been re-measured using a concerted setup of the NSCL 3 Counting System (BCS) [3] and 16 detectors from the Segmented Germanium Array (SeGA) [4]. The BCS relies on a highly-segmented Si detector to correlate implantations and subsequent B decays on an event-by—event basis. The correlation method employed to deduce half-lives and other properties of the fi decay required that the average time between implantations be larger than the half-life of the nuclide under study. Consequently, the overall implantation rate into this detec- tor must be carefully controlled, without negatively affecting the typically low rate of the desired isotope. The recently constructed Radio Frequency Fragment Separator (RFFS) [5] at NSCL was used to purify 84Mo based on relative time—of-flight differ- ences between the beam species of interest, isotonic contaminants, and contaminants due to the overlap of low momentum tails of high-yield beam species. A half—life of 22(2) 3 was deduced for 84Mo, based on a sample of 1037 implantations, more than 30 times larger than the previous study. The new half-life reduced the uncertainty in the amount of 84Mo formed in the rp process, and the consequent amount of 84Sr, to less than a factor 2. Implications of the new half-life on theoretical treatments of nuclear level density near A = 84 along N = Z will also be discussed. The perfor- mance capabilities of the RFFS in rejecting unwanted isotopes associated with the production of 84Mo will be reported as well. ACKNOWLEDGMENTS I must start with my advisor, Paul, for at least one very good reason: without my advisor I would not be writing this page. Paul aided my Ph.D. progress by honing my mind to elucidate nuclear properties via 0 decay, but his influence didn’t stop there. Paul, I appreciate the group lunches, Tuesday morning basketball games, trips to your cottage, and your ability to keep nearly any meeting to one hour or less. I will always remember the support and friendship from my ,6 group contempo- raries Weerasiri, Jill, and Heather. You have been and will continue to be a good friends. Weerasiri, I appreciate your jovial personality and the chance that to take many classes together. Jill and Heather, thank you for always having a smile on your faces and for always caring. I appreciate your support throughout graduate school, especially in executing my thesis experiment, which I could not have completed on my own. I thank also Paul’s previous students, both those that I interacted with and learned from directly, and those that left a legacy to build on. I am also grateful for my several officemates. Thank you for your insights and conversations to breakup many tense work days. My family certainly has a place here also, even if I was constantly badgered by my younger sisters for choosing a school so far from home. I appreciate that all of you care for my success and were willing to do whatever was in your power to assist me. Mom and Dad, thank you for it all. iv And every shrewd turn was exalted among men and simple goodness, wherein nobility doth ever most participate, was mocked away and clean vanished. THUCYDIDES The more ignorant men are, the more convinced are they that their little parish . . . is an apex to which civilization and philosophy has painfully struggled up. SHAW TABLE OF CONTENTS LIST OF TABLES vii LIST OF FIGURES viii 1 Introduction 1 1.1 The Astrophysical rp Process ...................... 2 1.1.1 X—ray Burst Nucleosynthesis ................... 6 1.1.2 80Zr-83Nb Cycle ......................... 7 1.2 Shape Deformation Along N = Z .................... 7 1.3 Previous 84Mo Measurement ....................... 11 1.4 Re—measurement of the 84Mo Half-Life ................. 14 2 Technique 15 2.1 fl Decay .................................. 15 2.2 'y Decay .................................. 20 3 Experimental Setup 24 3.1 Isotope Production ............................ 24 3.1.1 Projectile Fragmentation ..................... 25 3.1.2 A1900 Projectile Fragment Separator .............. 25 3.1.3 Radio Frequency Fragment Separator .............. 27 3.2 Experimental Endstation ......................... 35 3.2.1 ,8 Counting Station ........................ 36 3.2.2 Segmented Germanium Array .................. 46 4 Particle Identification 55 4.1 as Isomers ................................. 55 4.2 Charge-state Identification ........................ 59 5 Experimental Results 65 5.1 Fragment-fl Correlation .......................... 68 5.2 Maximum Likelihood Method ...................... 71 5.3 84M0 .................................... 80 5.3.1 Maximum Likelihood Analysis .................. 84 vi 5.3.2 ,B-Delayed 'y’s . 00000000000000000000000000 5.3.3 DSSD Implantation Profiles ................... 5.3.4 Discussion . . . 6 Summary and Outlook APPENDIX A A.1 6 Detection Efficiency BIBLIOGRAPHY oooooooooooooooooooooooooo vii 86 93 97 106 109 109 109 115 1.1 2.1 2.2 3.1 3.2 3.3 3.4 5.1 5.2 5.3 5.4 A1 LIST OF TABLES Kienle et al. Half-lives .......................... 12 ,B-Decay Selection Rules ......................... 17 Weisskopf Single-Particle Transition Rates ............... 22 K500, K1200, and A1900 Settings .................... 26 Selective Rejection of RFFS ....................... 33 CAEN V977 Channel Assignment .................... 43 '7-ray energies used for Ge detector calibration ............. 54 Previously Reported Half-lives of Principle Nuclei ........... 66 Yield of Principle Nuclei ......................... 68 MLH Input Parameter Table ....................... 72 Dependence of Determined Half-lives on Bin Size ........... 84 Efficiency Parameters ........................... 113 viii LIST OF FIGURES 1.1 Artist’s Rendition of an X-ray Binary .................. 3 1.2 X-ray Burst Reaction Flow ........................ 4 1.3 Sn—Sb-Te Cycle .............................. 5 1.4 Reaction Flow of Zr-Nb Cycle ...................... 8 1.5 Yrast States in Even-Even N = Z Nuclei ................ 9 1.6 QRPA Half-Lives Compared to Experiment .............. 10 3.1 K500, K1200, and A1900 Layout .................... 25 3.2 LISE++ Bp Plot of Asymmetric Momentum Distribution ....... 28 3.3 Schematic of the RF FS .......................... 29 3.4 overhead View of NSCL ........... ‘ .............. 30 3.5 RF FS Beam Sinusoid at Slit ....................... 31 3.6 Overhead View of S2 Vault ........................ 32 3.7 Plot of Before/ After RF FS PID ..................... 34 3.8 BCS Detectors Schematic ........................ 38 3.9 DSSD Electronics Schematic ....................... 40 3.10 SSSD Electronics Schematic ....................... 41 3.11 PIN Electronics Schematic ........................ 42 3.12 228Th Spectra For DSSD Strip 21 Front and Back ........... 45 3.13 9OSr Spectra for DSSD Strip 21 Front and Back ............ 45 3.14 SeGA and BCS Hardware Schematic .................. 47 3.15 SeGA Electronics Schematic ....................... 48 3.16 First Calibration Individual Ge Detector Residuals .......... 50 3.17 First Calibration Residuals From Sum of All Detectors ........ 51 3.18 Individual Ge Detector Residuals .................... 52 ix 3.19 Third Calibration Residuals From Sum of All Detectors ........ 53 3.20 Absolute Efficiency Log-Log Plot .................... 53 4.1 PIN1 AE* vs. TOP-cyclotron RF Gated on 361 keV '7 ........ 56 4.2 Spectrum of 7 rays Coincident with 73As Implantations ........ 56 4.3 Chart of N uclides ............................. 57 4.4 PIN 1 AE* vs. TOP-cyclotron RF with RFFS ............. 58 4.5 PIN 1 AE* vs. PIN2 AE* without RFFS ................ 60 4.6 PIN2 AE* vs. PIN3 AE* without RFFS ................ 61 4.7 PIN 1 AE* vs. TKE* without RFF S ................... 62 4.8 PIN1 AE* vs. DSSD.front AE without RFFS ............. 63 4.9 PIN1 AE* vs. TKE*, AE Filtered, without RFFS ........... 63 4.10 PIN1 AE* vs. TKE*, AE Filtered, with RFF S ............. 64 5.1 DSSD Implantation and Decay Logical Conditions ........... 68 5.2 Five-Pixel Correlation Geometry ......... - ........... 70 5.3 DSSD Implantation Profile for 84M0 and All Fragments ........ 74 5.4 DSSD Implantation Profile of 80Y and 798r 9 .............. 75 5.5 84Mo 6 Decay Least-Squares Fit .................... 82 5.6 84Mo ,8 Decay Poisson Distribution Fit ................. 83 5.7 Histogram of First, Second, and Third MLH Decay-times ....... 85 5.8 Energy Spectrum of ’7 rays Coincident with 84Mo B—Decay ...... 87 5.9 Level Scheme Below 1 MeV in 84Nb ................... 88 5.10 fl-gated 7-7 Coincidence Projection for A = 84 ............. 90 5.11 6 Decay Level Scheme for 84N b —> 84Zr ................ 92 5.12 ,6 Decay Level Scheme for 80Y —> 80Sr ................. 95 5.13 Systematic Error in Kienle et al. Half-lives ............... 98 5.14 QRPA Half-Lives Compared to Experiment .............. 99 5.15 rp-Process Simulation of Mass 84 Abundance ............. 100 5.16 rp-Process Simulation of Mass 92, 94, 96, and 98 Abundances . . . . 102 5.17 Mass Fractions from rp Process ..................... 103 5.18 Overproduction Factors from rp Process ................ 104 A.1 84Mo ,8 Decay Poisson Distribution Fit ................. 111 A2 83Nb 6 Decay Poisson Distribution Fit ................. 112 A3 81Zr 5 Decay Poisson Distribution Fit ................. 113 xi CHAPTER 1 Introduction 84M0 is a fl-unstable even-even nucleus with an equal number of protons and neutrons (N = Z), located near the extreme of neutron-deficient stability on the chart of the nuclides. The half-life of 84M0 is of order seconds, decaying through the emission of a positron. This starts a chain of decay that ends with the fi-stable 84Sr, which is found on earth. However, even the most intense natural processes on earth do not create the necessary conditions of temperature, density, and composition for the synthesis of nuclei. Consequently, we must look elsewhere for the production of short-lived isotopes that help to explain the chemical makeup of the world we experience every day. Stellar nucleosynthesis [6] describes the formative mechanisms for many of the stable elements. For nuclei of Z > 26, it is convenient to separate the nuclei into three categories termed the s-, p-, and r-nuclides. These categories are correlated with the location of these nuclei on the valley of nuclear stability and their produc- tion mechanism: The s—nuclei are the stable and longest lived nuclei for each element that are formed in neutron capture reactions that occur at a slower rate than their ,6 decay. The r-process nuclei are generally the heaviest isotopes of a given element that are formed by the rapid capture of neutrons in an explosive environment. The lightest stable isotopes for each element with multiple stable masses are exclusively p-nuclides. The determination of other nuclei being either mixed or exclusively cat- egorized depends upon the [3 shielding caused by stable isotopes for a given mass number [6]. 1.1 The Astrophysical rp Process The discovery of X-ray binaries occurred in 1976 [7]. Space observatories were re- quired to view the emissions of these high energy photons because their energy lies outside the visible region of the electromagnetic spectrum and does not penetrate the atmosphere [8]. X—ray binary systems provide the stellar reaction conditions for the rp process. The rp process begins with the accretion of hydrogen and helium rich matter onto neutron stars from nearby companion stars, as is illustrated in Figure 1.1. Gravitational energy is released in the form of X rays as matter reaches the surface of the neutron star. The matter is compressed as it forms an accretion disk and travels through the gravitational field gradient towards the neutron star, which eventually results in thermonuclear burning. The time evolution of an X—ray burst is character- ized by a peak X-ray emission (thermonuclear burning) on top of a persistent X-ray flux (gravitational contraction). The tail of the burst peak is typically long relative to the rise time indicating explosive ignition and the gradual consumption of hydrogen as the burst proceeds. Understanding the mechanism of X-ray bursts provides infor- mation about the neutron stars involved [9], and is crucial to determining the relative abundances of stable isotopes formed during the burning process. Formally, the rp process is a sequence of (pm) reactions and intermingled [6+ decays beginning at 415C (see Figure 1.2). The 418C seed nuclei are produced by a series of fast (a,p) and (p,’)’) reactions on CNO-cycle nuclei. The alternating (a,p) and (par) reactions up to 418C result in a net consumption of 10 He nuclei per 418C produced. The formation of 418C Accretion X-ray heating disc \ ‘ ‘ , Hot spot .. ./ ‘ , T \ Accretion Disc wind stream Companion star Figure 1.1. Artist’s rendition of an X—ray binary system. Description in text. Modified from Ref. [11]. from all the available helium leaves 90 H nuclei per Sc atom prior to the sequence of rapid proton captures and fl decays finishing out the nucleosynthesis, assuming that hydrogen and helium are accreted with a ratio typical of the 9 H to 1 He solar abundance ratio and that this ratio is maintained until burst ignition. An unchecked sequence of roughly 1:1 alternating proton captures and fi decays could end the X—ray burst cycle somewhere in the region of Z w 66. However, the mass procession of the rp process is influenced by the properties of the binary star system; these properties govern the overall duration and peak temperature of the nuclear burning stage of X-ray bursts [10]. Schatz et al. [10] demonstrated that the rp process cannot proceed beyond 107’1ggTe, since known ground state a emitters create a process ending cycle. In Figure 1.3 the reactions are shown that are calculated to occur at the closeout of the rpprocess pathway where Te undergoes (ma), beginning an Sn—Sb—Te cycle [10]. Accurate modeling of X—ray bursts requires nuclear physics data for over a thou- sand isotopes. Masses, proton capture Q values, and fi-decay half-lives are all neces- sary data for the rp process. To determine the proton capture rates, the masses and excitation energies of rp-process nuclides should be known within 10 keV [12]. While Xa(54) Te(52) Sn-Sb-Te cycle Sn(50) cum) Pd(46) Ru(44) Zr (40) Sr(38) Kr(36) 89(34) Ge(32) Zn(30) ' Ni(28) Fe(26) Cr(24) 11(22) Ca(20) Ar(18) 3(15) Si(14) MGM) Ne(10) 0(8) C(6) 39(4) rp process or p process 30: reaction n(0) Figure 1.2. Reaction flow time integrated over a complete X-ray burst. The Sn—Sb-Te cycle is shown in detail in Figure 1.3. Modified from Ref. [9]. (ta) 105Te 106Te i 107Te 108Te 4 4 1048b 1053b 1063i; 1078b _ t 3.41,”) 103811 104811 IOSSn lOéSn 3+ : t t t t 102111 103111 104111 105111 Figure 1.3. The reactions in the Sn-Sb—Te cycle during an X-ray burst. Reaction flows of more than 10% (solid line) and 1%—10% (dashed line) are shown. Modified from Ref. [9]. mass measurements are ongoing, mass uncertainties of proton-rich isotopes along the rp process path of order 100 keV are still present for many nuclei in this region, lim- iting the accuracy of proton capture rates in X-ray burst simulations. In addition, recent mass measurements [12] in the region A = 80 have demonstrated differences from previously adopted values of order 1 MeV in some cases. The accuracy of rp process rate calculations will improve as such discrepancies in the relevant masses are resolved. Concerning the overall rate, temperature independent fl decays are the dominant contributor. Even-even nuclei along the rp-process path are in general longer lived with respect to [3 decay than the other rp—process reaction intermediates. At the proton drip-line, further mass processing through proton capture reactions is blocked until fl decay takes place and proton capture can again proceed through bound nuclei. Such proton unbound nuclei are termed “waiting points” along the rp- process pathway. At higher and higher densities, reaction flow through these “waiting points” are increasingly bridged to higher masses also via two—proton (2p) capture. Schatz et al. [1], using the 1992 Finite Range Droplet Model for masses, demonstrated that the contribution of 2p capture to the overall reaction rate can become significant at densities of order 106 g/cm3, resulting a faster procession to heavier nuclei. Mass procession continues until the burst reaction freezes out due to a lack of fuel. The unstable nuclei decay back to the valley of stability, making up the ash of the rp process . 1.1.1 X-ray Burst Nucleosynthesis Certain p—nuclei are produced in abundances that are not explained by current nu- cleosynthesis models. For example, the solar abundances of the p—nuclei 92’94Mo and 96’98Ru are at odds with current nucleosynthesis models. X—ray bursts remain an intriguing process to possibly explain the solar abundances of these p-nuclei [10] be- cause the mechanism is so suited to producing them. HoWever, the high gravitational field in the vicinity of neutron stars hinders the ejection of all but the most energetic ash, limiting the contribution of X-ray binaries to solar abundances [13]. The amount emitted into the interstellar medium depends on the amount of p—nuclei produced in each burst, the frequency of burst occurrences that produce p—nuclei, and the frac- tion that escapes the gravitational field of the neutron star[14]. The bulk of nuclei synthesized in the rp process would not escape the gravitational field. Nevertheless, the amount of ejected material is still being debated and the composition of material produced in an rp-process event relies on experimental data, and in instances where these data are lacking, predictions from nuclear structure models [8]. The produced material that is not ejected remains in the star crust and consequently affects the later chemical evolution in the neutron star. The half-life of 84Mo affects the mass processing above A = 84, and so is a necessary experimental parameter for modeling reaction flow. 84Mo most directly determines the abundance of 8481'. Measuring the 84Mo half-life would allow comparison of the corresponding 84Sr overproduction factor to those determined for 92’94Mo and 96’98Ru. 1.1.2 80Zr-83Nb Cycle Schatz et al. [1] also investigated specific contributions of 84Mo, a projected waiting point nucleus, to the rp process. The finite range droplet mass model (FRDM 1992) employed by Schatz et al. predicts substantially smaller a-binding energies near Z = 42 than other mass models [12]. Low a-binding energies correspond to high (p,oz) cross sections, making the 83Nb(p,oz)80Zr reaction more important in the reaction network. At high temperatures (_>_ 2 CK), a low a—separation energy for 84Mo would induce a Zr-Nb cycle (see figure 1.4). Such a reaction cycle could significantly impact the rp-process outcomes, including reaction flow and mass processing beyond A = 84. The fl-decay half-life for 802r is essential to determining the flow into this Zr-Nb cycle, while the 84Mo half-life governs leakage out of it. The half-life for 80Zr was previously measured in an experiment performed at the Holifield Radioactive Ion Beam Facility [15]. The 80Zr half-life was found to be shorter than the theoretical half—life employed by Schatz et al., so that any bottleneck in this region will be determined largely by the fi-decay half-life of 84Mo [16]. The previously measured 84Mo half-life of 37:63 3 is longer than the 1.1 5 value used by Schatz [1], which would make the Zr—Nb cycle bottleneck more pronounced than predicted. 1.2 Shape Deformation Along N = Z Given the importance of the heavy N = Z nuclei in astrophysical processes, it is useful to review the nuclear structure of these nuclei. Deformed nuclei in general exhibit different single-particle level spacing and higher level densities than spherical nuclei. Single-particle levels, level densities and nuclear masses are important ingredients for The Zr-Nb cycle [3 mm -— >4mo|olg 0w 1.2-4W9 ---- 0.4-1.2moiolg -- <0.4mdolg :3‘42) Tc Zr (40) Y Rates: FRDM1 Sr (38) T = 2 GK Rb D p = 106 91cm3 32343838404244 Figure 1.4. The time integrated reaction flow for the Zr-Nb cycle at a density of 106 g/cm3 and a temperature of 2 CK. The legend shows the limits of the proton drip-line as well as the density of reaction flow. Taken from Ref. [1]. calculating proton—capture rates and fl-decay half-lives [1]. The ratio of the 4+ and 2+ yrast state energies [R4/2 E E(4i")/E(2'1")] can be used as an indicator of shape deformation in even-even nuclei, with a smaller value representing a less deformed nucleus [17]. The R4/2 ratio for even-even nuclei along the N = Z line reveals a deformation maximum at 76Sr and 80Zr (see Fig. 1.5) [18]. The smaller R4/2 ratio of 2.52 for 84Mo marks the beginning of a transition towards the presumed spherical, doubly magic 100Sn. Theoretical predictions for the fl-decay half-life of 84Mo within the Quasi-particle Random Phase Approximation (QRPA) vary from 2.0 s by Sarriguren et al. [21] to 6.0 s by Biehle et al. [22]. Fig. 1.6 shows a comparison of the half-lives calculated by Sarriguren et al. (QRPA-Sk3, QRPA—SG2) and Biehle et al. (QRPA-Biehle) with experiment. The principle difference between these theoretical approaches is the set of nuclei used to calibrate the self-consistent interaction parameters for the particle- particle coupling strength and the nuclear deformation. The QRPA-Biehle prediction relies on the nuclei 88’QOMo, 92Ru, and 94Pd, which do not exhibit the same level of deformation (2.1 S R4/2 S 2.23) [23, 24, 25, 26] as 5.181 McVLF— 1.714 8+ 1.567 3.467M v91.___ + c 1.404 fl—i— 1.100 1.362 3" 3+ “-995 1.063 + 3+ 1.005 9* 1 4+ LL— 0.892 “-964 2.053 MeV—fir 4+ 0.792 L L_. 1.088 6+ 0.869 4.. ELL—— 0179 .._4+ _. _ 0.698 + 0.300 0.012 5__ 0.902 MevZZ—__ _2:______ + 4+ [ 4+ 0.074 0.9102 2..__ """"""" 0.853 0.110 0.483 0537 L— Z—L._ L‘mg 0.444 0616 0.000 MevL_ L_ L1_. LE2 L+ 0" EL...— 64 68 72 76 80 84 88 Ge Se Kr Sr Zr Mo Ru R4,2 2.27 2.27 1.86 2.86 2.86 2.52 2.30 Figure 1.5. Yrast states up to 8+ in even-even N =Z nuclei. The transition energies are given in keV. R4/2 ratios are shown just below 0+ state. Modified from Ref. [19, 20] that observed in the N = Z region near A = 80, lengthening the predicted half-lives. On the other hand, the self-consistent parameters for the QRPA—Sk3 and QRPA-SG2 cases were derived from experimental data from nuclei in the region of interest, and mostly reproduce the experimental half-lives using self-consistent deformations that minimize the energy. The previously measured half-life of 84Mo reported by Kienle et al. [2] falls between the two calculations. This would imply a level of deformation unique to the mass region, perhaps inconsistent with the observed trend of measured 124/2 ratios in the even-even N = Z nuclei. 100 C 1 1 1 l r 1 l l I ‘_\ 1 ‘h‘ 1 O \ i 10 :— \‘ q T; ’ -. """1 1 v "' 1 ‘3 $8! é ‘. 1 ‘- \ g 1— x\..‘ 4 1 _- --v-- QRPA - Sk3 *fxé 1 I -X- QRPA - 8G2 ‘ ‘ 1 -O- QRPA - Biehle ‘V .1 0 Experiment 4 -] 0.1 1 1 1 1 1 1 1 1 “Ge “Se 72Kr 76Sr ”2r 84Mo 88Ru 92Pd Figure 1.6. Half-lives of even-even N = Z nuclei (A = 64 — 92) deduced using the QRPA. Details of different theoretical self-consistent parameters are given in text [21, 22]. Theoretical predictions are compared to reported experiment values for A = 64, 68, 72, 76, 8O [27] and A = 84, 88, 92 [2]. 10 1.3 Previous 84“Mo Measurement The previous 84Mo half-life measurement reported by Kienle et al. provides only a few details on the measurement and treatment of the background [2, 28]. It is difficult to draw a conclusion about the accuracy of the measurement based on the published information but there are indications from subsequent work that some of the reported half-life values measured by Kienle et al. are too long [15, 29]. The half- life of 84Mo was reported as 3'7:L(l):(8) s in a set of multiple fi—decay half-lives obtained by a maximum likelihood analysis [30] that accounted for the decay contribution of the parent, daughter, and granddaughter nuclei during a fixed observation time. The experimental setup employed a highly segmented Si detector system to correlate ,8 decays to specific implantations. After each implantation and decay, the daughter nucleus remains in the detector system, and will subsequently decay if radioactive. Consequently, the background rate in each pixel is directly related to the implantation rate into that pixel, as well as the number of H decays that must occur for each parent to reach 6 stability. The B decays from previous implantations are the chief source of background in these systems. Neither the measured background rate nor a method to approximate the background rate is mentioned in the work by Kienle et al. [2]. The reliability of their fitting method was demonstrated by separately fitting the previously known fl-decay mean lifetimes of the 78Y ground and isomeric states. Kienle et al. reported half-life values of 55:2 ms and 5.7(7) s that agreed well with the previously measured values of 55(12) ms [31] and 58(6) 8 [32] for the 78Y ground and isomeric states, respectively. This good agreement for 78Y was used by Kienle et al. to validate their half-lives deduced for other isomeric and ground state parent decay. However, this example does not ensure that the Kienle et al. half-lives determined from multi-generation decay chains are similarly correct. The Kienle et al. report also leaves out the values of the daughter and granddaughter decay generation half-lives provided for each parent 11 decay fit. Such details are necessary to reproduce the results reported in the Kienle et aL study. Table 1.1. Experimental half-lives determined by Kienle et al. [2] compared with [15, 29] 13-7 correlated measurements. Nucleus ' J7r Kienle et al. [2] [3-7 correlated 802r (0+) 5'3i6iga 4.1i86§7[15] :3Rh (9/2+) 13.94500:59 11.91‘003275 [29] 2 + + . + , Rh (26 ) 5.6_8'g 4.66_8.33 [29] 91Rh (9/2+) 1.71032 1474:0322 [29] The relative rates of background and isotope decays are important for gauging potential contributions of systematic error to the deduced half-life. A log-linear plot of parent-decay activity vs. decay time gives a straight line with a slope determined by the half-life. The slope becomes less steep for longer parent half-lives. Resolving the slope of a parent decay-curve from background becomes increasingly difficult as the parent decay constant decreases and the background rate increases. Having relatively few events in the decay curve exacerbates this problem. High background rates impact the slope of the fit, of course, always leading to a half-life value that is too long. The number of implantations collected in the Kienle et al. study are available for each analyzed isotope in a dissertation [28], but the unreported 6 detection efficiency prevents an estimate of the observed number of 6 events. 6 detection efficiencies may have been anywhere from 30-70% for the system employed in the Kienle et al. study. Counts of 40 and 80 ,6 events for the respective 78Y ground and isomeric states are estimated based on a [3 efficiency of 40% and no contribution from background or daughter decay events. The 5 decay correlation time following each 78Y implantation is not provided so it is not possible to determine the contribution of 78Sr daughter or the contribution of background events, which are not reported. The half-life of 788r is 2.65 min, which would not impact a fit to either the 78Y ground or isomeric state. 12 However, the daughter half-lives of some of the other nuclei in the Kienle et al. study, including 84Mo, are short enough to impact a fit to the parent decay. In addition, the half-life of the 84Mo daughter has since been re—measured. Though the daughter half-life used in the Kienle et al. fit was not reported, it is likely that Kienle et al. used the previously published value of 12(3) 3 [33], which is longer than the newer value of 9.5(1.0) s [34]. Given identical data sets, using a longer daughter half-life to fit multiple decay generations will yield a longer value for the extracted parent half-life. Extending the 6 efficiency approximation of 40% to 84M0 indicates that 14 decay events should have been observed from the 37 reported implantations [28]. The half—life of the 84Mo daughter, 84Nb, is relatively short. This assures that some portion of those 14 [3 events are from the daughter, consequently reducing the actual number of parent decays. The low number of 6 events collected from 84Mo decay would make extracting an accurate half-life difficult in any background environment. Without knowing the B decay correlation time or background rate, the parent half-life fitting conditions cannot be accurately reproduced. The probability density functions in the maximum likelihood fit used by Kienle et al. are intended to deconvolute the decay events correlated to a single nucleus into parent, daughter, granddaughter, and background decay components. The extracted half-life represents a half-life deduced solely from parent decay events if: 1) the prob- ability density functions are correctly formed, and 2) the fixed input parameters are correct. Another approach to removing non-parent decay generation events and back- ground is through selecting only 5 events that occur in coincidence with 7 rays in the daughter nucleus. The results of subsequent measurements of the half—lives for 80Zr [15] and 91’92’93Rh [29], using 7 gating for background suppression, are shown in Table 1.1. These background-suppressed measurements are all systematically lower than the Kienle et al. values, at times by more than 10, suggesting a systematic error due to background and / or non-parent decay events in the Kienle et al. study. 13 1.4 Re-measurement of the 84Mo Half-Life The potential systematic uncertainty in the Kienle et al. T1/2 values along N = Z could have a dramatic impact on the rp—process simulations. This dissertation details a re—measurement of the T1/2 value of 84M0. The goal was to determine the accurate 84Mo half-life within an uncertainty of better than :1: 0.2 s, a factor 5 improvement over the previous measurement. The measurement was performed at NSCL with a concerted setup of the NSCL [3 Counting System (BCS) and 16 detectors from the Segmented Germanium Array (SeGA) aimed at reducing the background by obtain- ing a 7—gated decay curve. Achieving the optimum performance with this setup for fragment-64 correlation requires a balance among the overall implantation rate, the half-lives of the implanted species of interest, and the number of daughter decays by each implanted isotope to reach ,8 stability. Production of 84Mo through projectile fragmentation produces a myriad of (unwanted) fragments that dominated the beam composition due to the exotic nature of the desired product, inflating the overall implantation rate to unmanageable levels. Additional selective beam reduction was required beyond that usually achieved at NSCL with the A1900 separator. Therefore a new device, the NSCL Radio Frequency Fragment Separator (RFFS), was imple- mented to reduce the beam rate of proton-rich nuclei to make the measurement of fragment-,6 correlations for 84Mo experimentally tractable. The details of experimental conditions, setup, and results are provided in later chapters as follows: Chapter 2 provides a review of the physics principles relevant to this dissertation. The experimental apparatus, setup, and calibration procedures are described in Chapter 3. Chapter 4 entails the identification and isolation of each principle nucleus produced during this study. Chapter 5 details of the experimental analysis and astrophysical and theoretical implications based on the new half-life result for 84Mo. Chapter 6 provides a brief summary and outlook. 14 CHAPTER 2 Technique The goal of the present study was to measure the B-decay half-life of 84Mo and then determine the rate of mass processing above A = 84 in the astrophysical rp-process. This chapter discusses the B and '7 decay processes relevant to the 84Mo measurement. 2.1 fl Decay Any process of radioactive decay where the nuclear mass number A remains constant while the atomic number Z changes is classified as 6 decay. In general, nuclear species [3 decay along a given isobar chain until they reach the most stable nuclide (lowest mass). Relative nuclear stabilities can be calculated from the mass of a given nucleus with the expression: MZ(Z,A).c2 = [Z-MH+(A—Z)-MN]-c2—EB (2.1) where the masses in the expression are multiplied by C2 to express their values in units of energy. M Z - c2 is the atomic mass and M H - c2 and MN - c2 are masses of the hydrogen atom (938.791 MeV) and the neutron (939.573 MeV), respectively [35]. EB is the nuclear binding energy which contains all the information on the relative 15 stability of the nuclei and can be expressed using the semi-empirical mass formula: E8 = [ -k(N_,;-Z.)2] WW [1-k(¥)2l —C3Z2A—1/ 3 + 12422.41—1 + 6. (2.2) When EB is expressed in units of MeV, the coefficients take on the following values: c1 = 15.677 MeV, c2 = 18.56 MeV, C3 = 0.717 MeV, C4 = 1.211 MeV, and k = 1.79. 6 represents the nuclear pairing energy and takes on the value of +(-—)11/A1/2 MeV for even-even (odd-odd) nuclei, and is zero for all other nuclei. Equation (2.1), with Equation (2.2) substituted for E B1 can be shown to be second order in Z and is a parabola for constant A. One can find the minimum Z along an isobar chain through differentiation of Equation (2.1) with respect to Z, holding A constant. The set of nuclei that lie at the minimum of each mass parabola form what is called the valley of B stability. Nuclei that are not at the bottom of the mass (energy) parabola are unstable and may decay towards stability through the weak process, or 3 decay. There are three types of 6 decay that occur depending upon the relative position of the nucleus relative to the most stable isotope and atomic number. fi‘(MZ > MZ+1) : éXN H§+1YN-1 +fl" +v+ Q3 (2.3) Electron Capture(MZ > MZ—I) : éXN + 6“ 42H YN—l + u + Qg (2.4) ,B+(MZ > Mz_1+ 27113) I f21X'N —+%I_1YN+1+,B+ + V+ QB (2.5) where me is the electron mass, 6“ an electron, fii is a ,8 particle, V is a neutrino, and 77 an anti-neutrino. Q5 is the difference in mass (energy) between the ground states of the decaying parent nucleus and the daughter. M Z represents the atomic mass of a nucleus with Z protons. 6+ decay is possible only if the decay energy exceeds 2mec2 (1.02 MeV), the amount of energy necessary to create an electron/positron pair. Competition between Electron Capture (EC) and 6+ decay increasingly favors 5+ decay as Q5 increases above the 1.02—MeV threshold. 16 Table 2.1. fi-decay selection rules. Decay Mode AI A7r Al Allowed 0,1 no First-forbidden 0,1,2 yes Second-forbidden 2,3 no Third-forbidden 3,4 yes Fourth-forbidden 4,5 no #OOMI—‘O The energy of the positron emitted during 6+ decay is attenuated through in- teraction with the surrounding medium and it eventually becomes thermalized. At this point, the positron will combine with an electron and annihilate, producing two 511 keV '7 rays that propagate in opposite directions. The principle nuclei produced in the present study are 6+ emitters and the presence of their associated 511-keV '7 rays was seen throughout the fl-delayed ’7 spectra. Conservation Laws Conservation laws dictate that the angular momentum, shared by the recoiling parent nucleus and emitted fl and neutrino, must be conserved during [3 decay. This con- servation governs the likelihood of decay from the initial ground state to final states of particular spin (J) and parity (7r) in the daughter. Decays are classified into two main types: Gamow-Teller (GT) and Fermi, depending on the orientation of the spins of the created 3 particle and neutrino being parallel (GT) or anti-parallel (Fermi). Where there is no change in the orbital angular momentum, Al = 0, the decays are termed “allowed.” The change in total nuclear spin, AI, in this case is determined solely by the vector coupling of the 6 particle and neutrino. Possible values for AI are then 0 and 1 for CT decay, and 0 for Fermi decay. The feature that A7r = (-1)l forces the parity between the initial and final states to be the same for allowed decays. Decays where Al > 0 are termed “forbidden,” but actually occur in nature 17 with decreasing probability for each incremental increase in Al. Forbidden decays are formally distinguished as first forbidden, second forbidden corresponding to Al = 1,2. . .. Possible values for AI must include the orbital angular momentum con- tribution to the [3 particle and neutrino vector coupling so that a Al value of 1 would give AI values of 0 or 1 for Fermi decay and 0, 1, or 2 for CT decay. A summary of the selection rules associated with fi-decay transitions are shown in Table 2.1. fl Decay Kinetics A ,B-decay half-life determination requires monitoring the rate of 6 decays from a known sample as a function of time. The disintegration of a parent nucleus into a daughter nucleus through 6 decay is a first-order reaction with respect to the amount of the parent nucleus. Therefore, the fl-decay rate of change of a radioactive sample of N parent nuclei into daughter nuclei per unit time (—d[N]/dt) is described by the product of the decay constant )1 and the total number of parent nuclei in a given sample at time, t, and is defined as the activity (A) of a sample: d[N] = __ = N 2. A dt /\ ( 6) Nt _ —At Integration of (2.6) and use of the boundary condition that N = N0 at t = 0 yields (2.7), where t is time, No is the number of parent nuclei at time zero, and Nt is the number of parent nuclei at time t. The half-life of a nucleus represents the average time needed for a parent sample to satisfy the condition Nt/NO = l / 2, and is therefore defined as: ln2 t1/2 = T, (2.8) 18 The process of 6 decay may feed one or more states in the daughter nucleus, with a unique rate observed for the decay into each state. A partial rate constant can be defined for each transition if the branching ratio of 6 feeding into each state is known via the expression: )‘i = BRZ' - /\ (2.9) where A,- is the rate of decay into a particular daughter state i and BR,- is the branching ratio into that state. The half-life of state 2' can then be found by replacing /\ with )1,- in Equation (2.8), which will give a partial half-life, ti, of the parent nucleus. The comparative half-life, relating to the “allowedness” of a particular transition, is commonly reported as the log f t value, where t is the t,- for a particular state and f is the Fermi phase-space function, which depends on the endpoint energy of the H decay and the Z of the daughter nucleus. Empirical expressions for log f are available for atomic numbers from 0 < Z S 100 and endpoint energies from 0.1 MeV < E0 < 10 MeV. The expression used for the log f value for a positron decay in this work was: log ffi+ = 4.010gE0 + 0.79 — 0.007ZD — 0.009(ZD + 1)(log§39)2. (2.10) The maximum kinetic energy of the 6+ particle, E0, is entered in MeV and Z D is the atomic number of the daughter nucleus [35]. The decay of a nucleus far removed from 6 stability begins a decay chain of parent —* daughter —» granddaughter... until stability is reached. Bateman formulated a solution for the activity of the ith member of a chain based on the assumption that at t = 0 only the parent substance is present [35, 36]: e—A-t A- -t =A- A 27M) z’\l 2 i—ln10)21nkz(’\k_)‘j) J: kaéj where A1, A2, A3 are the decay constants of the parent, daughter, and granddaughter, (2.11) respectively. n,(t) represents the number of nuclei present at time t for the parent 19 (2' = 1), daughter (2 = 2), or granddaughter (i = 3). The total activity of the chain can be described by the sum of A1n1(t) + A2n2(t) + . . . + Aini(t). In this work up to three generations of a given decay chain need to be considered, so the expanded form of equation 2.11 is given for 2' = 1 to i = 3: A1n1(t) = A1n1(0)e_)‘1t (2.12) 12mm: ”2A1 n1(0)e—A1t-e-’\2t (2.13) A2—A1 e—Alt ,\ n t =,\ A /\ n o [ + 3 3() 3 211()(/\2_/\1)(A3_/\1) —)\2t -/\3t 6 e ] (2.14) + (A1 - A2)(/\3 - A2) (A1 - A3)(/\2 - A3) Experimentally, the assumption for an isolated parent population generally does not hold, necessitating the addition of a background term in Equations (2.12), (2.13), and (2.14) to fit the total activity. 2.2 7 Decay Many nuclear processes (i.e., fl decay, a decay, neutron capture) leave the product nucleus in an excited state. 7-ray decay is the process by which an excited nucleus releases excess energy without undergoing transmutation. This process is governed by the electromagnetic interaction and is the emission of a photon with discrete energy. The excited states of nuclei, generally represented as X * for a nuclear species X, have specific energies and character defined uniquely by the structure of a given nucleus. 7—ray decay is represented as: 7 rays are grouped in two categories for this work, those that are emitted from excited levels populated after 6 decay are termed “delayed,” whereas those from excited-state decay of implanted nuclei prior to particle decay are termed “prompt.” Prompt and 20 delayed 7-ray emissions were monitored to elucidate the low-energy quantum states and serve as a background filter for fi-decay half-life determinations. This work assigns 7 rays to either ,8 decay events or fragment implantation events based on the total energy and type of event in coincidence with the 7 ray (discussed below). Coincidence filtering of the data stream through the use of “gates” in software was used in this work for the assignment of 7 rays to either prompt or fi-delayed 7—ray spectra. 7—ray emission spectra consist of discrete lines corresponding to transition energies. The observed transitions vary between energies of 10 keV to 10 MeV. De-excitation schemes generally form a series of one or more transitions ending in the ground state. However, certain nuclei have energy states that are hindered from decaying due to some combination of parity, spin, or energy differences between the states. Relatively long lived excited state energy levels, generally with half-lives on the order of nanoseconds or longer, are known as isomeric states. Understanding the different character of photons emitted during 7 decay provides insight into the structure of the nucleus. The initial and final energy states of the nucleus have a definite angular momentum and parity, and so the photon emitted during the transition between these two states must conserve this momentum. The angular momentum of the initial and final states exists in discrete amounts as I h. The change in angular momentum l is defined l E AI = [(1, — I f)|h. AI = 0 is, in fact, forbidden as every photon must carry at least one unit of angular momentum. The photon may take on higher values of AI so that [(Iz- —— I f)| S l S (I,- + I f) represents the full range of allowed values of angular momentum for a photon. However, photons with larger values of l are progressively hindered. The dependence of photon emission on parity can be understood through the physical relationship of electric and magnetic fields. Protons are charged particles with spatial and orbital distribution in the nucleus. Spatial rearrangement of protons alters the electric field within the nucleus, whereas orbital or axial alignment changes 21 the associated magnetic field. The character of a particular decay is matched to the change in angular momentum and parity between the initial and final states of the decaying nucleus. The character can be labeled as an electric (El) or magnetic (Ml) transition for possible 1 values and A7r. Even l values for transitions with no parity change (A7r=no) require electric and odd values require magnetic transitions. The reverse is true for transitions where a change in parity occurs. This relation is described as: A7r(El) = (—1)l (2.15) mum) = (—1)‘+1 (2.16) The rate of 7-ray decay is inversely related to the angular momentum change, so the transition with the smallest I value usually dominates. The transition rates for a given character depend on the energy of the photon and the mass of the decaying nucleus. Table 2.2. Weisskopf single-particle transition rates (Rates given in units of s‘l, E7 is in MeV). Table modified from Ref. [37]. Transition Rate Electric Magnetic 1.03 x 1014 A2/3E§, 3.15 x 1013 E2 7.28 x 107 114/335y 2.24 x 107 114/3135, 3.39 x 101 A2137, 1.04 x 101 114/313); 1.07 x 10—5 A8/3EE; 3.27 x 10—6 A2132 rhOJMi—t“ Weisskopf derived separate expressions for the reduced magnetic and electric tran- sition probabilities by assuming that the transitions result from the change of a single particle inside a nucleus of uniform density. These expressions can be evaluated for different l values to provide relative transition rates as a function of mass and de- cay energy. The Weisskopf single-particle transition rates for electric and magnetic transitions with l values from 1 to 4 are listed in Table 2.2. The rate equations show 22 that for heavy nuclei an “I + 1” electric transition can compete favorably with an “I” magnetic transition [37]. 23 CHAPTER 3 Experimental Setup 3.1 Isotope Production Radioactive species are created in stellar environments, and most exist only for a short time after their formation. For laboratory study at NSCL, radioactive nuclei are synthesized through fragmentation reactions between two stable species. A projectile nucleus is accelerated up to 40% the speed of light and impinged on a stationary target, fragmenting some fraction of the projectiles. Projectile fragmentation results in a cocktail mixture of fragments that was selectively filtered using the NSCL A1900 Fragment Separator and Radio Frequency Fragment Separator (RFF S) before being transported to the experimental endstation. This work measured fl+-decay half- lives by monitoring the time until 6+ emission after the implantation of a known parent nuclei in the detection system. The rate constant A was extracted and a half-life determined from a fit of the ,B'l'-decay activity as a function of time. All 6 unstable particles analyzed in this study were 6+ emitters. This chapter presents the experimental subsystems in detail utilized to produce 84Mo and measure its half-life. 24 Figure 3.1. Layout of the K500, K1200, and A1900 components of the NSCL 3.1.1 Projectile Fragmentation The nuclei for this study were produced via the fragmentation of 124Xe projectiles ac- celerated to 140 MeV / nucleon in the NSCL coupled K500 and K1200 cyclotrons. The 124Xe beam was impinged inelastically upon a 305 mg/cm2 9Be target. A nucleus- nucleus collision fragmented the projectile through a two-step process of abrasion- ablation [38]. The abrasion step resulted in the formation of two or more fragments that are left in excited states, which may lose additional nucleons during a decay pro— cess termed ablation. Virtually all of the fragments retain enough forward momentum to be transported through the A1900 Fragment Separator [39]. 3.1.2 A1900 Projectile Fragment Separator The A1900 separation scheme employs a combination of magnetic rigidity and energy loss filtering, denoted Bp—AE—Bp, to discriminate the products of the intermediate energy collision by q, Z, and A. Magnetic rigidity is defined as: Bp=p/q= mv/q (3-1) 25 Table 3.1. A1900 and K1200 settings for the 84Mo production runs. The location of the target and dispersive image are indicated in figure 3.1. Effective values represent values input into LISE++ [40] simulations to approximate experimental conditions Parameter Nominal Value Effective Value K1200 Radiofrequency 23.14550 MHz 23.145 MHz 124Xe Projectile Energy 140 MeV/u 142.35 MeV/u 9Be Target Thickness 305 mg / cm2 327.986 mg/cm2 Dispersive Image Momentum Cut 1% 0 :1: 29.5 mm Bp1,2 2.9493 T- m 2.9493 T.m Dispersive Image Al wedge 180 mg / cm2 187.7 mg/cm2 Bp3y4 2.5635 T-m 2.5635 T-m where B is the magnetic field strength, p the radius of curvature, p the momentum, m the mass, 7) the velocity, and q the charge state of the ion. The first A1900 Bp selects nuclei based on the mass-to—charge ratio because the fragmentation mechanism produces all nuclei with nearly the same initial velocity [37]. A wedge-shaped degrader is placed at the intermediate image of the A1900 to induce an energy loss, which is proportional to the square of the fragment nuclear charge, the fragment mass, and energy as 2 ‘3; CC “Lg- (3.2) The wedge position is indicated by the “dispersive plane” label in figure 3.1. By means of this wedge, the velocity, and therefore Bp, is changed for all fragments prior to passing through the second half of the A1900. Values for the first and second Bp selection are set corresponding to the central momentum of a particular isotope, which was 84M0 for this study. The specific settings for the projectile energy, target, and A1900 are listed in Table 3.1. The fragment selection consisted of a cocktail beam of species matching the mag- netic rigidity of 84Mo. A simulation of the yields of the principle fragments produced in this study as a function of Bp is shown in Figure 3.2. The simulated peak pro- 26 duction Bp for 84Mo was slightly higher than the observed peak production Bp. The shaded region in Figure 3.2 labeled “1% Ap/ p cut” illustrates the range of Bp values for the observed peak 84Mo production and corresponds to the experimental BP1,2 values listed in Table 3.1 accepted through the first A1900 Bp selection. The yields of the principle beam contaminants are produced of order 105 times more than 84Mo. 3.1.3 Radio Frequency Fragment Separator The momentum distribution of nuclei produced in fragmentation reactions is asym- metric, resulting in a long low-momentum “tail” that overlaps the central momen- tum region of other products (see Figure 3.2). The central Bp selection of neutron- deficient nuclei near the drip-line therefore overlaps with tails from more stable and consequently much more abundantly produced nuclei. The production rate from the low-momentum tails of more stable species exceeded the peak productiOn rate of 84Mo to such a degree that a decay experiment was not feasible without additional beam purification after the A1900. The installation of the NSCL RF F S enabled new experimental studies on the neutron-deficient side of 6 stability. A schematic of the RF FS is shown in Figure 3.3. The RFFS [5] consists of two horizontally parallel plate electrodes 1.5 m long, 10 cm wide, and 5 cm apart installed inside a vacuum chamber attached to a straight section of beam line. An electric current supplied to a RF loop inserted into the chamber, such that the plane of the loop is oriented vertically. The electric current in the coil induces a magnetic field inside the chamber, with field lines that are in a plane perpendicular to the vertically oriented RF loop. The induced magnetic field forms a standing wave inside the chamber with a node located at the vertical center of the chamber; therefore the upper and lower halves of the chamber are always 180 degrees out of phase. The magnetic field induces an electric field that charges the upper and lower parallel plates with the opposite charge, creating a voltage potential across the plates with 27 A O V .1 % 1 5 t 1 A : 2 43— 768r e 1 .. +745. I— > 1p * --><--77Kr \1000 r ,5. fit -' m g 1 --+--73As 8 1;- :;Q 2’34”}. 0... 0° 1 . *— 78Rb 9; a ‘ ...o 1 --u- 768r ., 1o . x2 .. ‘. . W .5 ‘ 4 0.. . .1 1 "0" 79$r ; g " ‘ 1, ----k---82Zr 0.1 1 a ‘1’ ‘ +313 : o ,3“ 1% Aplp cut 1 *7 83Nb r 2‘“ 1 1 5 .95” 3 i 0001 1.161.1..11 1 1 1141 2.2 2.4 2.6 . 3 3.2 3.4 3.6 3.8 30 (T m) Figure 3.2. The isotope yield in particles per second (pps) as a function of Bp for the principle isotopes in this study as simulated by LISE++ [40]. The asymmetric momentum distribution of ions came from the “phenomenological” model in the code with the effective values listed in Table 3.1. 28 RF coupler Plate electrode Fine tuner Capacutlve tuner Figure 3.3. Schematic drawing of the RFFS. The outer wall of the RFFS chamber is transparent to make the components within visible. The parallel plate electrodes are the two larger triangularly shaped objects within the chamber. The smaller two triangular objects are capacitive tuners that control the amount of charge transferred to the plates from the RF loop, and may be adjusted by the stepper-motors attached at the upper and lower positions on the chamber. The RF loop is inserted from the RF coupler attached on the upper right part of the chamber. A fine tuner is attached at the lower left part of the chamber, which serves as a conductor to reduce the density of the induced electric field in the chamber. This fine tuner is wired to be automatically adjusted based on feedback from the resonant condition of the cavity i.e., to minimize the difference between the measured phase and the phase setting of the chamber. Figure modified from J. Ottarson. 29 Primary beam: 112$n at 120 MeV/u Experimental station: BCS and SeGA 7‘ ‘1 ELI 3 “I 1y .. lon source .. "I‘F‘1Fiq'x I a '71 a l ' ~ ..-’ 'l -'”"- '3‘ B... "'-‘-'-'-"I1~;:;1;;§g:2%: ; ' , . . f. "m [53:12 , . L'- . r-H" i"—VS§3‘ l I - - . ~ 111-52,; . Cocktail beam Be target sent to $2 Vault RF Fragment Separator: 195 mg/cm2 2 Additional purification of Kapton wedge 40-5 mglcm secondary proton-rich beams A1900 settings: Bp1lz=2.8802 T-m; Bp3I4=2.7710 T-m Momentum acceptance = 1 % Figure 3.4. Overhead view of NSCL beamline with nominal operational settings indicated. The location of the RFFS in the S2 vault is shown just upstream of the BCS endstation with 16 detectors from SeGA. an amplitude up to 100 kVpp. A voltage of 47 kVpp was applied for this work. The polarity of the electric current supplied to the RF loop alternates in time at a frequency matched to that of the K1200 cyclotron, which was 23.145 MHz (see Table 3.1). The RFFS is located approximately 51 meters downstream from the production target in the NSCL S2 vault, represented schematically in Figure 3.4. The drift space results in a time—of—fiight (TOF) separation of about 5 ns between successive isotones under the reaction conditions described in Table 3.1. The settings for the second Bp cut selected species with an average velocity of 11 cm/ns. An ion traveling the full 1.5 m length of the RFF S at this velocity takes roughly 1/3 of a RF period. The distribution of the beam species in TOF resulted in each fragment experiencing a different 1 / 3 of the voltage cycle, and therefore receiving a different vertical deflection. 30 After exiting the RFFS, the fragments drifted a distance of 5.38 m before entering a diagnostic box consisting of an adjustable vertical slit system sandwiched between two 80 I. 798': Y O O . ,Slit Selection ' Vertical Position [arb. units] N N N 8 8 8 N N O I l l l I l l l 1 1 l l I l l l | 500 600 700 800 TOF [arb. units] 1 1 1 l 1 1 1 1 1 Figure 3.5. Plot of the vertical beam position as a function of TOF after the RFF S. The gray rectangle highlights the region allowed to pass through the vertical slit system in the experiment reported here. The fragment of interest, 84Mo, was placed at the peak of the sinusoid so that the slits would block fragments that were not deflected by the RF FS, preventing damage to detectors at the end station in the event of a unexpected shutoff of the RFFS. Data were taken at the RFFS diagnostics port located 5.38 m downstream of the RFF S retractable parallel-plane avalanche counters (PPAC), which are followed downstream by a retractable telescope of Si PIN detectors. The PPACs are position sensitive detectors used to set the slit position for selective removal of unwanted fragments. A plot of the vertical position of fragments in the secondary beam after deflection in the RF FS is shown in Figure 3.5. The mass-specific vertical deflection after fragments have drifted to the RFFS diagnostic box is apparent in the figure. The phase of the RFFS can be adjusted relative to the cyclotron RF so that the fragment of interest 31 Experimental end station Figure 3.6. Overhead view of NSCL S2 vault showing a section of the beam line containing the RFFS, beam diagnostics port, and the experimental endstation. can be placed at a trough, peak, or node of the sinusoid as desired. Placing the fragment of interest at the peak of the sinusoid accomplished two objectives First, the location of the key contaminants 77Kr and 78Ru were then at the trough of the sinusoid and easily removed using slits. The vertical slits were narrowed to select out a specific deflection region that includes the fragment of interest and to eliminate key contaminants. Second, the slit position settings blocked fragments that occurred at the node of the sinusoid, i.e., fragments that were not deflected by the RFFS. Consequently, if the RFFS were to shut off unexpectedly the intense secondary beam would be blocked by the slits rather than be delivered to the experimental end station. Taking the full intensity of the beam into the end station would likely damage the detectors. Two beam steerers are located downstream of the RFFS diagnostic box and upstream of the experimental endstation to recenter the fragments onto the optical axis of the experimental endstation. The relative location of the RFFS, beam diagnostics port, beam steerers, and experimental end station within the S2 vault is shown schematically in Figure 3.6. The separation capability of the RFFS is quite powerful as demonstrated by the 32 Table 3.2. Isotope specific and total beam rejection rates observed in this work. The rejection factor is reported as the ratio of RF F SO f f / RFF Son for individual fragment yields. Rejection factors larger than 1 indicate a reduced transmission with the RFFS on. Rates for specific isotopes are given in particles per second per particle nanoAmperes of beam, normalized to the measured rate of 84M0. The beam intensity was attenuated when the RFFS was off (V = 0 kV) to preserve Si detector longevity. Comparative spectra representing data collected with the RFFS off and on are shown in Figures 3.7A and 3.73, respectively. Normalized Rates* V = 0 kV V = 47 kV Rejection Isotope slit = 50 mm slit = 10 mm Factor 84M0 1 1 1 83Nb 15 16 1 82Zr 30 40 2 81Z1 20 10 2 80v 130 200 0.6 79Sr 4000 35 47 78Rb 13700 0.4 46700 77Kr 13500 0.3 45000 7531 1150 15 77 74se 1980 5 400 73As 700 630 1.1 sum** 33 0.5 130 Primary Beam Intensity 0.8 pnA 10 pnA * Rates normalized to 84Mo, 5x10—4 pps/pnA ** Absolute rate in pps/pnA 33 '5' 900 .t.’ C 3250. 800 E 3 700 * l L£200 600 ,_ Z 500 D. n-n .1. l .1 1' 1' 1 l 10:1 1'1 l\1.l I 1 1 1-11 .1u11xT‘1‘1 I. ll-J—l. I fl'l :III ‘1 ' 0 W 200 250 300 350 400 450 500 559 TOF-cyclotron RF [arb. unlts] “a? _ . 33 ' '2 -(Bl 82 Nb ‘4 3250—, Z" 45 .12 E 5:200 10 <1 F E a 0-150 6 4 100 2 5° 200 250 300 ° 350 400 450 500 550 TOF-cyclotron RF [arb. units] Figure 3.7. Correlated values of the PIN1 AE* versus the cyclotron RF triggered TOF for RFFS settings of (A) 0 kV with a 50 mm slit gap (fully open) and (B) 47 kV with a 10 mm slit gap (set production width). The positions of various isotopic components in the beam are indicated by ovals. The spectra are normalized to ~470 counts of 80Y for visual comparison. Further details can be found in Table 3.2. 34 values listed in Table 3.2 for the overall and isotope specific rejection factors observed during the production and isolation of 84M0. The importance of both the selective rejection by the device and the overall rejection rate of unwanted fragments is evident. Selective rejection for the copious contaminants 78Rb and 77Kr was of order 4.5x104, while the fragment of interest 84Mo was not rejected at all by the RFF S. The overall rejection factor was 180. Fragment rates listed in Table 3.2 for a RFFS voltage of 47 kVpp were observed at the BCS endstation during the 84Mo production runs. The representative spectra in Figure 3.7 of PIN1 AE* vs. TOF (AE* represents a relative AE calibration, as discussed in Sec. 3.2.1 under BCS Calibration) taken at the experimental endstation with the RFFS off and on demonstrate the removal of the chief contaminants 78Rb and 77Kr without the rate of 84Mo being negatively affected. 3.2 Experimental Endstation The selectively filtered beam was delivered to an experimental endstation located downstream of the RFFS in the NSCL S2 vault. The principle detector system was the NSCL )6 Counting System (BCS) [3]. The NSCL BCS is a Si detector telescope designed for the correlation of B decays with continuously implanted parent nuclei to extract lifetimes. This device has been augmented with additional Si and Ge detectors for B calorimetry and can be combined with additional systems for either neutron or 7-ray detection. For the experiment described here, the BCS was surrounded by 16 detectors from the NSCL Segmented Germanium Array (SeGA) [4] to detect 7 rays emitted from nuclear excited states. The system is described in detail below. 35 3.2.1 6 Counting Station The BCS is a powerful detector system applied at NSCL to perform event-by-event correlations of fragment implantations with their subsequent ,B-decays. The system employed a Micron Semiconductor Double Sided Si Detector (DSSD) of dimension 995 pm x 4cm x 4 cm segmented into 40 l-mm strips in both the :1: and y dimensions. This segmentation provided 1600 individual 1 mm x 1 mm pixels and enabled unique implantation analysis in each pixel. The DSSD was used to detect the energy and position of implantations and the energy loss and position of fast electrons emitted in B decay. The successful correlation of implanted species with their )6 decays depends upon the rate and makeup of the beam cocktail. Following an implantation, a given pixel was monitored for fixed time determined by the half-life of the isotope in question. Should the overall implantation rate be too high, that pixel could receive another implantation prior to a I} decay event occurring for the first implantation during the fixed correlation time. This convolutes the correlation process and introduces uncertainty into the analysis process. Both the A1900 and the RFF S were used to reduce the overall implantation rate to acceptable levels. The makeup of the telescope is shown in figure 3.8. Three PIN detectors (PIN 1- 3), with PIN1 furthest upstream, served as active degraders upstream of the DSSD. The PIN detectors had thicknesses of 309, 488, and 503 11m. The active degrader thicknesses were selected such that fragments were stopped in the front 1/3 of the DSSD. Implanting fragments in the front 1/3 of the DSSD increased the probability of detecting the small AE signal of a 5 particle emitted in the downstream direction in the DSSD. PIN 1 was used for the AE and TOF start signal that made up the particle identification (PID). Six 5 cm x 5 cm Single-Sided Si Detectors (SSSD1-6), with SSSDl furthest up- stream, were mounted immediately downstream of the DSSD. Their thicknesses, pro- 36 ceeding in order from SSSDl, were: 975, 981, 977, 989, 988, and 985 pm, respectively. Each of the SSSDs was segmented into sixteen strips on one face. The SSSDs were ar- ranged so that successive detector segmentation alternated in the a: and y directions, beginning with SSSDl strips parallel to :5. Higher than normal noise levels observed in SSSD6 rendered this detector unusable during the experiment. The detector was left in the BCS chamber, but was disconnected from the analog electronics hardware. A Ge detector was placed at the end of the detector stack to provide a veto for light particles traversing the BCS. However, instability in the DSSD leakage current was observed during the cool down of the Ge detector to —140 °C. Consequently, the Ge detector was left in the BCS telescope uncooled and unbiased. BCS Electronics The DSSD was used to detect 6 and implantation events over a wide energy range. 6 particles that traverse the full thickness of the DSSD deposit energy of order 200 keV, whereas implanted fragments deposit GeV’s of energy. This large dynamic range of signals from the DSSD were processed with MultiChannel Systems (MCS) preamplifier modules. These modules were designated with inverting or non-inverting outputs so that signals originating in the front and back of the DSSD are produced with the same final polarity. Both high gain (2 V/pC) and low gain (0.1 V/pC) analog outputs were available, with impedance of 509. The low gain signals were sent directly to analog-to—digital converters (ADCs) with no additional shaping. The high-gain signals required additional processing to accurately separate the small AE signal from noise and also to define the trigger logic for the experiment. These signals were sent to Pico Systems shaper/ discriminator modules in CAMAC, with software adjustable gains and thresholds. The Pico Systems shapers provided separate energy and time signals for each channel, and a fast 16 channel OR output signal for logical signal discrimination, as depicted in Figure 3.9. The analog energy signals were 37 Beta Calorimeter PIN1 PIN3 [SSSDI SSSD3 SSSDS [ 1442-9 1061-18 2186-10 2194—12 2194—4 PIN2 SSSDZ SSSD4 SSSD6 1061-16 2136-5 2194-14 2194-9 " 1 0550 [ \ \ / / \995um[_7mm_[ /1( 309 um 488 um 503 um mm V Beta Counting System Ge Crystal \1 Figure 3.8. Schematic drawing of the detectors comprising the BCS. Drawing is not to scale. The thicknesses of detectors that served as beam degraders are given. Labels assigned to each detector will be used throughout this dissertation. Figure modified from Ref. [41]. 38 further processed by VME] ADCs. The time signals were sent to VME scalar modules for rate monitoring, and also to a coincidence register (see Table 3.3). The coincidence register provided a boolean signal to the readout software that determined whether or not the energy signals in a particular ADC were processed. The bit assignment of each ADC and the corresponding detector signals are listed in Table 3.3. Each ADC received 32 energy signals, so ADC] therefore handled both the 16 high-gain and 16 low-gain energy signals from channels 1-16 of the front DSSD strips. This setup allows strip-specific monitoring of event rates and energies, but the data collection software recorded the data from an entire ADC if any of the 16 channels registered an event. The SSSD electronic schematic is shown in Figure 3.10. Each SSSD was connected directly to a MCS preamplifier, with the output monitored only from the preamplifier high gain. The fast output from the SSSD Pico Systems shaper / discriminator module was supplied to a coincidence register. The energy signals from two SSSDs were processed by a single VME ADC, as detailed in Table 3.3, so that an energy signal in any of the 16 strips from either SSSDl or SSSD2 would trigger a readout of all the energy signals monitored by the ADC for SSSD] and SSSD2. Scaler signals were not monitored for the SSSDs. The schematic diagram for the PIN detector electronics is shown in Figure 3.11. Each PIN detector signal was connected directly to a Tennelec preamplifier and shap- ing amplifier. The energy signals from the shaping amplifier were then sent to an ADC for recording. The PIN 1 and PIN2 fast output signals were sent through a Tennelec constant fraction discriminator (CFD) before further monitoring. The PIN 1 CF D output was sent to the coincidence register with a bit assignment that governed read— out from an ADC that processed the energy signal for PIN s 1-3. The PIN1 and PIN 2 CF D outputs were sent to a scaler module for rate monitoring. A fragment TOF signal was generated for both PIN1 and PIN 2 from the difference in time between a 39 HVPS \ Low ain CAEN 735 ADC Grounding a DSSD Board Fast (OR of 16 strips) , Pico Sys. A High-gain Shaper/ Disc CAEN V977 D‘3'E'Y “ Coincidence .1 3 Register [13 7% CAEN 735 ADC 12 SIS3820 A Scaler SI53820 A(front Scaler MaSter Gate Master , A(back) w Live 1 Fan In/Out (C'OCK) Computer CAEN V977 Not Busy Coincidence Register (Gate) Figure 3.9. DSSD electronics diagram. The DSSD grounding board took the 40 signals from the DSSD and provided individual ground for each signal. These sig- nals were transfered to the MCS preamplifiers by 34-conductor ribbon cable. Figure modified from Ref. [41]. 40 CAEN 3527 HVPS SSSD Fast (OR of 16 strips) - CAEN V977 P1co Sys. . . . _ . ~ . —- Delay ~ Connc1dence - H1gh gain Shaper/ DISC Register g [_ Us CAEN 785 ADC Figure 3.10. SSSD electronics diagram. SSSD signals were transfered to the MCS preamplifiers by a shielded 34-conductor ribbon cable. The ground for each conductor is connected to the MCS preamplifier ground. Figure modified from Ref. [41]. 41 CAEN SY3527 $153820 HVPS CAEN 735 Scaler ADC CAEN V775 / TDC PIN __TC 173 TC 455 _. Dela 1,2,3 preamp f CFD Y \ CAEN V977 Fast / PINfbnl Coincidence PIN 1,2 only y Register Fan W0“ CAEN 735 Start TAC ADC Stop Rate Divider (2) l Cyclotron RF Figure 3.11. PIN detector electronics diagram. Figure modified from Ref. [41] PIN start signal and a stop signal provided by factor 2 rate-divided K1200 cyclotron radiofrequency (RF). A coincidence between the DSSD front and back signals was used to trigger the readout of all other detector systems during the experimental production runs. The Pico Systems fast OR signal for the DSSD front groups 1-16, 17-32, and 33-40 were logically OR’ed, with a similar logical OR made for the back channels. The front and back OR signals were then subject to a logical AND to create the master gate signal. This master gate made a logical AND with a computer-not-busy signal to provide the master live signal. Master live “opened” the data acquisition gate for ADC conversion, and processing the coincidence register information. The coincidence register was used to reduce the event size of data buffers by selective ADC readout. The coincidence register bit pattern is listed in Table 3.3. High voltage was supplied to each BCS Si detector, with the exception of the DSSD, through a CAEN SY3527 High Voltage Power Supply (HVPS). Individual software controls for voltage ramp rate, leakage current, and maximum voltage were 42 Table 3.3. Channel assignments for CAEN V977 Coincidence Register CAEN V977 Coincidence Register BIT Detector DSSD F01-16 DSSD F17—32 DSSD F 33-40 DSSD B01-16 DSSD Bl7—32 DSSD 833-40 SSSDl SSSD2 SSSD3 SSSD4 SSSD5 SSSD6 PIN 1 10 Ge 10 (empty) - (emptY) - cooosicscnasoomhso > D O l—ll—‘HHH ADOMF-‘O cocooooowxiczmaooww H 01 43 available for each detector connected to the CAEN HVPS. The resolution in leakage current for the CAEN HVPS was 200 nA. A Tennelec TC 953 HVPS, with leakage current resolution of 1 nA, was used for the DSSD. Each trigger event was tagged with an absolute time stamp created by a 32 bit SIS3820 sealer/counter module operating at 50 MHz as a system clock. The 32-bit word was stored for each event as two separate 16—bit words, clock.fast and clockslow, with the first 16 bits of the system clock signal assigned to clock.fast and the second 16 bits of the system clock signal assigned to clockslow. The nanosecond time resolution from the sealer module was not required to achieve the desired precision of order 0.1 s sought for in this work. Therefore, the clock variables were mapped to a 24-bit variable according to the equation: clock24bz't = (clock. fast + 65536 :1: clocl13..310112)/28 resulting in a time resolution for all events of 5.12 as, which more than satisfied the precision requirement. BCS Calibration Each SSSD and the DSSD was individually calibrated using a 908r ,6 source to adjust the signal hardware thresholds. The hardware (CF D) thresholds for each strip were also fine tuned during the experiment to suppress noise fluctuations. After the CFD thresholds were set, spectra were collected from a 228Th (1 source for gain matching. Representative a spectra from the front and back strip 21 of the DSSD are presented in Figure 3.12. The 90Sr spectra were collected on the gain-matched detectors, to establish the software low energy thresholds as indicated in Figure 3.13. The program LISE++ [42] was used to calculate the energy losses of the isotopes: 73As, 748e, 76Br, 79Sr, 80Y, 81Zr, 82Zr, 83Nb, and 84M0 in the PIN detectors 1-3. The observed centroid positions in PINS 1-3 were then assigned to the calculated energies to provide the calibration. The relative Total Kinetic Energy (TKE*) of 44 £120 Front 21 raw 54 MeV £120 7 Back 21 raw 3100 \ 3100 5.4 MeV 0 30 Offset U 80 Offset 60 40 20 0 200 400 600 800 1000 0 200 400 600 800 1000 Channel Channel 3120_ . 3120, r: : Front 21 9am matched : : Back 21 gain matched 5100 '1 E100 E 30} 30]» ll 200 400 600 800 1000 Channel Channel Figure 3.12. a decay spectra of 228Th for front and back strip #21 of the DSSD. Upper spectra show the raw energy spectra, with arrows indicating the location of the 5.4 MeV 01 peak and the size of the spectral offset used to generate the gain—matched spectra. £600 7 \ Front 21 gain matched £600 \ Back 21 gain matched 3500 New“ 3500 Threshold °400 ”400 300 300 200 200 100 100 _ 04‘ ‘50 "1m1" 111“211“‘2m 0"f'5d "161“ 1af”’2hi“231 Channel Channel Figure 3.13. Gain-matched 90Sr fi-decay spectra for the front and back strip #21 of the DSSD. Dashed lines indicate the location of the low energy software threshold. 45 fragments was determined by adding the calibrated energy loss for each PIN detector (AE*) and the (source calibrated) DSSD front-side energy loss (AE), so that the relative TKE* is given by TKE* = AEPINI + A13511172 + A15511113 + AEDSSD— front (33) 3.2.2 Segmented Germanium Array The experimental endstation incorporated l6 detectors from SeGA [4]. Each detector is composed of a cylindrically-symmetric n—type coaxial germanium crystal with a 7 cm diameter and 8 cm length. The outer contacts of the crystals are electrically divided into eight 10 mm disks along the length of the Ge cylinder. Each disk is subdivided into four quarters for a total of 32 segments. This high segmentation increases the position resolution of 7 rays in the detectors, and is useful for Doppler correction during in—beam studies [4]. The Ge detector segmentation was not utilized in the present work because fi-decay studies are performed on stopped beams so only total energy information from the central contact of each crystal was necessary. The 16 detectors were mounted on a frame designed to closely pack the cylindrical Ge crystals in two concentric rings of eight detectors around the BCS chamber, as shown in Figure 3.14. Each SeGA detector was mounted with its cylindrical axis parallel to the beam axis. The DSSD was located in the plane that separated the upstream and downstream Ge detector rings, thereby maximizing the overall detection efficiency of 7 rays emitted from nuclei implanted in the DSSD. A schematic electronics diagram for each Ge detector is shown in Figure 3.15. Data were collected for all Ge ADCs for events that produced a master live trigger. Ge Calibration The Ge detectors were energy-calibrated three times for this experiment. Two sources, 56Co and a Standard Reference Material (SRM) containing 125Sb, 152Eu, 154Eu, 46 Ge13 Ge12 73428 Ge14 \ " 73471 Ge04 ) 73446 73445 5805 ‘ , 73444 Ge03 , 73287 Ge06 6615 ,fi... Beam 73176 73471 Ge02 Line ) 73436 , ® Ge01 GeO / 73494 I 73474 Ge09 Secondary Beam Figure 3.14. Geometric arrangement of the 16 detectors from SeGA around the BCS. The BCS was centered to the two rings of eight detectors such that one ring lay upstream and the other downstream of the DSSD. Serial numbers indicate specific detectors that were used in each position. Figure modified from [41]. 47 Ortec 660 : 1—1 HVPS (“Sign _ Ortec 413A 8k ADC $153320 TC 455 Scaler Ge —7 preamp ___Ort_ 1 . .T . 1 . . . 9 0.5 _ Residuals.04 _ 0.5 _ [ [ Residuals.12 g 0 1 o l [ ' ¥ 8 ? + + . 0 1* l i [ "11' -0.5 l- ~£.5 1- + Q [ a -1 -1 . U 1 1 . . 1 ' r 1 h u g 0.5 _ Res1duals.05 0.5 _ [ 7 Residuals.13 (I) 04* l‘il? 1 1 :°~‘ [iii] [ [ . -0.5 . .-0.5 . 22 '1 -1 o 1 . ,. , 1 , r . g 0.5 _ Residuals.06 0.5 ”1 Residuals.“ m 0 _ o [ [ i» f i l. [ [ - 0 . [ Q l I [I [ U -o.5 . --o.5 . [ [ .K .1 . 1 . L .1 1 . 8 1 1 .1 . 1 , , , n- 0.5 . + Q Resrduals.07 . 0.5 _ Residuals.15 0 f . l I I l. 0 . . f + ' g I [ -o.5 . ] «0.5 . i ] .1 I '1 1 1 1 1 1 . . . 1 , , f R siduals.08 Residuals.16 0.5 - o [ g f - 0.5 . [ °- 6 i l - 0.. [’]l l -o.5 . ] [ .-o.5 . i i , l L 1 l 1 .1 1— l l l .1 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 y-Ray Energy [keV] Figure 3.16. Residual plots for 7-ray energies from each Ge detector from the first experimental calibration. Labels correspond to position number shown in Figure 3.14 50 l 0.4 — ResidualsSum (L2_ 1 - s'= N l r———e——1 -0.4 _ _ 0 10100 2000 3000 y-Ray Energy [keV] Centroi -Source Energy :3 I 161 161 "fiai 199-4 W Figure 3.17. Residual plot for 7—ray energies collected during the first calibration from the y-ray spectrum taken as a sum of all 16 SeGA detectors. at atmospheric pressure. A '7-ray spectrum was collected simultaneously using a PC—based multichannel analyzer (PCMCA) detector and the NSCL data acquisition system. The PCMCA collection used a preset live collection time of 3600 s so that the true collection time was identical for each detector, while the NSCL data acquisition relies on post-run corrections to the collection time using the recorded live time. The relative efficiency at high energies was deduced with a 56C0 source placed again at the DSSD position for a 7200 s collection time. This relative measurement was made for all 16 Ge detectors simultaneously with the NSCL data acquisition system only. The observed emission rate was normalized to the known activity of each isotope in the calibration sources. A log-log plot of efficiency versus energy is shown in Figure 3.20. The energy efficiency measurements were fit with a fifth-order polynomial in the energy range of 43-3273 keV. The calculated peak efficiency of the entire array was determined to be 6.6% for a l-MeV 'y ray. 51 u-l 05 1 Residuals.01 0.5 _ Residua|s_09 0 ° . o l 0 1. Q . o ' i + - 0 1- * o i . r * } -0.5 _ .-0.5 . '1 L .1 4 1 IR '3 I '02 1 IR iii I r10 05 . * esl ua s. 0.5 es ua s_ o i g . 0 1- § § . P ‘ o _ 0 é o g . § * % -o.5 1 f i 10.5 .1 A 1 1 .1 m 1 'Residualslo3 'Resiaualslfl 0.5 » 0.5 . 5' 03’ 11:1 *. 109+ +...L l 0: 10.5 _ 1 4.0.5 _ 1 i x -1 . H .1 L n g > 1 IR it! I '04 1 rR "d l '12 E) 0.5 _ es ua s. q M _ es: ua s. 0 f . . 1 . ‘0" ’°‘£+ ‘°' 11"?1 l I.” -0.5 1 90.5 . w '1 L 4 L .1 L 0 1 1 1 1 1 1 ,1 r a. Residuals.05 Resuduals.13 3 0.5 . + 0.5 0°, 04 {1,1110 L * . 0_H 00;. {.1 { 1 . -0.5. .-0.5. .1 _1 I- 1 , I r 1 I I ‘ 2 o Residuals.06 Residuals.“ +- .s . .0.5 . 1 c , . . . 4’ °’ "1”1 °”’ W" + l U -0.5 . .-0.5 _ x -1 1 -1 1 1° 1 1 .1 1 1 , , 1 g 0.5 . Resnduals.07 . 05 Residuals.15 0*” o'f'f- + 03* *.-11. * '°°5 ~ «0.5 . ’ 1 .1 L .1 1 rR if! I T08 1 IR " I '16 0.5 _ es ua s. _ 0.5 _ * esudua s. Q 0 .- 1 . . l, o . {1 o f O -0.5 _ l? i .-0.5 . i. i l - 1 1 r 1 1 .1 1 1 1 1 1 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 y-Ray Energy [keV] Figure 3.18. Residual plots for ’y-ray energies from each Ge detector from the third experimental calibration. Labels correspond to position number shown in Figure 3.14 52 0.4 - Residuals.$um 052- 1 — 0 (D <0 é £9 p.- -—-A i #> N I 1—-e——-1 l l -0.4 —1 0 1000 2000 3000 y-Ray Energy [keV] Centroid - Source Energy :3 Figure 3.19. Residual plot for 7—ray energies collected during the third calibration from the cy-ray spectrum taken as a sum of the gain-matched energy signals from all 16 SeGA detectors. -0.5 3: -0 7 /—u=p‘ 0 2 ‘\\.\\ .§ .0 9 _ , E 11 2;; 1’ E: -1.3 _3’ -1.5 \1 y = 0.17x5 - 2.73x4 + 17.10x3 - 52.72x2 + 79.68x- 47.74 '1.7 l l l l 1.5 2 2.5 3 3.5 log (Energy [keV]) Figure 3.20. The log(efficiency) versus log(energy) showing the absolute efficiency of the 16 detectors used from SeGA during this study. Measured efficiencies for energies up to to 3273 keV were fit with the fifth order polynomial shown in the figure. 53 Table 3.4. 7—ray energies used to calibrate the Ge detectors in this work [43, 44, 45, 46, 47]. The use of a particular energy peak in either the energy or efficiency calibration is indicated by a \/ in the appropriate column. _ . Calibration Source Energy (keV) Energy Efficiency SRM-153Gd 42.8 \/ SRM-155Eu 86.547(1) \/ SRM-155Eu 105.3080) \/ SRM-154Eu 123.0710) \/ \/ SRM-154Eu 247.9290) \/ \/ SRM-1258b 427.874(4) \/ SRM-1258b 463.365(4) \/ SRM-154Eu 591.7550) \/ \/ SRM-1258b 600.5970) \/ SRM-1258b 635.9500) ¢ SRM-154Eu 723.3010) \/ 1/ 5600 846763809) ¢ ¢ SRM-154Eu 873.180(7) \/ \/ SRM-154Eu 996.2620) \/ 1/ SRM-154Eu 10047250) \/ \/ 5600 1037.833304) \/ 5600 1238273602) \/ \/ SRM-154Eu 12744290) ¢ \/ SRM-154Eu 1596.487(17) \/ \/ 5600 1771.3270) \/ 1/ 56Co 2015.1760) \/ 5600 2034.7520) \/ 5600 2598.438(4) \/ ¢ 5500 3201.93001) \/ 5500 3253.4020) \/ 5600 3272.978(6) \/ 54 CHAPTER 4 Particle Identification 4. 1 p13 Isomers The fragments arriving at the BCS were distinguished according to their location on a plot of AE* vs. TOF. The AE* measurement was deduced from PIN 1. TOF information was determined from the time difference between a start signal provided by PIN1 and a stop signal given by the K1200 cyclotron RF downscaled by a factor 2. The PID was confirmed by the unambiguous identification of 73As through its characteristic isomeric 'y-ray decay. 73As has a known isomeric state at 427.76 keV [49], which decays via a 2-7 cascade with energies 67.03 and 360.80 keV. The 73As isomeric state has a half-life 5.7 (2) us, which is long enough to survive the ~600 ns flight time from the production target to the experimental endstation. Fragments that were coincident with the observed 360.80 keV 7 ray, shown in the spectrum in Figure 4.1, were therefore attributed to 73As. The opposite selection of ”y rays in coincidence with the fragments in the PID spectrum in Figure 4.1 is shown in Figure 4.2, where both transitions in the cascade from the 427.76 keV isomeric state are clearly present. The determination of the locations of specific isotopes was then based on their position on the AE* vs. TOF plot relative to 73As. 55 E ' llso §250_— f. g - -11 < 7 C > "1 ‘— C". O .1 O 5"30 z .' ’ E < 76 ' Si 150? 74$£1 Br . 1 5:20 100— i ' .-a . ..,:.'A:." ' On: ' u... a I on no a. u... 00’ '. o Illl‘f. .0 ' ‘0' It:v ' :1 ._ a. o. I. -' . .‘.- x 5 .:I. ' '5. 1‘: . rd". - “*1 11o soillIllllllllj_1_l_ljllllllLLllllllll lllLLlHo 200 250 300 350 400 450 500550 TOF-cyclotron RF [arb. units] Figure 4.1. The distribution of DSSD implantation events, given as PIN 1 AE* vs. TOF, observed in coincidence with a prompt 361 keV 7 ray. 10000 a i '2 mg 361 a L 8 wooE / 7000;— 2000; 1000; 07 11 1 1 111L1_L111111111 200 300 400 500 000 y-Ray Energy [keV] Figure 4.2. 'y-ray spectrum of events in prompt coincidence with 73A3 fragment im- plantations into the DSSD. The known 67 and 361 keV transitions which depopulate the 428 keV 73A3 isomeric state, via cascade, are clearly present in the data. 56 H O E Z :1 9. O A: I Stable 34 [Z] Q(fl+)>0 I Q(B-) >0 P . . l . WW — Proton Drip-Linc 32 34 36 38 4O 42 Neutron Number Figure 4.3. Section of the chart of the nuclides in neutron-deficient region near A z 65 — 90. All highlighted nuclei are [3+emitters except the stable 74Se. The strong contaminants 78Rb and 77Kr were largely removed using the RFFS, with smaller fractions of 79Sr and 76Br also being removed. The principle nuclei sent to the experimental endstation were: 73As, 74Se, 76Br, 77Kr, 78Rb, 798r, 80v, 812:, 82Zr, 83Nb, and 84Mo. A partial chart of the nuclides provided in Figure 4.3 highlights the location of these principle nuclei relative to stability. The bulk of the beam contaminants from the initial fragmentation process were removed through a combined application of the N SCL A1900 [39] and RFFS [5]. The RFFS significantly reduced contamination in the beam due to 77Kr and 78Rb, as was demonstrated in Sec. 3.1.3. A PID plot obtained with the RFFS on, given as PIN1 AE* vs. TOF, is shown in Figure 4.4. Individual isotopes are clustered together in “blobs” with a TOF width related to the 1% distribution in momentum passed through the A1900. 57 H .3 €250 no. .é ”1:9 :31: 700 .2. r71)“ : ;.. tuzoo_ ' 600 Q 1. 500 3 L150 { ~* 74 400 300 100: - 2°° 100 5° 200 250 300 ° 350 400 450 500 550 TOF-cyclotron RF [arb. units] Figure 4.4. PID plot, given as PIN1 AE* vs. TOF, with the RFFS on. This plot contains all of the data collected for determining the 84Mo half-life. In contrast to Figure 3.7, there are 1054202 80Y implantation events in this plot. The repeating pattern, separated by ~25O us, in TOF arises due to the downscale of the cyclotron RF signal by a factor 2. 58 4.2 Charge-state Identification The 124Xe primary beam was accelerated in the K1200 cyclotron in the 48+ charge state. Primary beam interactions in the target and fragment interactions in the A1900 intermediate-image wedge can result in either the pickup or loss of orbital electrons. The presence of one (hydrogen-like), two (helium-like), or more (lithium-like and so forth) orbital electrons attached to beam fragments allows some of these fragments to have a p/ q [see Eq. (3.1)] within the A1900 acceptance of 84Mo42+ and contribute to beam contamination. Beam contamination from unwanted fragment charge states can be identified by the total energy of the ions by summing the AE* signals in PIN detectors 1-3 and energy signals in the DSSD. Fragments with one electron, in relation to fully stripped ions with similar p/ q, experience an appreciably higher energy loss [see Equation (3.2)] in the PIN detectors upstream of the DSSD. The fragments with orbital electrons will have a lower momentum than the fully stripped ions with the same p/ q. Consequently, the energy loss increased due to both a higher amount of energy being deposited per unit depth and a relatively lower momentum. The cumulative energy loss of fragments through the Si detectors in the BCS eventually brings each fragment to rest. The thickness of Si that a fragment passes through before coming to rest is the implantation depth of that fragment in the BCS. Recall that the PIN detector thicknesses were selected to ensure that fully-stripped ions are stopped in the most upstream 1/3 of the DSSD. The increased energy loss of fragments that contained orbital electrons prior to reaching the BCS (charge-state contaminants) resulted in many of them not reaching the DSSD. The majority of the charge-state contaminants deposited the bulk of their energy in either PIN 2 or PIN 3, though some of the more energetic one electron charge-state contaminants that reached the DSSD experienced an energy loss similar to some fully-stripped ions in the DSSD. Even the most energetic fragments with two or more orbital electrons 59 § 3 e‘ chargestates 2 9” Charge-states“ .1.” a: " ‘ J -. . . - ‘1 ‘, . ’\ :sfi‘t PIN1 AE* [arb. units] § § § , - ' 1' charge-states 0 'e' charge-states § _lllIITTIIIIITTIIIIIIITITIIIIIIIIII PIN2 AE“ [arb. units] Figure 4.5. Distribution of PIN1 AE* vs. PIN2 AE* signals obtained with the RFFS off. Groupings are labeled according to the number of orbital electrons associated with the ions. deposited only trace amounts of energy in the DSSD. Fragments that did not reach the DSSD could not be correlated to their subsequent ,8 decays. The distributions of PIN1 AE* vs. PIN2 AE* and PIN2 AE* vs. PIN3 AE* for runs with the RFFS turned off are shown in Figures 4.5 and 4.6. Separation between charge-state groups was observed along the diagonal of the PIN1 AE* vs. PIN2 AE“ plot. This separation between different charge-states along a diagonal was not seen with PIN3 (see Figure 4.6), as a result of charge-state—contaminant fragments coming to rest in PIN3. Events that deposited more than 3 GeV of energy in the DSSD led to an overflow of the electronic channel, and were not resolved in TKE*. The front side of the DSSD was used for energy information due to the slightly better signal-to—noise ratio it provided relative to the back side of the DSSD. The TKE* resolution remained poorer than that observed in TOF due to the fragments being scattered through 60 3 e' charge-states '2 V ' 2_e' charge-states PIN2 AE* [arb. units] § § § § § § § IllllllllllllIIJJLItIIITIII.J.I.I.I.III|IJIIIITII 200 100 #LzlllIllllllllllllllllkLJllLLllllllllllLLL o °0 100 200 300 400 500 600 700 000 900 PIN3 AE* [arb. units] Figure 4.6. Same as Figure 4.5, but for energy loss signals in PIN2 and PIN3 of the BCS. interactions in the BCS Si detectors. In addition, the TKE“ for all charge-states was similar enough that it could not be used as a principle means of isolating fully stripped ions. Figure 4.7 is a plot of PIN1 AE* vs. TKE* with the RFFS off, in which the similarity of the TKE* between the different charge-state species can be seen. 84Mo was the heaviest fragment and has the highest number of protons of all the isotopes sent to the BCS; consequently it experienced the highest energy loss in each PIN and the DSSD relative to other fully-stripped fragments. A fraction of the smallest PIN1 and PIN2 energy loss signals for charge-state contaminants with 1 orbital electron “bled” into the highest PIN 1 and PIN2 energy loss signals from fully-stripped fragments, including 84Mo. This overlap of the 0 and 1 electron charge state PIN1 AE* signals prevented their isolation based on either PIN1 AE* or TKE*. However, because fully stripped ions deposited the bulk of their energy in the DSSD they could be easily distinguished from charge-state contaminants that did not reach or only deposited small amounts of energy in the DSSD. In Figure 4.8 is shown a 61 -—~ 000 __ é : g 700 :— 3 e“ charge-states 1 % eoo :— ' , 7' : 2 e charge-states ‘- 5 1 e' charge-states ‘, *‘ ‘ 30° :— -. - f .4551? 1 a “ “ 24a ' 200 r -.-:v \,_ .. 3'“ _.--..‘.. . _ 1 1 . _,_._._ _ _ 100:- , ,:-.:_-;;_—':~ 1.. 1- 0 e charge-states : 1 ‘1:€€fi'.§rlgfw 1.; L"1 if . . . 1 . . . l “0 200 400 600 800 1000 TKE* [arb. units] Figure 4.7. Distribution of PIN1 AE* vs. TKE* signals obtained with the RF FS off plot of the PIN 1 AE* vs. DSSD AE, where the “bleed” of 1 electron charge-state contaminants into fully stripped fragments was not as prevalent as in the PIN1 AE* vs. TKE* plot shown in Figure 4.7. Fully-stripped ions were isolated by a gated selection of the O electron charge states shown in Figure 4.8. A cleaned PIN1 AE* vs. TKE* spectrum generated from these 0 electron events is shown in Figure 4.9. Identification of the implanted ions collected during the runs with the RFF S off provided the basis to identify implantations observed with the RFFS on. Although the energy losses and TOF of the ions should be the same except for the relative yields, the RFFS cut of the yield of 77Kr and 78Rb fragments prevented the stepwise identification of fragments along the line of isotopes described by the relation of N = Z + 6. However, the location of fragments observed in the spectrum shown in Figure 3.7A did not change when the RF FS was turned on. Consequently, a similar approach to that described above was employed to isolate fully-stripped ions produced with the RFFS on, starting with the locations of specific fragments as shown in Figure 4.4. The distribution of the values of PIN1 AE* vs. TKE*, subjected to the similar 62 § .5 on! ...“ . :1 e‘ charge-states _.. - a“; '- . .. - PIN1 AE* [arb. units] .. ‘1" ._~ M, . —'. r-‘g ,‘Ij. .. . .- r. . - I. —}‘-.-.~ .' .- llllllllIILLLJIIl‘llllllllllllllllllJijllllllll 50100150200250300350400450500 DSSD.front AE [arb. units] Figure 4.8. Distribution of PIN 1 AE* vs. DSSD.front AE signals obtained with the RFFS off. IllllIIIIIIIIIIIIIIIIITIIIIIIIIIIIIITII 1 l i i 1 l 800 1000 TKE* [arb. units] 0° N 8 O '— A ' .. JP} 0 .. 1’ m 8 Figure 4.9. Distribution of PIN 1 AE* vs. TKE* signals obtained with the RF FS off for 0 electron events isolated from the spectrum in Figure 4.8. 63 -—-500 £3 : S - 700 . 450 :- 2 — 600 5.! : 4 C . ‘- _ 1’ Z 350 r F; 400 o. I 300 300 E— 2 - ' 200 250 :— 100 — l l l I I l l l l l L L l I L I l l l l 2000 200 400 600 1000 o 800 TKE* [arb. units] Figure 4.10. Similar to Figure 4.9, except for 84Mo production runs with the RF F S on, with an expanded vertical scale. filtering as the spectrum in Figure 4.9, is shown in Figure 4.10 for the 84Mo production runs with the RFFS on. The cleaned PIN1 AE* vs. TKE* spectrum resolved charge state contaminants that were not seen in either PIN1 AE* vs. TOF (see Figure 4.4) or PIN1 AE* vs. DSSD AE (see Figure 4.8). Therefore, final event selection included events from this cleaned TKE* plot AND’ed with fragments identified in PIN 1 AE* vs. TOF. 64 CHAPTER 5 Experimental Results Each of the nuclei produced and identified during this study was studied previously and the half-life was measured. The previously reported values are shown in Table 5.1. Half-life values below 10 s (84Mo, 83Nb, 81Zr) are well suited to be measured by the above described setup and experimental conditions. This chapter centers on the analysis of 84Mo; extracting the half-life of this nuclide was the principle aim of this work. A summary of the analysis of 83Nb and 81Zr, relevant to determining the ,B-detection efficiency (efl), is included in Appendix A. The energy spectrum for ’7 events that occurred in coincidence with 84Mo 6 decay is presented. It was hoped that ,8 decay from the 0+ ground state of 84Mo would populate excited states in the 84Nb daughter that would '7 decay to the ground state. The fl-delayed 7 rays from 84Mo could then be used to isolate coincident 84Mo parent 6 decays from other decay generation and background fl-decay events, providing a decay curve with reduced background. Unfortunately, no such ’y rays were identified in this work. The implications on the spin assignment of the 84Nb ground state based on the absence of delayed ’7 rays in the 84Mo fi-delayed 'y-ray spectrum are discussed. Three separate fitting methods were applied to the observed decay data to obtain a new half-life value for the 84Mo ground state. The first was a least-squares linear 65 Table 5.1. Previously reported half-lives of the principle nuclei produced during this study. Nucleus fi-Decay T112 84Mo 37:6}; 8 [50] 83Nh 41(3) 3 [51] 82211 32(5) 8 [52] 81Zr 5.3(5) s [53] 80v 30.1(5) s [54] 79Sr 225(1) m [55] 76m 16.1(2) h [56] 74Se Stable (0.89% Abundant) 73As 8030(6) d [57] regression method (Gaussian fit), the second approach involved the maximization of a Poisson distribution log-likelihood method (Poisson fit), and the third employed a custom probability density function (Maximum Likelihood fit) built to describe the decay of a radioactive nucleus of up to three generations. A Gaussian distribution fit requires the data to be grouped in time-bins large enough that the histogram of the number of decay events as a function of time do not have bins with zero counts, which may cause the method to fail. Decay curves will always have an exponentially distributed error. An exponential error distribution violates the normal distribution expected for a least-squares analysis, though the exponential distribution (for a single order exponential) converges to the standard normal table at ~60 counts/ bin [58]. The second decay-event curve analysis procedure based on the maximization of a Poisson probability log-likelihood function and is, in principle, the same as the Gaussian fit procedure except for the error minimization. The x?) minimization determined for the maximization of a Poisson distribution does not fail with zeroes present in the data set, yielding fit parameters that are independent of the number of 66 counts in a bin [59]. A Poisson distribution strictly holds for nuclear decay processes that are characterized by a constant mean value observed over a collection time that is short compared to the half-life of the source [60]. The time window of five half-lives used to search for fragment-fl correlations violated the condition of a correlation time that is short with respect to the half-life of the parent source. In addition, both the Gaussian and Poisson approaches require each event to be independent, which is not true of daughter and granddaughter (and so forth) decays in a radioactive chain. Over a correlation time of five parent half-lives, the contribution of daughter and granddaughter decay events to the total number of observed decay events can be significant, depending on the relative half—lives. This is especially true if the daughter and / or granddaughter half-lives are of the same order as the parent decay. In light of these shortcomings, a third, more rigorous approach for determining the fl-decay half-life was employed. The third approach was based on the maximization of a custom log-likelihood function. This Maximum Likelihood (MLH) fitting algorithm has been applied in previous work to determine fi-decay half-lives from very few decay events [61, 62]. The likelihood functions used here were logical combinations of mathematical rep— resentations of the probabilities of observing one, two, or three decay events within an observation time equal to a window that is ten times the half-life of the nu- cleus of interest. The method assumes that the decay half-lives of the daughter and granddaughter generations are long enough that zero probability exists for a fourth generation decay event to occur within the allotted correlation time. The probability functions are based on the Bateman equations for the parent, daughter, and grand- daughter decay events and a Poisson probability distribution for background events, and provide a correct mathematical model for the probability of observing up to three decay events. 67 Table 5.2. Table showing the yield of each isotope isolated during this study. Nucleus Implantations 84M6 1037 83Nb 20121 82Zr 56602 81 Zr 37246 80v 1054202 79Sr 181544 7GBr 192441 74se 98164 73As 511185 DSSD.front —1 DSSD.back ——1 DSSD.front— “Implant” DSSD.back —@—“Decay" PINl— PIN1—o PIN2-— SSSDl—-O Figure 5.1. DSSD logical conditions set in software to determine the assignment of trigger events as implantations or decays. 5.1 Fragment-fl Correlation To correlate the implantation of an ion and its subsequent decay, each event has to be categorized as a decay or an implantation event. Logical conditions, shown in Figure 5.1, were established in software and used to assign trigger events as either implantations or decays. Implantations were identified by events that produced a signal above threshold in PIN1 and PIN2 and the front and back sides of the DSSD, with an additional condition that no signal was observed in the most upstream SSSD (SSSDl) i.e., fragments that stopped in the DSSD. Decays were identified by events that produced a signal above threshold in the front and back sides of the DSSD AND’ed with a requirement of no signal in PIN1. 68 In most cases, the event position can be determined by the strip with the largest energy signal. At times, the energy deposited by an event is nearly equal in adjacent strips on either the front or back side of the detector, which can result in an implan- tation or decay receiving the wrong position assignment to a pixel adjacent to where the event actually occurred. For this reason, the search algorithm for geometrically pairing implantation and decay events was expanded to consider events in nearby pixels. Software analysis algorithms were used to pair implantations to decay events that occurred within fixed correlation time in the same-pixel and nearest-neighbor pixels. This five-pixel search geometry (see Figure 5.2) was applied for implantation and subsequent decay events that occurred within a correlation time equal to five times the half-life of the nucleus under study; the resulting decay curves were fitted by the Gaussian and Poisson distribution error minimization methods. The five-pixel search geometry was then extended to determine fragment correlations with up to three subsequent decay events that occurred within a ten half-life correlation time after an implantation; the resulting decay chain data were fitted by the custom MLH algorithm. The maximum possible correlation time was limited by the average time between successive implantations in a single pixel. Since the five-pixel search geometries as— signed decay events to the immediately preceding implantation in the search area, a fragment implantation has some probability to be correlated to a decay from any of the previously implanted fragments within the search geometry. The likelihood for a false correlation therefore increases if a fragment implantation occurs within both the search geometry and correlation time of a short-lived (84Mo, 83Nb, 81Zr) previous implantation. The low overall implantation rate of 10 Hz distributed over roughly 3 / 4 the face of the DSSD corresponded to an average time between successive implanta- tions in a single pixel of ~120 s. A correlation time of ten times the half-life of 84Mo, taking the previously measured literature value as an upper limit, would be 47 s at 69 Nearest Neighbor Pixel Nearest Neighbor Pixel Nearest Neighbor Pixel Implantation Pixel Nearest Neighbor Pixel Figure 5.2. Schematic representation of the five-pixel correlation geometry used for correlating implantation and decay events in this work. Center pixel marked “Im- plantation Pixel” indicates the location of the fragment implantation. Grayed out boxes represent pixels that were searched for decay events within a fixed correlation time to pair to the implantation. most, well within the 120 s limit. A correlation time that is well below the average time between implantations in a single pixel does not guarantee that each decay will be correlated to the proper fragment. For example, as the 120-8 time between implan- tations represents an average, half of 84Mo implantations will occur within less than 120 s of another implantation in the same pixel. In the event that an implantation occurred in the same pixel after a 84Mo implantation but before a decay event in the five-pixel search geometry, the decay event was linked to the second implantation. Therefore, if the ordering of the 84Mo and the second implantations were reversed, the 84Mo implantation was linked to the decay. The improper linking of a decay and implantation will result in a false correlation. It is not possible to distinguish be- tween decays from recent and previous implantations through methods of geometric and time correlation. Consequently, each fit performed in this analysis contained a component of background to approximate the contribution of false correlations to the 70 total number of 6 events correlated to a particular isotope. 5.2 Maximum Likelihood Method The full development and formal description of the MLH method have been described previously [30, 63], only a brief summary will be provided here. This description, as explained in the introduction to Chap. 5, demonstrates the logical and mathematical correctness of the MLH method for describing the probabilities for observing up to three decay generations of a parent nucleus within a fixed correlation time. fi-Detection Efficiency The implantation of radioactive fragments into the front 1/3 of the DSSD optimized the path length through the detector for ,6 particles emitted in the downstream di- rection. The probability for detecting a given decay event is a necessary parameter for a probability density function that describes the observed decay sequence in a ra- dioactive chain. 813 is defined as 5;; E (N 5 /N I), where N '3 is the number of observed ,8 events from a parent nucleus and NI is the number of observed parent implanta- tions. NI was determined directly from the number of fragments identified for each isotope from the particle identification plot. The NI for each isotope are listed in Table 5.2. N16 was determined for 84Mo, 83Nb, and 81Zr from the fitted decay curve data as described in detail in Appendix A. The value 55 = 0.34(2) was deduced from a weighted average of the values of 85 for 84Mo, 83Nb, and 81Zr, as given in detail in Table A.1. Data Input Format The text input file for the MLH fit contained a user defined header that immediately preceded the decay-chain data. The input parameters are specified in Table 5.3. Each 71 Table 5.3. Table of input parameters and data provided to MLH fit program. The first five lines of input are reserved for a user-defined header. Decay-times immediately follow, input as four-element arrays. All time values are entered in units of seconds. Probabilities are entered as decimal fractions. The symbols are defined as follows: to - correlation time; 16D - fi-decay daughter; 00 D - fi-decay granddaughter; PD — proton—decay daughter; PG D - proton—decay granddaughter; ,BD-PD - proton-decay daughter of fl-decay daughter; t fii - time of 1th observed ,Bevent; Tb - background rate. Tcorr T1/2 [Parent] (guess) T1/2 [16D] Tl/2 [5GB] Pn [Parent] Pn [,BD] Pn [P Dl T1/2 [PD] T1/2 [PGDl T1 /2 [IBD'PD] efi [Parent] 55 [6D] 55 [,800] tm t62 Mn 7‘6 fragment implantation was correlated with up to three decay events that occurred within a five-pixel search geometry during a correlation time approximately ten times the half-life of the nucleus of interest. The decay-chain data were stored as separate four-element arrays for each decay sequence that contained entries for the times of the first, second, and third observed decays and the background rate in the pixel where the decay chain was observed. Background Treatment The implantation density distribution of the secondary beam over the face of the DSSD was not uniform. The non-uniformity of the distribution was exacerbated by the position-TOF correlation created by the RFFS. In fact, the TOF dependent ver- tical deflection experienced by beam fragments resulted in each receiving a unique placement on the DSSD detector face. Consequently, a particular isotope was concen- trated in a region of only roughly 1 / 3 the area of the DSSD. The histograms in Figure 5.3 depict the DSSD implantation profiles for 84Mo and for all isotopes. A similar 72 set of histograms for the principle beam contaminants 80Y and 79Sr are shown in Figures 5.4A and B, respectively. The unique placement of each isotope on the DSSD face resulted in a unique background environment in each pixel. Some isotopes were implanted in a similar region of the DSSD as 84Mo; other isotopes were not, and thus did not significantly contribute background to 84M0 analysis. Therefore approximat- ing the background rate by an average value for the entire face of the DSSD would not be an appropriate representation of the background. Ideally, a history of the implantations in each DSSD pixel would be extracted from the data. A background rate in a particular pixel for a given time period could then be determined from summing the background contribution of each isotope implanted in that pixel. The background contribution at a particular time from each isotope can be calculated based on the decay constant and the implantation time of the isotope; this method was employed in a recent work measuring the fl-decay half-life of 1OOSn with very few implantations [62]. The statistics gathered for 84M0 were 100 times what was collected for 100Sn, and the observed background rate in this experiment was low enough that the probability to observe a background event during the correlation time was ~2%. Therefore, it was considered sufficient in this work to approximate the background with a moving boxcar method that measured the observed background rate per pixel for the run during which a decay chain was observed. The length of each single run was approximately one hour. The applied background rate for each MLH decay chain was interpolated from the background measurement in the relevant pixel during the overlapping one-hour period. Decay events were considered non-correlated (background) if either they did not fall within the correlation-time window, or if they were the fourth or higher decay event to occur during the correlation window. Background events are assured to occur independently of the decay-chain events; the probability for observing a number (n) of background events within a correlation time 73 14000—3 -------- [ 10000—55 Figure 5.3. Implantation profiles over the face of the DSSD. (A) The implantation profile specific to 84M0. (B) The same for all fragments. A background rate was measured in each pixel to accurately account for the unique environment at each pixel position. 74 Figure 5.4. Similar to Figure 5.3. (A) The implantation profile specific to SOY. (B) The same is shown for 79Sr in the image below. The high production rates and relatively short half-lives of these species made them the principle sources of decay- event background. 75 (tc) for a measured background rate (Tb) was described by a Poisson probability _ (Tbtclne_rbtc _ n! Bn , (5.1) where Bn indicates the probability of observing 11 background events within tc. BO is the probability of observing zero background events within to, BI is the probability of observing one background event within tc, etc. Probability Density Functions The DSSD AE signal from the fi decay of implanted nuclei does not provide an unique energy signature for identification. The fact that 53 < 100% allows events other than the parent 6 decay to be detected as the first event after an implantation. The decay times of fi-decay events along the decay chain are not independent, so the likeli- hood function must account for this dependency. The decay constants of the parent, daughter, and granddaughter nuclei are defined here as A1, A2, and A3, respectively. The probability density function, f;(/\1, A2, . . . , A;, t), for a radioactive decay at time t from a single parent nucleus for the parent, daughter, and granddaughter species are described by a form of the Bateman equations given by Equations (2.12), (2.13), and (2.14) with 121(0) = 1 and satisfy the relation 00 / fi(/\1,)\2,m,)\z',t)dt=1- (5.2) 0 The integration time is limited by the average implantation rate into each pixel, therefore, the integration in this analysis was carried out over a value of to. The probability that a decay will occur within tc is therefore not unity, so a normalization constant is required to properly implement the probability density function into the fitting algorithm. The probability for occurrence is distinct from the probability for detection, which factors in 55 and the rate of background decays. The integrated form of the probability for occurrence of the first three members of a decay chain are: 76 1101.15) = 1 — e-iltc (5.3) A2A1 [1 -At 1 4.1] FA,>\,t =1——————e 10——e 26 5.4 F(A,\,\ ) 1 AAA[ {We 1 1 it = _ + 3 3 2 1 C 3 2 1 J\1()\2--)\1)(/\3-/\1) (We + (We ] (5 5) /\2(/\1-/\2)(A3-A2) A3(/\1-)\3)(/\2-/\3) ° ' The total likelihood function considers circumstances where 0, 1, 2, or 3 decay events are detected within to. Multiple scenarios exist that can result in the detection of each number of events. Since sfl is not unity, the detection of one event can be attributed to observing a parent, daughter, granddaughter, or background decay. 53 for parent, daughter, and granddaughter decays is uniquely displayed as 8 51’ 5W’ and 533, respectively, to provide clarity in the following equations. However, 831 = 552 = 853 was assumed during the analysis. The notation Efl represents the quantity 1 — 58' The probability for each circumstance of zero to three detected decays is determined by logically combining (+ for OR, - for AND) the probabilities for observing a given decay chain or background event. The four scenarios describing one detected event used in this analysis are as follows: (1) The decay of the parent was observed, the daughter and granddaughter decays did not happen or were not observed, and a background event did not occur: P1? = 01531 - (52 + 02518253 + 02§fl2D3Efi3) - Bo. (5.6) (2) The decay of the daughter was observed, the parent decay happened and was not observed, the granddaughter decay did not happen or was not observed, and a background event did not occur: Pld = 0158102682 ' (53 + D3583) - 30 (5-7) 77 (3) The decay of the granddaughter was observed, the parent and daughter decays happened and were not observed, and a background event did not occur: P19 = 171551023532 - D3Efi3 - Bo. (5.8) (4) A background decay was observed, the parent and daughter and granddaughter decays did not happen or were not observed: Plb = (El -i- 0155152 + 01513113253253 + D1531D25fi2D5fl3) - Bl (5.9) where D,- (52-) represents the probability that a decay of the 1th generation happens (does not happen). The subscript of the function label denotes the number of ob- served decays and the decay-generation member or background to which the decay is assigned, where p is a parent decay, d a daughter decay, g a granddaughter de- cay, and b a background decay. Therefore P1p indicates the probability for detecting one parent decay event. Plda Fly, and Plb similarly imply detection of a daughter, granddaughter, and background event, respectively. A similar mathematical description can be written for the ten possible scenarios that describe observing two decay events, which must account for combinations of decays as well as the order in which they occurred. Consistent with the notation above, the scenarios are indicated by P2pda P2199, P2190, P2dg, P2d01 P291), P2bp, P2bd1 szg, and P2bb- For example, P2pd is the probability for detecting a parent decay followed by the detection of a daughter decay; this parent-daughter detection scheme considers that the granddaughter did not happen or was not observed and that a background event did not occur. The meaning of the other notations representing two event detection probability is similarly consistent with the ordering of the letters in the subscript. There are twenty possible detection scenarios for observing three decay events, which are: P3pdg’ P3pdb’ P3pgb1 P3pbd1 P3pb91 P3pbb’ P3dgb1 P3db91 P3dbba P3900, P3bpd’ P361091 P301101 P3589, P3bdb1 P3696, P3561» P3bbdw P3659: P3000- 78 Of course, only one scenario exists to describe the probability for observing no decay events (P0). The probability distribution functions for detection of one decay during to are a mathematical extension of the logical construction of observation probabilities. The probability density functions for observing one decay event at time t1 within tc are: p1p(/\1) = C1'f1(/\1,t1)'€fi1‘171(A21tc — t1) + (72(A2J31tc - t1) - F102, tc - t1)) '%2 + F202, A31tc -t1) '5fi25331'30 (5-10) 1111101) = C1 - f2(>\1,/\21t1) '5fl15fl2 ' [7103,12 - t1) + F1(/\3,tc “51)5031'30 (5.11) 101904) = C1 -f3(/\1, A2, A31t1) fgfimem ° 30 (5-12) P1b(’\1) = C1 ° [7101112) + (72(A1J21tc) - 7101112)): 561 + (73(A11A21A31tc) - 72(A11A21tc)) 551502 + F301, A2, A3, to) “5015025531 '31 'tEl- (5-13) The sum of the single decay probability density functions define the joint probability density function for one observed decay event: 19101) = 1311201) + 1711100) + 191901) + PlbO‘l): (5-14) where the normalization constant Cl fulfills the equation: to / p1(A1,t)dt1 = 1. (5.15) 0 The joint probability density functions p201) and p3(/\1) are similarly formed from the sum of all two— and three—decay scenario probability density functions. 79 Likelihood Function The resulting likelihood function combines the one-, two-, and three—decay joint prob- ability density functions: N123 £123(/\1)=H([5(nzP1(7%/\1)+5(1-2)'p2(A1)+5(n1-3)°P3()\1)l- (5-16) 6(3) represents the delta function, where 6 (1:) = 1 for a: = 0, and 6 (51:) = 0 for all other values of 1:. Equation (5.16) considers the combined set of N123 observed decay chains with one (71,- = 1), two (71,- = 2), or three (71.,- = 3) decay events within tc. The most probable value of A1 determined from Eq. (5.16) was then corrected for implantation events with no observed decays (N0) within to using an iterative numerical method. The value of N0 within tc depends on P0011): _ P0011) N _1——PW)N 123 (5.17) A value of to more than five half-lives of the parent nucleus ensures that this correction applied for No events is less than 5%. If the average rate of implantation into a single pixel is low enough, a to equal to ten half-lives should be used to make the N0 correction less than 1%. A longer value of tc potentially allows for contributions from decay generations beyond the granddaughter species, voiding the assumption of three decays used for the construction of the likelihood function. 5.3 84Mo The decay curve for 5 events that occurred within 10 s in the same pixel or the four nearest-neighbor pixels of a 84Mo implantation is shown in Figure 5.5. In total, 532 correlated decay events were observed. Each species along the decay chain of 84Mo reaching to [3 stability, along with background events, are potential contributors to the overall decay curve. The Gaussian fit of the decay data shown in Figure 5.5 80 was based on a least-squares regression analysis that considered the contributions of parent, daughter, and granddaughter decays [described by equations (2.12), (2.13), and (2.14)] and a linear background component. The daughter and granddaughter half-lives were taken as fixed parameters, based on the previously determined half- lives of 9.5 s [54] and 25.9 min [64] for the daughter (84N b) and granddaughter (84Zr), respectively. The data were histogrammed in 1 s time bins to ensure that no data points had zero counts. The difficulty with the Gaussian fit is illustrated in Table 5.4. Time binning of 1 s produced some data points that contained fewer than the value of 60 counts per time bin necessary to approximate a normal error distribution required for a “good” least-squares fit. An increase in the time bin size to 2.5 s was necessary to achieve 2 60 counts/ time bin. However, such binning resulted in only one degree of freedom in the fit and an overestimation of the experimental error. The half-life and error determined using 1 s bins was 1.9(4) s. The contribution of daughter and granddaughter decays to the total number of observed decays were calculated based on this 1.9 s half—life. The integrated contribution of the granddaughter decay, as anticipated, was not significant (3 0.01 counts/ 10 s) as a result of its relatively long half-life. A half-life of 2.0(4) s was deduced for 84Mo from the Poisson fit of the decay curve, considering the decay of the parent and daughter and a linear background. The fit using Poisson probability distributions did not include the decay of the granddaughter, since its contribution was shown in the Gaussian fit to be small. The half-life of 84Mo from the maximization of a Poisson distribution log-likelihood function provided the advantage of yielding the same result independent of the histogram bin size. Table 5.4 contains the half-lives deduced for 84Mo based on the selected bin size. The robustness of the Poisson probability likelihood maximization fit to a change in bin size is clear, though an extreme reduction in the number of degrees of freedom results in an overestimate of the experimental error. The number of parent and 81 84Mo: PDGB-gaussian m g ' T112(B)=1-9(4)s g 102 r ' 8 : : Parent “ Daughter rm 1O :— 1 1 Li L J [LL 1 l l l L l 11 L J l 1 l I I o 1 3 5 6 7 a 9 10 Figure 5.5. Decay curve for 84M0. The fit represents the results of a least-squares regression analysis. Data were fitted by the sum of the Bateman equations [Equations (2.12), (2.13), and (2.14)] corresponding to contributions from the parent, daughter, and granddaughter, and a constant background term. The daughter and granddaugh- ter half-lives of 9.5 s and 1554 s, respectively, were taken as fixed parameters. Only the initial activity, parent decay constant, and background were free parameters in the fit. The fitted background rate of < 0.1 counts/s and the granddaughter component, which integrates to < 0.01 counts, lies below the horizontal axis. 82 in _ ‘- T112(15) = 2-0 (4) S \1025- g : c : Parent 3 t O _ U Daughter m 10E— 1 11111111111411l.1111111111111111111h1111111.11... o 1 3 4 5 6 7 a 9 1o T1me(s) Figure 5.6. Decay curve for 84M0. The fit represents the results of the maximization of a Poisson distribution log likelihood function. Data were fit by the sum of the Bateman equations [Equations (2.12) and (2.13)] corresponding to contributions from the parent and daughter, and a constant background term. A daughter half-life of 9.5 s was taken as a fixed parameter. The initial activity, parent decay constant, and background were free parameters in the fit. The fitted background rate of < 0.1 counts/s lies below the horizontal axis. daughter nuclei contributing to the decay curve were determined from the fit. Of the 532 decays correlated with 84Mo implantations, 135(11) were attributed to the daughter. Therefore, ~25% of the total data set cannot be considered independent. Accurate determination of the 84Mo half-life required that these daughter events either be filtered from the data set by identifying a parent-decay-coincident ’y-ray, or be properly accounted for by the probability distribution function used for maximum likelihood determination. 83 Table 5.4. Comparison of the half-lives deduced using Gaussian and Poisson proba- bility distributions for 84Mo based on bin size. The x?) minimization using Poisson statistics can be robustly applied to data sets independent of bin size. Probability Distribution Fraction of No. of s / bin Gaussian Poisson Bins with 0 Counts Bins 0.01 1.1(1.4) 2. 0(4) 0.748 1000 0.02 1.8(1.5) 2. 0(4) 0.578 500 0.05 1.3(3) 2.0(4 ) 0.15 200 0.1 16(3) 2. 0(4) 0.06 100 0.2 2.0(4) 2.0(4 ) 0 50 0.5 2.1(4) 2. 0(4) 0 20 1 1.9(4) 2.0(4) 0 10 2 1.9(4) 1.9(4) 0 2.5 2.0(5) 2.0(5) 0 5.3.1 Maximum Likelihood Analysis The histograms representing the decays that occurred within 20 s in the same pixel of a 84Mo implantation are shown in Figure 5.7 as a plot of log time. The data are marked to indicate decays observed as the first, second, or third decay events within to. The probability distribution functions determine the maximum likelihood for the assignment of decay-chain events as parent, daughter, granddaughter, or background events. In total, 640 correlated decay chains were observed. The header of input parameters entered into the MLH is detailed in Table 5.3. A half-life of 2.2(2) s was determined for 84Mo using the MLH analysis. This value is consistent with the values deduced from the Poisson and Gaussian distributions. The improved precision is a reflection of the larger data set analyzed due to the 20 s tc and the mathematical treatment of daughter and granddaughter decay times as dependent parameters. 84 30 ~ I First Decay 25 . E Second Decay . 3 Third Decay l - l i 2‘? .."1 IIIIIIJI/I/I/II. “ ' "’ "' ““- -- n“-*ld——1 «- w. om».— _. ‘1 -1 m_--vm‘— » a. I .W -u-V"M III/IIIIII/I/l/II/l *’ 'V' . .. nun-mm ‘I l/l'IIll/Il/I/l/I/II/lII/l/l/II/t fl'm~‘*j Ill/III/I/I/IIII/ll/IIIII ‘ III/Illlllll " ' 'lll/Il/I/I/I ' “5" "- I/Il/ll/I/a ' "' (1111/11/11111 ‘ W W VII/111114 III/Ill/II/l 'l m. - .1... I’ll/III]! 'I/I/II. II [III] 'I- "" ' I d é a: o c on d L09 t (s) Figure 5.7. Histogram representing the natural log of the decay times relative to and correlated with 84Mo implantations within a five-pixel geometry during a 20 s time window. The closed histogram represents the first detected correlated fl decays, which represent a combination of parent, daughter, and background events since 63 was not unity. The second decays, represented by the open histogram, principally are made up of daughter decays due to the low background rate. The third observed decays, represented by the thatched histogram, consist largely of background events since the half-life of the granddaughter was long. 85 5.3.2 fi-Delayed 7’s As noted earlier, another way to isolate 84Mo parent 5 decays would be to gate the decay curve on known 7-ray transitions in the 84Nb daughter. Unfortunately, no information on ,B-delayed 7 rays following 84Mo was available. As part of the measurements reported here, the energy spectrum for 7 events that occurred in co- incidence with the 84Mo 5 decay chain was recorded and is shown in the spectrum in Figure 5.8. The peak at 511 keV represents the energy of the photons produced during positron annihilation. The only obvious 7 ray energy peak, with the exception of the 511-keV annihilation peak, is labeled at 386 keV (13 counts), and represents the decay of the 215 state in 8OSr fed from 80Y 3 decay. The B decay from 80Y was the chief source of background in this 84Mo analysis due to the full position overlap on the DSSD face of 80Y and 84Mo implantations (see Figures 5.3A and 5.4A); the rate of 80Y implantations; and, the half-life of 80Y, which is of order seconds. A fuller discussion of 8OY background from ,8 events is provided in Sec. 5.3.3. Allowed [3 decays from the 0+ 84Mo ground state would populate 1+ states in 84N b. Identifying 84Nb 7-ray transitions from one or more 1+ states fed from 84Mo 0 decay would allow the isolation of parent decay events from daughter decay events. Previous work [65] identified high-spin excited states in 84Nb populated through the 58Ni(28Si,pn7) reaction, and reported a 3+ assignment for the 84Nb ground state. Such spin-parity assignments are consistent previous fl—decay work [33, 66]. However, the tentative spin and parity assignments of the higher-lying states shown in Figure 5.9, as well as later 84N b fi-decay studies [34] do not rule out the possibility of J 7r = 1+ or 2+ for the 84Nb ground state. The states below 1 MeV established in Ref. [65] are shown in the level scheme in Figure 5.9. A more recent in-beam study of 84N b excited states confirmed the energies of the states identified in the spectrum in Figure 5.9, as well as identifying the transition to the ground state from the 48—keV level [67]. The 84Nb levels at energies 48.0, 65.0, 205.0, and 217.5 keV are potential 86 1". _ m ‘1 J7r = 1']' candidates, based on their direct decay transitions to the J7r = 1+, 2+, or 3+ ground state. However, the 338.0 keV (5‘) isomeric state directly feeds the 205.0 level, making a 1+ assignment unlikely. The (5") isomeric state also feeds both the 48.0 and 65.0 keV levels via a 2-7 cascades, reducing their likelihood of being 1+ states as well. The 217.5 keV level was the most obvious J” = 1+ candidate, as it is fed solely via a 4—7 cascade from the (8+) state at 865.4 keV. 30L 1 1 1 1 1 1 L E 511 25: - > 203 4 .11 g 2 \ .- .1‘3 15: § : O 10: - U : 386 1 5} _ / 540 -. 0: i1 lidllllllliu i1: i111111 11 l mindiumuhquuug 100 200 300 400 500 600 700 800 Energy (keV) Figure 5.8. Spectrum of 7 rays in the energy range 50—800 keV in coincidence with fi-decay events occurring in the same and the four nearest-neighbor pixels within 10 s of a 84Mo implantation. The transition with energy 386 keV represents the decay of the 215 state in 80Sr fed from 80Y fi-decay, the principle source of background decay events. Additional details are in the text. Based on the assumption that 100% of the 84Mo B—decay fed states in 84Nb 87 .3 O A > 924.1_ 0 1- E 0.8 — > - no 9 8' d) 0.6 - c I.” - 0.4 — V .. . S40] ' q 1752 1 9' 0.2 - 1 _ 7 162.7 u, O 1400 .. 2176 3.11 g 40.0L °‘ 0.0 _ 0.0 v V 050 3,, Figure 5.9. Level scheme below 1 MeV for 84Nb established from the 58Ni(288i,pn7) reaction. Taken from Ref. [65]. 88 cascade through a single state within the 60—400 keV energy range and knowing that the absolute efficiency for SeGA in this energy range was 12% or greater, more than 45 counts should have been observed, perhaps at 217 keV, in the delayed 7-ray spectrum depicted in Figure 5.8. For comparison, the 511-keV annihilation peak has 99 counts. The absence of 7 rays from known excited states in 84Nb prevented isolation of parent decays from daughter decays and background events using [3-7 coincidence filtering of the 84Mo decay curve. Absence of the 84Nb delayed 7 rays in the spectrum in Figure 5.8 also has implications on the ground-state spin of 84Nb. Previous fl-decay work would support spin and parity assignments to the 84Nb ground state of 1+, 2+, or 3+ [34]. Decay from the 0+ ground state of 84Mo directly to the 84Nb ground state would suggest a 1+ spin and parity assignment. The tentative spin and parity assignment of 1+ to the 84Nb ground state is also supported by the absence of 7—ray transitions attributable to B-fed states in the 84Mo granddaughter, 84Zr. The study of excited 84Zr states fed by B decay was reported in Ref. [34]. The projection of the fl-gated 7—7 matrix for all A = 84 isobars produced via the 58Ni(32S,012p)84Zr reaction is shown in Figure 5.10. The 7-ray transition at 540.0 keV in the spectrum in Figure 5.10 represents the known 21*" —> 0+ transition in 84Zr. The level scheme deduced from the 7 rays observed in the spectrum in Figure 5.10 is shown in Figure 5.11. A ground state branching ratio of 0% was assumed. Based on this level scheme, greater than 88% of the 84Nb —> 84Zr 6 decay will feed states that depopulate through the 540.0 keV state in 84Zr. A total of 14(9) counts would therefore be expected at this energy in the spectrum in Figure 5.8, based on the number of 84Mo correlated decays observed. Absence of observed 7-ray transitions attributable to fi-decay feeding of 84Zr excited states suggests direct feeding feeding to the ground state, a possibility acknowledged in Ref. [34]. The branching ratio into the ground state during 84Nb —> 84Zr ,6 decay also has 89 ' l ' l ' I ' l ' l [200 I400 1(m I I I I l l j I I I ' ’540.0 . . 800-1 3 B - ‘y- ‘yprojecuon ._ 19 1'8 _ g600— \ — o ‘ £5 8 ’ 0400— N “I, f2 — '10 / v ‘Q 4 g§$ 8 g: g g: N. - 200— I \1 1 s13 ,_ :: ‘3 - MU l' 1 I T .. 0- .. 800 000 l ENERGY (keV) Figure 5.10. The projection of the )B-gated 7-7 matrix for A = 84 from 400-1400 keV. The peak at 422 keV arises from levels fed in the ,8 decay of 83Y’” —> 83Sr. The 475-keV peak similarly results from the 83Zr —> 83Y B decay. The peak at 793.3 keV receives counts from levels fed in both the 84Ym —> 84Sr and 83Zr —> 83Y 5 decays. The label Cd represents the 558.46 keV transition in 114Cd in the sheets of natural Cd placed around the Ge detectors to suppress Pb X-rays. All other energies were assigned to the 84Nb —> 84Zr 6 decay, with the notable peak at 540.0 keV representing the known 21‘" -—> 0+ transition in 84Zr. Modified from Ref. [34]. 90 implications on the spin assignment of the 84Nb ground state. The log ft values in Figure 5.11, which assumed no ground state feeding, were calculated based on branching ratios deduced from the relative intensities of the 7 transitions assigned to the 84Zr nucleus, and a half-life of 9.5 s. The calculated log f t values for the 2‘; and 23' levels at 540.0 keV and 1119.5 keV, respectively, are less than six, indicating allowed transitions and supporting a positive-parity assignment for the ground state of 84N b. The log f t value for the 4+ state at 1263.0 keV contradicts possible ground state spins of 1+ or 2+, which led to the previous assignment of (3+) [46, 65, 33, 66]. However, the spin 3+ level at 1575.7 keV was preferentially fed relative to the 1263.0- keV level in the 84Zr level scheme (see Figure 5.11) implying that the 1263.0-keV state may be populated through 7 cascades from fl-fed levels not observed in Ref. [34], and extending the possible 84Nb ground state J7r assignment to 2+ or 3*“. 84Zr 5 decay must The implications of direct 84Zr ground state feeding in 84Nb —> also be considered, based on the absence of 7 transitions at 540.0 keV in the spectrum in Figure 5.8. In this scenario, the branching ratios in the 84Zr level scheme (see Figure 5.11) are overestimated and the corresponding log f t values are underestimated due to direct feeding of the 84Zr ground state. An increase in the log f t values for transitions to the 2'15 and 23' states would classify them as forbidden. However, a positive parity for the 84Nb ground state would still be supported, since direct ,8 feeding to the ground state would suggest allowed decays. Allowed decay to the 0+ ground state of 84Zr further supports a (1+) spin assignment for the 84Nb ground state, and is consistent with the generally weak intensities of all the 84Zr 7 lines reported in Ref. [34]. To summarize, the absence of 7-ray transitions attributable to 6 fed states in either 84Nb or 84Zr therefore suggests a majority of the 5 decay sequence flows through the ground state pathway of 84Mo (J7r -_— 0+) —+ 84Nb (.I”r = (1+)) —» 8421: (fl = 0+). 91 (112.3)+ 0.0 Tm: 9.5 s 84 41 M343 1 B"'/EC Q = 9610 keV BR (‘76) log for 8.2 6.0 1966.7 121 5.9 3+ 5.9 6.3 “x : «1 15757 < L...) ........... ln§lmbflui “““ 1119.5 35.0 5.6 2/ xx. a] Q § 5 .5: E 5% a 34.4 5.8 2+ 1 V V 5 0* V 84 Zr 40 44 Figure 5.11. )8 decay level scheme of 84N b -—> 84Zr. Log f t values are determined from relative branching ratios that assume no ground state feeding. Transitions indicated by a dashed line have been placed tentatively. Taken from Ref. [34] 92 5.3.3 DSSD Implantation Profiles The previous discussion in Sec. 5.1 indicated that a correlation time of 20 s was well below the average rate of implantations into a given DSSD pixel. However, two considerations were mentioned: half of the 84Mo implantations would occur within less than 120 s of another implantation; and, the half-life of the isotope implanted within the correlation time impacts the probability for a false correlation. Both of these considerations were investigated. To address the first consideration, the times of each implantation were tracked up to 20 3 prior to each 84Mo implantation. In total, 32% of the 84Mo implantations occurred within 20 8 following another implantation (back-to-back implantation) for a given pixel. The time distribution of those 84Mo implantations relative to another implantation is described by the relation 76‘”, where r is the rate of implantations into a single pixel and t is the time between a 84Mo and another implantation. The fraction of implantations that should occur within 20 s prior to a 84Mo implantation is given by the integral: 20 / rertdt (5.18) 0 Evaluation of equation (5.18) determined that ~16% of the 84Mo implantations should occur within 20 s following another implantation, based on the average rate of one implantation per 120 3 per pixel. As noted earlier, the implantation profile over the face of the DSSD was not uniform. The implantation profile on the face of the DSSD for 84M0 compared with that for all fragments is shown in Figure 5.3, and demonstrate that the location of 84Mo on the face of the DSSD was roughly congruent with the majority of the implanted isotopes. This geometric overlap of 84Mo with the bulk of the implantations explains why two times the number of back—to—back implantations occurred over that expected from the average rate of implantations per pixel. In response to the second consideration, the DSSD profile was generated for each 93 major isotope in this study. The RF FS-induced vertical displacement was unique for each isotope and determined the implantation profile observed on the face of the DSSD. The relative positions of 80Y and 798r, the two most abundantly produced fragments in this study, were shown in Figure 5.4. 80Y was the most prolifically pro- duced fragment and dominated the character of the overall implantation profile; 80Y implantations also overlapped strongly with the 84Mo implantation profile, whereas 798r did not. An analysis of implantation times relative to 84Mo implantations was completed to determine the identities of each isotope implanted back-to-back with 84Mo. 80Y accounted for ~51% of these back-to—back implantations, while ~36% were attributable to 73As. Not a single back-to-back implantation was attributable to 79Sr. The half-life of 73As is ~80 days, so back-to—back implantations with 73As will not result in a false correlation and were ignored. The possible contribution of 80Y to false correlations is more complex. An 80Y back-to-back implantation within 20 3 occurred for 16% of the 84Mo implantations (8% for a 10 s correlation time). 80Y also has two fi—decaying states. The isomeric 1‘ state of 80Y decays with a half-life of 4.7(3) 8, whereas the 4" ground state has a half-life of 30.1(5) s. Decays from the 80Y ground state, therefore, would not be a large contributor to false correlations. The isomeric decay is more problematic, due to its shorter half-life. Assessment of the 80Y impact on the 84Mo correlation therefore requires knowledge of the isomer / ground state production ratio. The amount of 80Y in the isomeric state is directly related to the rate of the background decays out of that state. Too high of a rate would result in a background that could not be assumed to be random/flat within tc. The level scheme for 80Y [3 decay from the 4‘ ground state and 1' isomer is shown in Figure 5.12. The 1" isomeric state also decays via a 229 keV isomeric transition to the 4’ 80Y ground state. This back-to-back implantation analysis concerned only the fraction of 80Y that 6 decays out of the 1" isomeric state. The fi-decay branching ratios and half-lives from each state are shown. Greater than 99% of all the fl-decay 94 38 sr42 3 >- 00 f: + I . 3‘2 1' 000 cats Ugo—xx 00—1 «I g g g; 3:445 2663 3456 ~06th ~96 f l_i—r" S? 0,103 1409‘- txo-g as Ix .411 q '9 Q U IV 06 Ov-Or-I ~00 all) It‘s 6 ° 3 01% E E. >3 ~42 ? Q as .. '2 1' 8;; ‘0 z. 2.. a: 0'1: Figure 5.12. ,8 decay level scheme of 80Y —> 80Sr. 'Ii‘ansitions indicated by a dashed line have been placed tentatively. Taken from Ref. [54] 95 branching from the 80Y ground state reaches the 386 keV 215 state either directly or via 7 cascade. However, both the 80Y 1‘ isomer and the ground state decay feed 80Sr levels that eventually populate the 2? state in 80Sr, which decays to the ground state via a 386 keV 7-ray transition. A state in 8OSr that is uniquely fed via 3 decay from either the 4‘ ground state or 1‘ isomer is required to determine the relative amounts of each decay pathway. The 981 keV 41]" state in 80Sr is populated either directly or via 7 cascade by ~53% of the states in 808r fed from B decay from the 80Y ground state. Feeding of the 4+ state is not expected following decay of the 1‘ state of 80Y. The 4? state in 808r decays to the 2'1]— state via a 595-keV 7-ray transition, therefore, the intensity of the 595-keV peak can be fully attributed to 7 decay from states fed by the 80Y ground-state ,8 decay. The intensity of the 595 keV 7-ray transition is given by A595/87595, where A595 represents the intensity of the transition at 595 keV and 57595 represents the absolute efficiency of SeGA at 595 keV. This 595-keV intensity can be normalized to the full 7-ray intensity attributable to decay from the 80Y ground state by dividing by the fl-branching ratio (~0.53) that reaches the 981- keV 80Sr level either directly or via 7 cascade. A similar normalization to the full 7-ray intensity could be performed for the 386-keV transition except that the portion of the 386-keV intensity attributable to just the 8OY ground state is not known. However, both the absolute SeGA efficiency at 386 keV (57386) and the 80Y ground state branching through the 386 keV state are known. Therefore, the intensity of the 386—keV transition (A386) attributable to the 80Y ground state [A386(g.s.)l can be roughly determined by equating the two normalized equations as: (A595) 1 = (A386(g.s.)) 1 (5.19) 87595 0.53 57386 0.99 The value of A386(g.3.) determined from this relation represents ~91% of the total 1386' Therefore, the 1‘ isomeric state, with half-life 4.7(3), accounts for ~9% of the total 80Y H decays. Consequently, a 6 decay from the 1‘ 8OY isomeric state occurred for only 1.4% (0.7% for 10 s correlation time) of the 84Mo implantations. 96 The contribution from the principle source of potential false correlations was then small. Considering the background rate in each of the Gaussian, Poisson, and MLH fits as random / flat was therefore appropriate. 5.3.4 Discussion - The new half-life value of 84Mo, deduced as T1/2 = 2.2(2) s, is more than 10 below the value of 3.7 115(8) 3 deduced from 37 implantations by Kienle et al. [2]. This shorter value continues the observed systematic trend observed in other re-measurements of half-lives first reported in Ref. [2], as shown in Table 1.1. The previously measured half-lives listed in Table 1.1 are shown in Figure 5.13, with the newly-determined half-life value for 84M0. The difference in the 84Mo results is more pronounced than that for any of the other re—measurements. This larger deviation may be attributed to low statistics, or other uncertainties in the fl-decay chain parameters at the time of the Kienle et al. measurement. For instance, the 55, tc, and half-lives of the daughter and granddaughter decay generations were needed to perform an MLH analysis of the 84Mo decay chain data. The daughter half-life of 9.5i1.0 s [34], held as a fixed parameter in this study, was not published until two years after the 84Mo half—life was reported by Kienle et al. It is likely that Kienle et al. employed the previously adopted value of 12:1:3 s [33] for 84N b to fit their 84Mo decay data, which would give a half-life for 84Mo that was longer than what would be deduced using a 9.5i1.0 8 daughter. The newly measured half-life can be used to differentiate between the two theoret- ical treatments of N = Z half-lives at A = 84 were initially shown in Figure 1.6. The comparison of the new half-life value of 84Mo with these theoretical results is shown in Figure 5.14. The new half-life is consistent with the previously discussed level density functional employed by Sarriguren et al. [21]. The Sarriguren et al. half-lives relied on a mean field approximation calculated from density functionals using the 97 1h 4 0.13.3”? .‘i : . ._ . .5 O 14 I_ x Kienle etal. PPNP 40 (2001) _- : 0 Dean at al. EPJ A 21 (2004) 3 12 - 0 Ressler at al. PRL 84 (2000) - T - This work i A ~ ‘ £3. 10 :- 7 . L 1 91-, a ; —‘ —I h 1 2: : l m 6 r )E ‘ :1: t 1 i 4 -_ 1 — L I _ 2 l 3 o F 802" 84Mo 91Rh 92Rh 93Rh Figure 5.13. Plot of the previously measured half-lives for 80Zr [2, 15] and 91‘93Rh [2, 29], which are listed in Table 1.1, and the previous literature [2] and newly determined half-life values for 84Mo. level densities of the nuclei of interest. The level density is not directly related to the half-life of a nucleus, so a measured half-life that was inconsistent with their calcula- tion may have implied that their assumptions for other factors, such as the overlap between the initial and final decay states, needed to be revised. The generally good agreement that was observed between the Sarriguren et al. calculated half-lives with experimental values is now extended to 84M0, further demonstrating the robustness of the QRPA approach in this region using the Skyrme and SG2 functionals. The consistency of the newly measured 84‘Mo half-life with a equilibrium shape calculated from a self-consistent level density affirms the trend towards a spherical 100Sn implied by the measured values of 114/2 for 84Mo and 88Ru [19]. 98 100, ‘-..‘.- .. ‘1, 1*. ‘Q\ .5. 1 b --V--QRPA - Sk3 “~§..‘_6 a T1l2 (S) -)<- QRPA - SGZ --O-- QRPA - Biehle Y 0 Experiment 0 This Work 0.1 1 1 1 1 1 1 1 1 64Ge 68Se 72KI' "Sr ”Zr $4Mo 88Ru 92Pd Figure 5.14. The lines show half-lives of even-even N = Z nuclei (A = 64 — 92) deduced using the QRPA. Details of different theoretical self-consistent parameters are given in text [21, 22]. The experiment values for A = 64,68, 72, 76,80 [27], A = 84, 88, 92 [2], and this work are shown by the points with error bars. Astrophysical Implications The impact of the newly measured 84Mo half-life on the final A = 84 abundances produced during the rp-process was calculated using a single zone X-ray burst model based on ReaclibVl rates from the J IN A Reaclib online database [68]. The abundance as a function of burst duration is shown in Figure 5.15 for 84Mo (solid lines) and for all A = 84 isobars (dashed line). The shaded region results from the range of previously predicted half-lives (0.8 s S T1/2 S 6.0 s) from various models [21, 22, 69]. The dot-dashed line represents the yield calculated using the experimental upper limit of 4.7 3 taken from the previously adopted 84Mo T1/2' Such time-dependent abundance calculations also rely on the masses of rp process nuclei, and will become more accurate as the uncertainties in these masses are reduced [12]. 99 J.” 1 Abundance 3. 10.7 ' .- 1 , J. 0 so 100 150 200 Time (s) Figure 5.15. Impact of 84Mo half-life on the final A = 84 isobar abundance using a single zone X-ray burst calculation. Abundance is reported as a ratio of (mass fraction) / (mass number). Time zero corresponds to the hydrogen-ignition start time. The solid line, bounded above and below with dotted uncertainties, shows the result using the newly-measured 84Mo half life [T1 /2 = 2.2(2) s]. The dashed line corre- sponds to summed abundance of all A = 84 isobars. The dot-dashed line represents the yield calculated using the experimental upper limit of 4.7 8 taken from the pre- viously adopted 84M0 T1/2. Shaded regions highlight the range in abundance based on half-lives predicted previously (0.8 s S T1/2 S 6.0 s). 100 The location of 84Sr as the most proton-rich A = 84 stable isobar shields all other A = 84 masses from ,6 decay processes from the proton-rich side of the valley of 6 stability. Therefore, the final abundance for all A = 84 isobars is equivalent to the final abundance of 84Sr. The order of magnitude uncertainty in the final 84Sr abundance is reduced to less than a factor 2 with the new, more precise, half-life of 84Mo reported here. The ratio of the mass fraction of an isotope produced in a particular process to its mass fraction in the solar system is called the overproduction factor of an isotope. Assuming the rp process was the astrophysical reaction sequence solely responsible for producing 84Sr, then the rp-process overproduction factor determined for 84Sr would be larger than that determined for every other isotope. Similarly, if the rp process was responsible for the bulk solar production of two or more isotopes, than the overproduction factors for the predominantly synthesized isotopes would need to be large relative to that determined for other isotopes that were not chiefly produced in the rp process. The values of the overproduction factors determined for isotopes produced in the rp process are given below. A similar calculation was performed for the abundances of A = 92, 94, 96, and 98 isobars. The final abundances of the mass 92, 94, 96, and 98 isobars directly determine the amount of 92M0, 94M0, 96Ru, and 98Ru, respectively, that are produced in the rp process. 92Mo and 96Ru showed significant overproduction factors in this calculation. The abundances with respect to burst duration are shown in Figure 5.16. The abundances were determined using the newly-measured 84Mo half-life. The isobars are represented by the solid (A = 92), dotted (A = 94), dashed (A = 96), and dash-dot (A = 98) lines. The uncertainty in abundances for the A = 92, 94, 96, and 98 isobars depends upon the uncertainties for all the rate—determining steps in the rp-process reaction sequence prior to A = 92; so the abundance uncertainties determined solely from the 84Mo half-life uncertainty are small, and are not included in Figure 5.16. A comparison of the final isobar abundances in Figures 5.15 and 101 10'3_ 8 4 =10 E' “3 E 1:, -5: £10 .— 10“, 10"" , 1 . 0 50 100 150 200 Time (s) Figure 5.16. Similar to Figure 5.15, except for A = 92, 94, 96, and 98. The abundances were determined using the newly-measured 84Mo half life [T1 /2 = 2.2(2) s]. The isobars are represented by the solid (A = 92), dotted (A = 94), dashed (A = 96), and dash-dot (A = 98) lines. The rp-process isobar sums for masses 92, 94, 96, and 98 are equivalent to the final abundances of 92M0, 94M0, 96Ru, and 98Ru, respectively. Details are in the text. 102 5.16 reveals that the rp process produces amounts for A = 84,94, and 98 are of the same order. Consequently, this simulation was extended to determining the rp- process overproduction factors. Considerations of the rp process as a source of solar production for 94Mo and 98Ru must also include 84Sr, if the overproduction factors are of the same order. Mass Fraction A=64 [L 60 64 68 72 76 80 84 88 92 96100 Mass Number Figure 5.17. Plot of mass fractions from A = 60 — 100 determined from a single zone X—ray burst rp-process simulation. A plot of the mass fractions with respect to the total rp-process yield shows which isotopes were the most prolifically produced. Figure 5.17 is a plot of the mass fractions of species produced in a single zone X-ray burst simulation with A = 60 — 100. The peaks at mass 64, 68, 72, 76, 80, and 84 correspond to the p—nuclei produced from ,8 decay out of the rp-process waiting points 64Ge, 688e, 72Kr, 768r, 80Zr, and 84M0. The peaks at A = 94 and A = 98 represent the mass fraction attributed to the nuclei 94Mo and 98Ru. The rp-process overproduction factors for 84Sr, 92M0, 94M0, 96Ru, 103 A J O O a. 0 O "I _1 .3 O a "l Abundance Ratio to Solar 3 l l l L 60 65 ‘7'0 75 so 85 90 95 100 Mass Number Figure 5.18. Plot of overproduction factors for A = 60— 100 determined from the ratio of mass abundances, calculated from a single zone X—ray burst rp-process simulation, to solar abundancas. 104 and 98Ru were determined from the mass fractions shown in Figure 5.17 and known solar abundances [70]. The overproduction factors for the mass range A = 60— 100 are shown in Figure 5.18. The new 84Mo half-life of 22(2) 8 reported in this work reduces the overproduction factor for A = 84 by a factor of 2 relative to that determined using the previous half-life of 3.7:(1):g 3. However, the direct impact of the new 84Mo half- life on the rp-process production of A = 92 and above is small. Nevertheless, the A = 84 isobar remains one of the more prolifically produced masses in the rp process. The plot of the ratio of rp-process abundances to known solar abundances, shown in Figure 5.18, demonstrates that the A = 84, 94, and 98 isobars receive the highest contribution from the rp process, using the conditions specified here, to their solar abundances relative to other masses. Based on the X-ray burst simulations performed in this work, rp-process scenarios with burst duration of order 100 s or greater produce a substantial amount of 84Sr, 94Mo, and 98Ru. It is conceivable that an rp process as discussed in this paper would contribute to the solar abundances of these isotopes, though underproduction of 92Mo and 98Ru shown here require additional proton capture reaction mechanisms for the production of p-nuclei, which have been proposed [71]. The newly reported half-life is still longer than the 1.1 3 value used for simulations in Ref. [1]. A longer half-life leads to a more pronounced bottleneck in a Zr-Nb cycle rp-process endpoint than predicted. A measurement of the 84Mo a-separation energy is critical to verify the establishment of a Zr—Nb cycle and the full impact that 84Mo may have on the rp-process mass flow. The a—separation energy is determined in part from the calculated mass value for 84M0. The demonstrated offset between measured and extrapolated masses in this region [12] of up to 1 MeV make a measurement of the a-separation energy especially necessary. 105 CHAPTER 6 Summary and Outlook A new half-life of 22(2) 3 has been deduced for the ground state of 84M0. The 84Mo ions were produced by the fragmentation of a fast 124Xe beam. The isolated 84Mo fragments represented a sample size that was more than 30 times larger than previously realized. The correlation of 6 decays with beam fragments required a carefully controlled rate of implantations into each DSSD pixel. This was achieved through A1900 filtration coupled with the first application of the RFF S towards selective rate reduction of fast fragmentation beams at NSCL. An overall reduction of order 102 was achieved with the RFFS, with principle contaminants being rate reduced of order 105, while the rate of the isotope of interest was not affected. The TOF-specific vertical deflection applied to each fragment by the RFF S resulted a unique implantation profile on the face of the DSSD for each fragment. Fragments implanted in the same pixel within tc of a 84Mo implantation were analyzed to ensure that a random treatment of the background was appropriate. All nuclei implanted into the DSSD were monitored for prompt and fl-delayed 'y rays using 16 Ge detectors from SeGA. Prompt 7 rays from the known us isomer in 73As were used to provide unambiguous identification of the isotopes implanted into the DSSD. The half-life for 84Mo was deduced from the decay times of 6 events corre- 106 lated with 84Mo fragment implantations. The 84M0 decay curve was fitted consider- ing decay contributions from parent, daughter, and granddaughter decay generations and a random background, taking the daughter and granddaughter decay half-lives as fixed parameters. The new half-life value of 22(2) 8 reinforces the observed trend of re-measured half-lives that are systematically lower than the values originally re- ported by Kienle et al. The 30 difference from the Kienle et al. value with the new value reported in this work is attributed to higher statistics, improved background treatment, and more accurate information on daughter and granddaughter decays. The 84M0 fl-delayed 7 rays were analyzed to identify candidate fi-delayed 7 rays that could be used to isolate the 6 particles specific to the 84Mo parent decay. Un- fortunately, no 7 rays attributable to the 84Nb known level structure were identified. Implications on the 84Nb ground state, favoring a J7r = 1+ spin assignment, were presented based on the lack of 'y rays observed in the 84Mo fi-delayed 'y-ray spectrum. Collecting 84Mo fl-decay statistics sufficient for identifying one or more fl-decay fed excited states in 84Nb would be valuable for two reasons: First, a 84Mo half-life could be deduced from parent 6 decays in coincidence with 7—ray transitions out of the 84N b excited states. This 84Mo half-life deduced from a background-suppressed B—decay histogram would provide a check on the 84Mo half-life determined from the MLH fit algorithm presented in this work. Second, the log ft values elucidated from the 84Mo 6 fed excited states in 84Nb would allow characterization of the 84Nb ground and excited states. Collecting the statistics necessary to characterize the 84Mo B-decay fed excited states in 84Nb would probably require an accelerator facility that could produce 84M0 at intensities of order 10 to 100 times more than what was realized in this study. Improving the efficiency of H and 7 detection would also aid in improving the number of statistics collected. The new 84 Mo half-life value is in line with the theoretical predictions of Sarriguren et al. of the mid-mass N = Z region consistent with a 84Mo nucleus that begins a 107 shape transition towards a spherical 100Sn. 84M0 is an important waiting point in the rp process, determining mass abundance at and impacting mass procession above A = 84. A measurement of the 84Mo a—separation energy is critical to determine the existence of a Zr—N b cycle high temperature endpoint and the full impact of 84Mo on the rp—process mass flow. Rapid proton capture processes have also been postulated to be aided by neutrino winds, which may reduce the impact of fi-decay waiting points on reaction progression to higher masses [72]. The new 84Mo half-life may also be incorporated into such models that occur on accreting neutron stars and in other astrophysical rapid proton reaction environments; most notably would be the rapid proton capture sequences believed to occur in supernovae [6]. 108 APPENDIX A A.1 6 Detection Efficiency The efficiency for ,6 detection was a fixed parameter for MLH half-life analysis. efl was determined from the ratio: efl = Nfi/NI (A.1) where NI is the number of implantations observed for a parent nucleus and N 5 is the number of parent [3 events observed within to. NI was determined directly from the number of experimentally observed fragment implantations for a given isotope. N fl was determined by integrating the parent component of the decay curve fits for a given isotope. Equation (2.12): /\1n1(t) = *1n1(0)e_’\1t, taken from the Bateman equations, describes the parent contribution to the decay curve. Recall from Equation (2.6) that A = N A. Where A is the activity of the sample, N is the number of nuclei present, and A is their decay constant. The number of counts observed during an experiment is a 109 product of the activity of the sample and the efficiency of the detector. C = A - 815 (A2) A simple substitution of Equation (A.2) into (2.12) yields: 0,; = (Joe—212. (11.3) N g was defined as the total number of parent decay events observed from t = 0 to t = to. N 5 can therefore be directly determined through the integration of Equation (A.3) from t = 0 to t = tc to A N), = / C’Oe_ ltdt (AA) 0 where tc represents the fragment-fl correlation time. Equation (A.4) can be simplified to read: CO —A t N fl = A—1'(1 — 8 1 C). Where Co represents the number of decays observed from the parent nucleus at t = 0. The error in the efficiency is calculated from the relation: 0 2 2 0% 2 (Ni?) 8% + (113,11) 5%. (A5) Where UNI and a N 6 are the errors associated with NI and N ’3, respectively. The parameter NI is taken directly from an experimental measurement. UNI was deter- mined solely based on Gaussian statistics from \/N—I- The uncertainty in N fl depends on the parameters Co, Al, and to and was calculated via two different methods. First, via the relation: 6N 2 6N 2 BN 2 2 _ £3 2 fl 2 fl 2 The necessary partial derivatives to evaluate Equation (A6) are: 3N6 1 A _ = _ _ — 120 A. 000 /\1 (1 e ) ( 7) 5NB 00 -1 1 A _ = _ _ _ - ltc _ —)\1tc 3N [3 : Cog-Alto (A9) ate 110 The second method for evaluating the uncertainty in N3 was to integrate Equation (A.4) using the ilo range of the parameters C0 and A1 to define the upper and lower limits of N3. For example, the +10 (-10) value for N3 was calculated by simultaneously inserting the CO + 000 (Co — 000) and the A1 — 0A1 (A1 + ”All into Equation (A.4) and integrating over to. The second method produced slightly larger uncertainties for N3 relative to the uncertainties determined through the error propagation formula provided by Equation (A.6). These larger, more conservative values were taken for a N 15' The values of 63 for 84Mo, 83Nb, and 81Zr were deduced from their individual decay curves. These particular nuclei were the only nuclei available which could be reliably correlated (see Table 5.1) based on their known half-lives and the average implantation rate per pixel in this work. The decay curve for each of these nuclei, with time bins of 1 s, was fitted based on the maximization of a Poisson probability distribution function, which was independent of e 3, that considered contributions from the exponential parent decay and the exponential growth and decay of the daughter, and a linear background. The value of tc for each decay curve was 20 3, consistent with the to used for extracting the 84Mo half-life with the MLH fit. The fit deduced for 84M0 is provided in Figure A.1. Values of 282(47), 18(3) 8, and 027(5) were obtained for N3, T1/2, and 8 3, respectively, using Equation (A6) to determine the uncertainty for N3. By integrating Equation (A.4) using the ila range of the parameters 00 and A1, values of 282(66) and 027(6) were obtained for N3 and 53, respectively. The decay curve obtained for 83N b is shown in Figure A2. A daughter half-life of 37.8 s [73] was taken as a fixed parameter. The granddaughter had a long T1/2 and was effectively included in the background. The correlation time for 83Nb was taken as 20 s, and decays and implantations were correlated using a 5-pixel search geometry. Values of 5927(378) and 029(2) were obtained for N3 and 5 3, respectively, 111 Counts I1 5 1O \ Background T1/2(l3) = 1-3 (3) S .11 L 1 AA 1 I I I l I l I l I I l I I I I I 6 I L I L 1 8 20 Tlme (s) 8 1O 12 Figure A.1. Similar to Figure 5.6. A daughter half-life of 9.5 s was taken as a fixed parameter. The initial activity, parent decay constant, and background were free parameters in the fit. d ‘2. lllllIy Counts I 1 s 102 T1120” = 3-3 (2) S Parent 1 i :— Daughter ”14.1.11.1M11\111 0 2 4 6 8 10 12 14 16 18 2O T1me(s) Figure A2. Similar to Figure 5.6, except for 83Nb. A daughter half-life of 37.8 s was taken as a fixed parameter. The initial activity, parent decay constant, and background were free parameters in the fit. The fitted background rate of < 70 counts/s lies below the horizontal axis. 112 T1120» = 4-5 (2) 8 Counts / 1 5 Parent d 9. llTllF] l .. ..1...1.-1 14 16 18 20 Time (s) O N b 01 O .1 O .1 N Figure A.3. Similar to Figure 5.6, except for 81Zr. A daughter half-life of 72.0 s was taken as a fixed parameter. The initial activity, parent decay constant, and background were free parameters in the fit. The exponential growth and decay of the daughter and the fitted background rate of ~100 counts/s both lie below the horizontal axis. using Equation (A6) to determine the uncertainty for N3. By integrating Equation (A.4) using the 3:10 range of the parameters Co and A1, values of 5927(454) and 029(2) were obtained for N3 and 53, respectively. The half-life of 3.8(2) s deduced for 83N b is in good agreement with the previously reported value of 41(3) 3 [51]. The parameters deduced for 83N b are summarized in Table Al. The decay curve obtained for 81Zr is provided in Figure A3. A daughter half-life of 72.0 s [55] was taken as a fixed parameter. The correlation time for 81Zr was taken to be 20 s, and decays and implantations were correlated using a 5-pixel search geometry. Values of 13900(746) and 037(2) were obtained for N3 and 5 3, respectively, using Equation (A6) to determine the uncertainty for N 3. By integrating Equation (A.4) using the :1:10 range of the parameters 00 and A1, values of 13900(795) and 037(2) were obtained for N3 and 53, respectively. The half-life of 46(2) 3 deduced for 81Zr agrees, within error, with the previously reported value of 5.3(5) s. The 113 parameters deduced for 81Zr are summarized in Table Al. The total 53, was computed from the weighted average of the £3 deduced in- dividually for 84Mo, 83Nb, and 81Zr. The parameters deduced for the individual isotopes that were used to determine the total 5 3 are summarized in Table A1. The values and uncertainties for the parameters N3 and 53 provided in Table A.l were determined using the above mentioned method of integrating Equation (A.4) using the 3:10 range of the parameters Co and A1. Table A1. Parameters for determining 53. The T1/2 and N3 parameters were deduced from the decay curves in Figures A1, A2, and A3 for the nuclei 84Mo, 83Nb, and 81Zr, respectively. The uncertainties in the N3 were determined by integrating Equation (A.4) using the :tla range of the parameters Co and A1. The NI were determined directly from the number of fragments identified for each isotope from the particle identification plot. Isotope T1/2 (s) N3 NI 83 84M0 1.8(3) 282(66) 1037(32) 027(6) 83Nb 3.8(2) 5927(454) 20121042) 029(2) 81zr 4.6(2) 13900(795) 37246(193) 037(2) Weighted Average 034(2) 114 BIBLIOGRAPHY [1] H. Schatz, A. Aprahamian, J. Gorres, M. Weischer T. Rauscher, J F Rembges, F K Thielemann, B Pfeiffer, P Moller, K L Kratz, H Herndl, B A Brown, and H Rebel. Phys. Rep. 294:167, 1998. [2] P. Kienle, T. Faestermann, J. Friese, H. J. Korner, M. Munch, R. Schneider, A. Stolz, E. Wefers, H. Geissel, G. Munzenberg, et al. Prog. Part. Nucl. Phys. 46:73, 2001. [3] J. I. Prisciandaro, A. C. Morton, and P. F. Mantica. Nucl. Instrum. and Methods A 505:140—143, 2003. [4] W. F. Mueller, J. A. Church, T. Glasmacher, D. Gutknecht, G. Hackman, P. G. Hansen, Z. Hu, K. L. Miller, and P. Quirin. Nucl. Instrum. and Methods A 466:492, 2001. [5] D. Gorelov, V. Andreev, D. Bazin, M. Doleans, T. Grimm, F. Marti, J. Vin- cent, and X. Wu. RF—Kicker System for Secondary Beams at the NSCL. In C. Horak, editor, Proceedings of 2005 Particle Accelerator Conference, page 3880. Knoxville, TN, 2005. [6] E. M. Burbidge, G. R. Burbidge, W. A. Fowler, and F. Hoyle. Rev. Mod. Phys. 29(4):547, 1957. [7] J. Grindlay and H. Gursky. Astrophys. J. Lett. 205:L127, 1976. [8] J. Jose. Nucl. Phys. A 75225400, 2005. [9] H. Schatz. Nucl. Phys. A 746:347c, 2004. [10] H. Schatz, A. Aprahamian, V. Barnard, L. Bildstein, A. Cumming, M. Oullette, T. Rauscher, F K Thielemann, and M. Wiescher. Phys. Rev. Lett. 86:3471, 2001. [11] R. Hynes. Http://www.phys.lsu.edu/ rih/. [12] A. Kankainen, L. Batist, S. A. Eliseev, V. V. Elomaa, T. Eronen, U. Hager, J. Hakala, A. Jokinen, I. Moore, Yu. N. Novikov, et al. Eur. Phys. J. A 29271, 2006. 115 [13] N. Weinberg, L. Bildstein, and H. Schatz. Astrophys. J. 639:1018, 2006. [14] R. N. Boyd. Eur. Phys. J. A 132203, 2002. [15] J. J. Ressler et al. Phys. Rev. Lett. 84(10):2104, 2000. [16] W. Walters. Beta Decay Half-Life of 84Mo, 1998. Proposal to the Holifield Radioactive Ion Beam Facility. [17] R. F. Casten, N. V. Zamfir, and D. S. Brenner. Phys. Rev. Lett. 71(2):227, 1993. [18] D. Bucurescu, C. Rossi Alverez, C. A. Ur, N. Marginean, P. Spolaore, D. Baz- zacco, S. Lunardi, D. R. Napoli, M. Ionescu-Bujor, A. Iordaschescu, et al. Phys. Rev. C 56(5):2497, 1997. [19] N. Marginean, C. Rossi Alvarez, D. Bucurescu, C. A. Ur, A. Gadea, S. Lun- dardi, D. Bazzacco, G. de Angelis, M. Axiotis, M. De poli, et al. Phys. Rev. C 63(031303), 2001. [20] N. Marginean. Eur. Phys. J. A 20:123, 2004. [21] P. Sarriguren, R. Alvarez-Rodriguez, and E. Moya de Guerra. Eur. Phys. J. A 24:193, 2005. [22] G. T. Biehle and P. Vogel. Phys. Rev. C 46(4):l555, 1992. [23] E. J. Kaptein, H. P. Blok, L. Hulstman, and J. Blok. Nucl. Phys. A 260:141, 1976. [24] M. K. Kabadiyski, C. J. Gross, A. Harder, K. P. Lieb, D. Rudolph, M. Weiszflog, J. Altmann, A. Dewald, J. Eberth, T. Mylaeus, H. Grawe, J. Heese, and K. H. Maier. Nucl. Phys. A 260:141, 1976. [25] C. Lingk, A. Jungclaus, D. Kast, K. P. Lieb, C. Teich, M. Weiszflog, C. Ender, T. Hartlein, F. Kock, D. Schwalm, et al. Phys. Rev. C 56(5), 1997. [26] C. Plettner, H. Grawe, I. Mukha, J. Doring, F. Nowacki, L. Batist, A. Blazhev, C. R. Hoffman, Z. Janas, R. Kirchner, et al. Nucl. Phys. A 733:20, 2004. [27] G. Audi, 0. Bersillon, J. Blachot, and A. H. Wapstra. Nucl. Phys. A 729:3, 2003. [28] E. Wefers. Zerc’z’lle extrem neutronenarmer Keme unterhalb von 1OOSn. Ph.D. thesis, Technischen Universitat Munchen, 2001. [29] S. Dean, M. Gorska, F. Aksouh, H. de Witte, M. Facina, M. Huyse, O. Ivanov, K. Krouglov, Yu Kudryavtsev, I. Mukha, et al. Eur. Phys. J. A 21243, 2004. 116 [30] R. Schneider. Nachweis und Untersuchung des Zerfalls von 1005n and benach- barter K erne. Ph.D. thesis, Technischen Universitat Munchen, 1996. [31] C. Longour, J. G. Narro, B. Blank, M. Lewitowicz, Ch. Miehe, P. H. Regan, D. Applebe, L. Axelsson, A. M. Bruce, W. N. Catford, et al. Phys. Rev. Lett. 81(16):3337, 1998. [32] J. Uusitalo, D. Seweryniak, P. F. Mantica, J. Rikovska, D. S. Brenner, M. Huhta, J. Greene, J. J. Ressler, B. Tomlin, C. N. Davids, et al. Phys. Rev. C 57(5):2259, 1998. [33] G. Korschinek, E. Nolte, H. Hick, K. Miyano, W. Kutschera, and H. Morinaga. Z. Phys. A 281(409), 1977. [34] J. Doring, R. A. Kaye, A. Aprahamian, M. W. Cooper, J. Daly, C. N. Davids, R. C. de Haan, J. Gorres, S. R. Lesher, J. J. Ressler, et al. Phys. Rev. C 67(014315), 2003. [35] G. Friedlander, J. W. Kennedy, E. S. Macias, and J. M. Miller. Nuclear and Radiochemistry. John Wiley & Sons, 1981. [36] H. Bateman. Proc. Cambridge Phil. Soc. 15:423, 1910. [37] W. Loveland, D. J. Morrissey, and G. T. Seaborg. Modern Nuclear Chemistry, page 420. John Wiley & Sons, Inc., 2005. [38] R. Pfaff, D. J. Morrissey, W. Benenson, M. Fauerbach, M. Hellstrom, C. F. Powell, B. M. Sherrill, M. Steiner, and J. A. Winger. Phys. Rev. C 53(4):]753, 1996. [39] D. J. Morrissey, B. M. Sherrill, M. Steiner, A. Stolz, and I. Wiedenhoever. Nucl. Instrum. and Methods B 204:90, 2003. [40] O. Tarasov, D. Bazin, M. Lewitowicz, and O. Sorlin. Nucl. Phys. A 701:661, 2002. [41] S. N. Liddick. Beta-Decay Studies of Neutron-Rich Nuclides and the Possibility of an N = 34 Subshell Closure. Ph.D. thesis, Michigan State University, 2004. [42] O. B. Tarasov and D. Bazin. Nucl. Phys. A 746:411c, 2004. [43] R. G. Helmer and C. van der Leun. NIM A 450:35, 2000. [44] C. W. Reich and R. G. Helmet. Nucl. Data Shts. A = 154 85(2):171, 1998. [45] C. W. Reich. Nucl. Data Shts. A = 155 104(1):1, 2005. 117 [46] L. P. Ekstrom and R. B. Firestone. WWW Table of Radioactive Isotopes, database version 2/28/99. Http://ie.lbl.gov/toi/index.htm. [47] J. Katakura. Nucl. Data Shts. A = 125 86(955):1, 1999. [48] W. T. Milner. DAMM. TXX. Oak Ridge National Laboratory, unpublished. [49] D. Quitmann, J. M. Jaklevic, and D. A. Shirley. Phys. Lett. B 30(5):329, 1969. [50] T. Faestermann. Astrophys. J. A 15:185, 2002. [51] T. Kuroyanagi, S. Mitarai, B. J. Min, H. Tomura, Y. Haruta, K. Heiguchi, S. Suematsu, and Y. Onizuka. Nucl. Phys. A 484:264, 1988. [52] C. F. Liang et al. Z. Phys A 309:185, 1982. [53] W. X. Huang, R. C. Ma, X. J. Xu, 8. W. Xu, Y. X. Xie, Z. K. Li, Y. X. Ge, Y. Y. Wang, C. F. Wang, T. M. Zhang, et al. Z. Phys. A 359:349, 1997. [54] J. Doring, A. Aprahamian, R. C. de Haan, J. Gorres, H. Schatz, M. Wiescher, W. B. Walters, L. T. Brown, C. N. Davids, C. J. Lister, and D. Seweryniak. Phys. Rev. C 59(1):59, 1999. [55] C. J. Lister, P. E. Haustein, D. E. Alburger, and J. W. Olness. Phys. Rev. C 24(1):1981, 1981. [56] R. K. Girgis, R. A. Ricci, and R. van Lieshout. Nucl. Phys. 13:473, 1959. [57] J. Kyles, J. C. McGeorge, F. Shaikh, and J. Byrne. Nucl. Phys. A 150:143, 1970. [58] J. A. Rice. Mathematical Statistics and Data Analysis. Wadsworth-Brooks Cole, 1995. [59] G. F. Grinyer. High Precision Measurements of 26Na 6" Decay. Master’s thesis, The University of Guelph, 2004. [60] G. F. Knoll. Radiation Detection and Measurement, page 787. John Wiley & Sons, Inc., 2000. [61] P. T. Hosmer, H. Schatz, A. Aprahamian, O. Arndt, R. R. C. Clement, A. Estrade, K. L. Kratz, S. N. Liddick, P. F. Mantica, W. F. Mueller, et al. Phys. Rev. Lett. 94(112501), 2005. [62] D. Bazin, F. Montes, A. Becerril, G. Lorusso, A. Amthor, T. Baumann, H. Craw- ford, A. Estrade, A. Gade, T. Ginter, C. J. Guess, et al. Phys. Rev. Lett. , (accepted). 118 [63] A. Stolz. Untersuchung des Gamov-Teller-Zerfalls in der Nachbarschaft von 100Sn. Ph.D. thesis, Technischen Universitat Munchen, 2001. [64] S. K. Saha, P. E. Haustein, D. E. Alburger, C. J. Lister, J. W. Olness, R. A. Dewberry, and R. A. Naumann. Phys. Rev. C 26(6):2654, 1982. [65] N. Marginean, D. Bucurescu, C. A. Ur, D. Bazzacco, S. M. Lenzi, S. Lundardi, C. Rossi Alvarez, M. Ionescu—Bujur, G. de Angelis, M. De Poli, et al. Eur. Phys. J. A 4:311, 1999. [66] J. K. "[1111. Nucl. Data Shts. A = 84 81(331):331, 1997. [67] C. Chandler, P. H. Regan, B. Blank, C. J. Pearson, A. M. Bruce, W. N. Cat- ford, N. Curtis, S. Czajkowski, Ph. Dessagne, A. F leury, et al. Phys. Rev. C 61(044309), 2000. [68] S. Warren. Http://www.nscl.msu.edu/~nero/db. [69] K. Takahashi and K. Yokoi. Nucl. Phys. A 4042578, 1983. [70] M. Asplund, N. Grevesse, and J. Sauval. Nucl. Phys. A 777:1, 2006. [71] J. Pruet, R. D. Hoffman, S. E. Woosley, H. T. Janka, and R. Buras. Astrophys. J. 644:1028, 2006. [72] C. Frohlich, G. Martinez-Pinedo, M. Liebendorfer, F. K. Thielmann, E. Bravo, W. R. Hix, K. Langanke, and N. T. Zinner. Phys. Rev. Lett. 96(142502), 2006. [73] E. Hagberg, J. C. Hardy, H. Schmeing, E. T. H. Clifford, and V. T. Koslowsky. Nucl. Phys. A 395:152, 1983. 119 “'11111111111111111111111ES 62 6117