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Decay spectroscopy of N ~ Z nuclei in the vicinity of ¹⁰⁰Sn Park, Joochun (Jason) 2017

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Decay spectroscopy of N ∼ Z nuclei in thevicinity of 100SnbyJoochun (Jason) ParkB.Sc., The University of British Columbia, 2012A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Physics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)March 2017c© Joochun (Jason) Park 2017AbstractThe nuclear shell model (SM) has been very successful in describing the properties and the structureof near-stable and stable isotopes near the magic nuclei. Today, the advent of powerful facilitiescapable of producing radioactive isotopes far from stability has enabled the test of the SM on veryproton-rich or neutron-rich magic nuclei. 10050Sn50 is a proton-rich doubly-magic nucleus, but isnearly unstable against proton emission. Key topics of nuclear structure in this region include thelocation of the proton dripline, the effect of proton-neutron interactions in N ∼ Z nuclei, single-particle energies of orbitals above and below the N = Z = 50 shell gaps, and the properties of thesuperallowed Gamow-Teller decay of 100Sn.A decay spectroscopy experiment was performed on 100Sn and nuclei in its vicinity at theRIKEN Nishina Center in June 2013. The isotopes of interest were produced from fragmentationreactions of 12454Xe on a94Be target, and were separated and identified on an event-by-event basis.Decay spectroscopy was performed by implanting the radioactive isotopes in the Si detector ar-ray (WAS3ABi) and observing their subsequent decay radiations. β+ particles and protons weredetected by WAS3ABi, and γ rays were detected by a Ge detector array (EURICA).Of the proton-rich isotopes produced in this experiment, over 20 isotopes as light as 88Zr and asheavy as 101Sn were individually studied. New and improved measurements of isotope/isomer half-lives, β-decay endpoint energies, β-delayed proton emission branching ratios, and γ-ray transitionswere analyzed. In general the new results were well reproduced by the SM, highlighting a relativelyrobust 100Sn core. However, the level scheme of 100Sn’s β-decay daughter nucleus 100In was notconclusively determined because of several missing observations which were expected from variousSM predictions. Significantly higher β-decay and γ-ray statistics are required on several nuclei,including 100Sn, to evaluate the limit of the current understanding of their structure.iiPrefaceThis dissertation is based on the 100Sn experiment RIBF9 which took place in June 2013 at RIKENNishina Center, in the framework of the EURICA collaboration. I was one of the two principalanalysts of the experimental data; the other was D. Lubos, a PhD student collaborator at TechnischeUniversita¨t Mu¨nchen who performed an independent, parallel analysis on the same dataset withemphasis on the superallowed Gamow-Teller β decay of 100Sn. On the other hand, I was the maininvestigator of the β-delayed proton and γ-ray data. None of the text in this dissertation is takendirectly from previous publications.In Chapter 3, the calibration methods for EURICA detectors’ time, energy, and efficiencyinformation were developed on my own, and parts of them were presented in an article titled“Gamma-spectroscopy around 100Sn” which was published in RIKEN Accel. Prog. Rep., vol. 48,page 29 in 2015. Energy calibration constants for each Si strip of WAS3ABi were provided fromD. Lubos. However, I carried out independent calibrations of the timing and the high-energy dataof WAS3ABi to improve the accuracy of the implantation position.In Chapter 4, the discovery of new proton-rich isotopes 90Pd, 92Ag, 94Cd, and 96In was publishedin an article titled “New Isotopes and Proton Emitters-Crossing the Drip Line in the Vicinity of100Sn” in Physical Review Letters, vol. 116, pages 162501-6 in April 2016. The main authorof this article is I. Cˇelikovic´. As a co-author and a member of the EURICA collaboration, Iprovided editorial corrections to the manuscript. A preliminary report on the isotope productionwas published with the title “Study of the superallowed β-decay of 100Sn” in RIKEN Accel. Prog.Rep., vol. 47, page 7 in 2014. The discussion of isomeric states in 95Ag was discussed in private withtwo EURICA collaborators: K. Moschner and A. Blazhev from Institut fu¨r Kernphysik, Universita¨tzu Ko¨ln. They have analyzed a separate dataset and have obtained consistent results of the half-lives. Based on the division of topics and their initiative to perform the experiment on 95Ag, themain authorship of a future article on its isomeric decays belongs to them. On the other hand,the discovery of new isomeric γ-ray transitions in 96Cd was independently verified from a separateexperiment RIBF83 by R. Wadsworth and P. J. Davies from the University of York (in the UnitedKingdom). A joint article on the structure of 96Cd is in preparation, with me being the secondauthor. My contributions to the article include writing a supplementary section for combining thetwo consistent experimental results.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Shell model of atomic nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Nuclear mean-field potential and the formation of N = Z = 50 shells . . . . 21.1.2 Interacting shell model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1.3 NuShellX: shell model calculation software . . . . . . . . . . . . . . . . . . . 41.2 Decay spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.1 β decay: Fermi and Gamow-Teller . . . . . . . . . . . . . . . . . . . . . . . . 51.2.2 γ decay and electromagnetic transition strength . . . . . . . . . . . . . . . . 81.2.3 Proton emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3 Structure of 100Sn and nuclei in its vicinity . . . . . . . . . . . . . . . . . . . . . . . 101.3.1 Doubly magic nucleus 100Sn . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.3.2 Proton-neutron interaction in the g9/2 orbitals . . . . . . . . . . . . . . . . . 121.3.3 Limit of proton binding at Z ≤ 50 . . . . . . . . . . . . . . . . . . . . . . . . 121.3.4 N = 50 shell gap, single particle energies . . . . . . . . . . . . . . . . . . . . 131.4 Thesis objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.5 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 Experiment method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.1 Isotope production and separation at RIBF . . . . . . . . . . . . . . . . . . . . . . . 162.1.1 Radioactive isotope production . . . . . . . . . . . . . . . . . . . . . . . . . . 162.1.2 Separation and identification . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 Decay spectroscopy setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20iv2.2.1 WAS3ABi: ion, β particle and proton detectors . . . . . . . . . . . . . . . . 202.2.2 EURICA: HPGe γ-ray detectors . . . . . . . . . . . . . . . . . . . . . . . . . 222.2.3 Data acquisition triggering scheme . . . . . . . . . . . . . . . . . . . . . . . . 232.3 Summary of the experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.3.1 Primary beam intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.3.2 Data collection rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.1 Merging data from different detector systems . . . . . . . . . . . . . . . . . . . . . . 273.2 Detector calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.1 EURICA - energy, time and efficiency calibration . . . . . . . . . . . . . . . 283.2.2 WAS3ABi - energy and time calibration . . . . . . . . . . . . . . . . . . . . . 353.3 WAS3ABi event classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3.1 Ion implantation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3.2 β decay and proton emission . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.3.3 Background rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.4 Implantation-decay correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.4.1 Position correlation scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.4.2 Correlation time window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.5 Techniques for experimental observables . . . . . . . . . . . . . . . . . . . . . . . . . 433.5.1 Half-life associated with particle emission . . . . . . . . . . . . . . . . . . . . 443.5.2 β endpoint energy determination . . . . . . . . . . . . . . . . . . . . . . . . . 463.5.3 Half-life associated with γ-ray emission . . . . . . . . . . . . . . . . . . . . . 483.5.4 Isomeric ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.5.5 Determination of deadtime loss . . . . . . . . . . . . . . . . . . . . . . . . . 504 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.1 Isotope production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.1.1 Limits of proton stability: 89Rh, 93Ag, and 97In . . . . . . . . . . . . . . . . 524.2 Isomeric γ-ray/internal conversion electron spectroscopy . . . . . . . . . . . . . . . 524.2.1 Half-life and isomeric ratio measurements . . . . . . . . . . . . . . . . . . . . 524.2.2 Isomeric ratios and the sharp cutoff model . . . . . . . . . . . . . . . . . . . 564.2.3 Structure of 96Cd from isomeric γ-ray spectroscopy . . . . . . . . . . . . . . 614.3 Particle spectroscopy of β, βp, and proton decays . . . . . . . . . . . . . . . . . . . 654.3.1 Half-life measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.3.2 Experimental Qβ and QEC values . . . . . . . . . . . . . . . . . . . . . . . . 704.3.3 Limits of proton binding in 97In . . . . . . . . . . . . . . . . . . . . . . . . . 754.3.4 βp branching ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754.3.5 Direct proton emission search in 94Ag . . . . . . . . . . . . . . . . . . . . . . 774.4 γ-ray spectroscopy following β and βp decays . . . . . . . . . . . . . . . . . . . . . . 80v4.4.1 Low-spin structure of 90Ru and the spin of 90mRh . . . . . . . . . . . . . . . 804.4.2 Low-spin structure of 92Rh . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.4.3 β, βp-delayed γ rays of 96Cd . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.4.4 Identification of negative-parity states in 97Cd and 97Ag . . . . . . . . . . . 854.4.5 β, βp-delayed γ rays of 98mIn . . . . . . . . . . . . . . . . . . . . . . . . . . . 894.4.6 Low-spin structure of 99Cd . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894.4.7 Structure of 100In, and 100Sn’s log(ft) and BGT values . . . . . . . . . . . . 934.4.8 Low-spin structure of 101In and the ground-state spin of 101Sn . . . . . . . . 985 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1025.1 Highlights of the results and implications . . . . . . . . . . . . . . . . . . . . . . . . 1025.1.1 Isomer γ-ray spectroscopy and isomeric ratios . . . . . . . . . . . . . . . . . 1025.1.2 β, βp spectroscopy of N ∼ Z ∼ 50 nuclei . . . . . . . . . . . . . . . . . . . . 1025.1.3 β/βp-delayed γ-ray spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 1035.2 Prospective experiments in the 100Sn region . . . . . . . . . . . . . . . . . . . . . . . 104Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106AppendicesA γ-ray gates for isomer T1/2 determination . . . . . . . . . . . . . . . . . . . . . . . 112B Electromagnetic transition strengths . . . . . . . . . . . . . . . . . . . . . . . . . . 113C Proton emission T1/2 as a function of ` and Qp . . . . . . . . . . . . . . . . . . . . 115viList of Tables1.1 SM model spaces employed for nuclei around 100Sn, available in the NuShellX soft-ware (see Section 1.1.3). The Core/Limit column refers to the inert core nucleusassumed in the model and the heaviest nucleus calculable by the allowed valencespace. For a more comprehensive list, see Table 3 in Ref. [1]. . . . . . . . . . . . . . 41.2 Comparisons of the two β-decay modes. Only allowed transition properties are given. 61.3 Average experimental values of 100Sn’s β decay compiled from previous experiments. 114.1 γ-decaying isomers with measured half-lives. Isomeric decay information (excitationenergy Ex, isomeric state’s spin and parity Jpi, isomeric ratio R, transition multi-polarity σ`, transition energy Eγ , total IC coefficient α, and branching ratio b) isgiven. Literature T1/2 are shown for comparisons, where the values are taken fromthe NuBASE2012 evaluation of nuclear properties [2]. Only α > 0.01 are tabulated. . 544.2 Relative intensities of the γ rays in the isomeric decay of 96Cd, normalized to themost intense 811-keV transition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.3 Properties of β-decaying isotopes and isomers (spin J , isomeric ratio R, T1/2 values,isomeric state energy Ex, and QEC values) with N ≥ Z ≥ 45 and T1/2 < 20 sobtained from β-decay data. Ex marked with & are NuShellX results, and thosemarked with # are extrapolated predictions taken from Ref. [2]. . . . . . . . . . . . 674.4 Summary of β-decay information on 91Pd, 95Cd, 97In, and 99Sn, in reference toFig. 4.11. 100% ground-state to ground-state β-decay branching ratios were assumedin calculating the log(ft) values. T1/2 constraints for the proton-emitting (1/2−)isomer 97mIn are also presented. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.5 Half-lives and βp branching ratios of isotopes with non-negligible bβp. Unless adoptedfrom β-decay measurements, the half-lives determined from βp events were comparedto the β-decay half-lives for consistency checks. The bβp values are compared to thosefrom literature [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.6 γ-ray energies, coincidences and relative intensities following 99In β decay, where therelative intensities were normalized to the sum of the two yrast transitions 441 keVand 1224 keV. Newly observed γ-ray energies are given in parentheses. . . . . . . . . 90A.1 γ-ray gates used to obtain half-lives of isomeric states presented in Fig. 4.2. . . . . . 112B.1 Numerical values of electromagnetic transition parameters. . . . . . . . . . . . . . . 114viiList of Figures1.1 Qualitative Woods-Saxon (WS) potential depth as a function of nuclear radii for ageneric nucleus from Eq. (1.1). The corresponding nuclear density, which is experi-mentally determined, is plotted above the x-axis. The orbitals and magic numbersgenerated from the WS potential and spin-orbit coupling are listed within the po-tential. The quantum number n of the orbitals here begins at 1, while throughoutthe thesis n starts at 0. This figure is taken from Ref. [3]. . . . . . . . . . . . . . . . 31.2 Decay processes of a hypothetical proton-rich nucleus with mass number A andproton number Z. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Segre` chart of nuclides around 100Sn, displaying radioactive nuclei with known half-lives (yellow), half-lives and excited states (red), and stable 102Pd (black). A theo-retical proton dripline is drawn in red dashed lines. This figure is taken from Ref. [1]. 101.4 Different types of isomers present in the nuclei of interest: (a) negative-parity isomerformed by a promotion of a proton from the p1/2 orbital into the g9/2 orbital; (b)spin-aligned pn pair with an attractive T = 0 interaction; (c) core-excited spin-gapisomer, where a neutron is excited across the N = 50 shell gap; (d) lowest-energy spinstates with a small transition energy. Hindered γ-ray transitions are labeled withtheir multipolarities. Each type of isomer has a rather pure wavefunction, allowingunambiguous extractions of SPEs and TBMEs of nuclei in its vicinity. . . . . . . . . 142.1 Schematic layout of RIBF, featuring different acceleration modes. The 124Xe ionbeam from SC-ECRIS was accelerated through RILAC2 and the four cyclotrons inthe fixed-energy mode. ST3 and ST4 represent the locations of the charge strippers,which enable greater acceleration of the ion beam through the fRC and the IRC.This figure was taken from Ref. [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 Layout of BigRIPS in conjunction with the ZeroDegree spectrometer. This schematicdiagram of RIBF was taken from Ref. [5]. The decay spectrometers for the experi-ment were placed after F11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.3 Left: model of WAS3ABi with the XY detector used in the Geant4 simulation. Onlyparts of the fully simulated geometry are shown for clarity. Right: photo of theactual WAS3ABi detector surrounded by the HPGe detectors of EURICA. . . . . . . 222.4 Left: front geometry of crystals in a Euroball cluster detector. Right: photographof the first hexagonal tapered Ge detector. These figures were taken from Ref. [6]. . 23viii2.5 Simplified block diagram of the DAQ systems for BigRIPS, WAS3ABi, and EURICA.A color scheme separates the detectors from other electronics. For simplicity, theDAQ electronics for other detectors of BigRIPS are not shown here. Each stream’sevent timestamp was recorded by its own Logic Unit for Programmable Operation(LUPO), to be used in offline data merging. Logic conditions and physical quantitiesare labeled around the arrows. The clock to start the DGF time measurement inEURICA operated at 40 MHz for a 25-ns time step. Other electronics, such as delaymodules, shaping amplifiers and discriminators are omitted in this diagram. Formore detailed block diagrams, the reader is referred to Figs. 2.10 and 2.14 of Ref. [7]. 242.6 Data collection rates as a function of beam time over the course of the experiment.The stoppage of data acquisition starting at around 55 hours occurred during theSRC troubleshooting period. The fluctuation of the rates were caused by the vari-ation in the primary beam rate, and different acceptance and transmission settingsof BigRIPS and the ZeroDegree spectrometer. . . . . . . . . . . . . . . . . . . . . . . 263.1 Event timestamp difference distribution for three pairs of detector/event type com-binations. The events shown in this histogram could be properly merged. . . . . . . 273.2 TDC distribution as a function of prompt γ-ray energies for one EURICA channel.A fit of the centroids of the energy slices is shown as a black line, the function ofwhich was used to correct for γ-ray energy-dependent time walk. . . . . . . . . . . . 293.3 γ-ray TDC time as a function of maximum DSSSD energy in β events. If the event’smaximum energy deposit in a DSSSD was low, the start trigger time in WAS3ABibecame delayed; hence the difference between the WAS3ABi time and the γ-raytime was reduced. A fit function (black line) was used to correct the time walk forβ-delayed γ rays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.4 γ-ray TDC time distribution of β events with energy deposits in single DSSSD strips.Depending on the position of the β decay, systematic offsets of up to 20 ns are visiblein the X-side strips. No such dependence is seen in the Y-side strips, except for asmall shift at the last strip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.5 Left: mean centroid positions of prompt γ ray times as a function of energy follow-ing ion implantation events, after time walk correction. For β-delayed γ rays, thecentroids of the prompt γ rays are poorly defined due to the strip-dependent timeoffsets, and are not reported here. Right: time resolution as a function of γ-rayenergy in EURICA for the 4 types of events. . . . . . . . . . . . . . . . . . . . . . . 323.6 Black histogram: γ-ray spectrum of high-energy isomeric transitions in 98Cd withoutaddback. Red histogram: the same spectrum produced with addback. An improve-ment in counts at 4156 and 4207 keV is evident with the addback method thatrecovers the full energy of Compton-scattered γ rays, an example event of which isshown in the inset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33ix3.7 Absolute detection efficiency of EURICA as a function of γ-ray energy in four dif-ferent modes. The addback scheme enhances efficiency at higher energies, but below300 keV some loss in efficiency occurs due to false addback. High energy thresh-olds for the TDC modules, which provided better timing resolutions than the DGFmodules, caused lower efficiencies at Eγ < 500 keV. . . . . . . . . . . . . . . . . . . . 343.8 γ-ray energies detected in EURICA versus the ADC channel values of one of theDSSSD strips of WAS3ABi from a 60Co source. Two diagonal bands are visible,whose energy sums should be 1173 and 1332 keV. Silicon strip energy calibrationconstants were obtained by fitting the energy profiles selected along the diagonalbands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.9 Projection of Z for A/q = 2 for a subset of BigRIPS data, leading to the identificationof N = Z nuclei. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.10 Left: TDC values for a DSSSD’s X-side strips during an implantation event. Theminimum value is found at strip 33. Right: energies of the Y-side strips of thesame DSSSD. The strip with the maximum value is 28, leading to the implantationposition coordinates (33, 28) for this event. . . . . . . . . . . . . . . . . . . . . . . . 393.11 Implantation position and depth distributions of 95Cd (top) and 99Cd (bottom).Only the implantations into the middle DSSSD are shown. The differences in thedistributions, caused by different A/q ratios and kinematics, are clearly visible. . . . 403.12 Single-pixel energy spectrum of decay events following 97Cd implantation. Protonevents could be classified with E > 1500 keV unambiguously from β particles, whose∆E per strip was usually far less. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.13 Implantation depth distributions of several abundantly produced isotopes from LISE++calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.14 Proton detection efficiency as a function of proton energy and implantation depthfrom the surface of a DSSSD as simulated in Geant4. . . . . . . . . . . . . . . . . . . 423.15 Geant4’s simulated event display of a few positrons in WAS3ABi. The XY detector,the 3 DSSSDs, and the 10 SSSSDs are visible. Positron tracks are drawn in blue, and511-keV annihilation γ rays are the green lines. Large scattering angles of positronsinside WAS3ABi and escape events enforced a Qβ analysis using simulations. . . . . 473.16 Qβ determination of98Cd’s most dominant GT-decay branch to a (1+) state in 98Agwith Geant4 simulation. The experimental energy spectrum (black) extracted witha 1176-keV γ-ray gate was compared with simulated spectra (red) at various trialenergies. The χ2 evaluation range is given by the arrow at the baseline, avoiding theenergy range containing ICEs emitted during EC. The inset shows the reduced χ2results with a minimum at 2830(30) keV. . . . . . . . . . . . . . . . . . . . . . . . . 484.1 PID plot of the isotopes produced in this experiment. Events corresponding to 100Snare circled and labeled. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51x4.2 Time distribution of isomeric γ-ray transitions and half-life fits. Half-lives obtainedwith ICE-γ coincidences in 95Ag and new γ-ray transitions in 96Cd are presentedin Fig. 4.4 and Fig. 4.7, respectively. For low-statistics data, unbinned MLH fits(data shown in linear scales with error bars) were performed to determine T1/2. Forsufficient statistics, χ2 fits were made on binned histograms in logarithmic Y-axisscales. See Section 4.2.1 for the half-life analysis of the (6+) isomer in 98Cd. . . . . . 534.3 γ-ray energy spectrum following 96Ag implantation. The black histogram corre-sponds to the time-delayed γ rays, and the red histogram is a scaled γγ-coincidencespectrum gated on the 667-keV transition. The peak at 43.7(2) keV correspondsto the (15+) → (13+) E2 isomeric transition, where the inset shows the γ-ray timedistribution of the low-energy peak with a consistent half-life for the (15+) state. . . 554.4 Black histogram: γ-ray energy spectrum with WAS3ABi total energy less than 500keV and in a time window between 0 and 20 ms after 95Ag implantation. Redhistogram: γ-ray energy spectrum gated on 267-keV ICE energies in WAS3ABi witha time window up to 500 ms. The insets show the half-lives of the two isomeric statesobtained with the different γ-ray gates. Transitions at 875 and 1294 keV are γ raysemitted from the higher-spin isomer which are randomly correlated with ICE events. 574.5 Comparison of experimental isomeric ratios to the sharp cutoff model calculations.Isomeric ratios of both γ-decaying and β-decaying states presented in Table 4.1 andTable 4.3 are presented. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.6 Upper limits on the half-life of a hypothetical 6+ isomer in 100Sn as a function ofγ-ray energy at different isomeric ratios. The dependence of the half-life based onthe theoretically predicted B(E2) range of the isomeric transition is drawn as a redband. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.7 Top: γ-ray energy spectrum following 96Cd implantation, where 50 < Tγ (ns) <1200. Bottom: individual half-lives of the labeled transitions deduced with the MLHmethod. The combined half-life and its uncertainty are presented in both numericalvalues and the fit line with a 1σ band. . . . . . . . . . . . . . . . . . . . . . . . . . . 624.8 Level schemes of 96Cd. The widths of the arrows on the proposed experimentallevel scheme indicate relative γ-ray intensities. Negative-parity states are drawn inred, and the experimentally verified β-decaying (16+) isomer [8] is marked in bluefor theoretical level schemes. The acronyms of the calculated level schemes indicatemodel spaces listed in Table 1.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.9 β-decay time distributions of isotopes and isomeric states. This list is not exhaustive.Spectra obtained with γ-ray gates are labeled as “βγ” beside isotope labels. χ2 andMLH fits were performed to obtain the half-lives. . . . . . . . . . . . . . . . . . . . . 66xi4.10 Left: half-lives of ground and isomeric states of odd-odd N = Z nuclei; the parentdecay components are presented as solid lines, and background and daughter decaycomponents are shown as dashed lines. Right: Qβ measurements of the same nucleiin reference to the ground-state energy; both the ground state and the isomeric statecomponents were included. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.11 Left: half-lives of N = Z − 1 nuclei obtained from experiment. MLH fits wereperformed with separate components: parent decay (black), daughter decay (dashedblue), and background (magenta). For 97In, the relative deficit of the parent decayamplitude was compensated by a β-decay component of 96Cd (dashed green) whichwould be populated by 1p emission from a hypothetical isomeric state. Right: Qβanalysis results of these nuclei. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.12 Half-life systematics of N = Z − 1 nuclei with valence protons in the g9/2 orbital.Odd-Z nuclei are proton unbound and possess very short half-lives compared to even-Z counterparts. For 97In, a long-lived β-decaying state has been confirmed withbetter precision. Circumstantial evidence points to a short-lived proton-emittingstate 97mIn with upper and lower limits on its half-life. . . . . . . . . . . . . . . . . . 704.13 Qβ spectra of92Pd (top), 96Cd (middle), and 100Sn (bottom) obtained from γ-raygates and fitted with different trial Qβ energies. . . . . . . . . . . . . . . . . . . . . . 724.14 Comparison of experimental QEC values of the select N ≤ Z nuclei measured in thiswork to different mass models and extrapolated data (see text for references). ForAME2012, the 1σ-uncertainty band is drawn. For 100Sn, two QEC values inferredfrom the first two possible level schemes shown in Fig. 4.32 are plotted. . . . . . . . 744.15 Left: Qp values of97In based on the half-life limits for l = 1 and l = 4, correspondingto proton emissions from either the pip1/2 or the pig9/2 orbital. A theoretical descrip-tion of the T1/2-Qp relationship is given in Ref. [9] and derived in Appendix C. Right:Sp values as a function of mass number for In isotopes. The predictions diverge for97In, and the Qp values deduced on the left plot occur as intermediate values. . . . . 764.16 Time distribution of βp decays of isotopes and isomeric states. For 94Ag and 98In,the time distributions were plotted and fitted in the same way as shown in Fig. 4.10.The amplitudes of the parent decay components were used to calculate bβp. Forseveral states/isotopes, the T1/2 values from β decays were adopted to determine bβp. 784.17 WAS3ABi energy spectrum following 94Ag decay with background subtraction. Forclarity, a minimum of 1500 keV was required for βp decays. Previously reported Qpvalues [10, 11] are marked. The observation of 5 events at 1900 keV is discussed inthe text. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804.18 γ-ray spectrum of 90Rh decay within the decay correlation time window of 3 seconds.Two new transitions were found at 1164 and 1316 keV. The inset shows the half-lifeof the isomeric state obtained with the labeled γ-ray gates, which is consistent with0.52(2) s listed in Table 4.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81xii4.19 Level scheme of 90Ru obtained from the β-decay of 90mRh. The widths of the arrowsindicate relative γ-ray intensities. The two new proposed (6+) states built by the1164- and 1316-keV transitions are in agreement with the calculated 6+ states shownin “90Ru pg”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824.20 γ-ray spectrum following 92Pd decay within 5 s of ion-β correlation. Only the 257-keV transition is attributed to the 92Rh daughter nucleus, and it populates the (2+)isomeric state. The inset shows the half-life determination of 92mRh using the timeprofile of the 865-keV γ ray in the granddaughter nucleus 92Ru. . . . . . . . . . . . . 824.21 Schematic diagram of the 92Pd-92mRh decay chain, with the interpretation of thenewly discovered 257-keV γ ray being the (1+)→ (2+) transition. The experimentallow-energy states of 92Rh are reproduced in the SM calculations labeled “92Rh pg”. . 834.22 γ rays following β decay of 96Cd. The black histogram corresponds to promptlyemitted γ rays assigned to the ground-state decay of 96Cd, and the red histogramshows delayed γ rays emitted from the (15+) isomer of 96Ag populated by the β-decayof 96Cd’s (16+) isomer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.23 γ rays following βp decay of 96Cd, where the labeled transitions are known from thehigh-spin structure of 95Pd [12]. The left inset shows the time profile of the 681-keVtransition, which shows a contamination of the 680-keV γ ray emitted after 96Ag’sβp decay into 95Rh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.24 Level schemes of 96Ag and 95Pd reproduced from the β/βp decay of 96Cd. It isunclear whether the βp decay populates the 33/2+ state in 95Pd. SM calculations of1+ states in 96Ag are shown on the right, in relation to the discovered but unassignedγ rays (dashed blue arrows, compressed energy scale). . . . . . . . . . . . . . . . . . 864.25 γ-ray spectrum following 97Cd decay. Three new transitions at 1245, 1418 and 1673keV are reported, and the β-decay time profile of these γ rays exhibits a half-life of0.78(7) s. This half-life is incompatible with both the ground state and the isomericstate half-lives, but agrees well with the predicted T1/2 = 0.65 s for the (1/2−) isomer[13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874.26 Level scheme of 97Ag obtained from the β-decay of 97Cd. The 1245-, 1418- and1673-keV γ rays are considered to depopulate three (3/2−) states in 97Ag after theβ decay of 97Cd’s (1/2−) isomer, in view of the SM calculations of low-energy statesperformed in the fpg model space shown on the right. . . . . . . . . . . . . . . . . . 884.27 γ-ray spectrum following 98In’s βp decay. Three intense transitions at 290, 763 and1290 keV are known to belong to the γ-ray cascade in 97Ag, with the highest spinbeing (21/2+). The assignment of the new γ rays in 97Ag is discussed in the text. . . 904.28 Level schemes of 98Cd and 97Ag reproduced from the β/βp decay of 98mIn. The threenew γ rays correspond to the transitions from the proposed (15/2+) and (11/2+)states in 97Ag, which are reproduced in the calculations. . . . . . . . . . . . . . . . . 91xiii4.29 γ-ray spectrum following 99In decay. Besides the known transitions in 99Cd (blacklabels), many new but weak transitions are present (blue labels). The half-life de-termined from the blue γ-ray gates are fully consistent with T1/2 = 3.35(11) s deter-mined from the overall β-decay fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 924.30 Proposed level scheme of 99Cd with J+ ≤ 13/2 from the β-delayed γ rays of 99In.A calculated level scheme resembling the experimental results is drawn on the rightfor comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934.31 Top: single and coincidence γ-ray spectra following 100Sn β decay within 5 s afterimplantation. No new γ ray has been found in comparison to Ref. [14], but theinset shows a more precise half-life determined from 100In’s γ-ray gates. Bottom:absolute intensities of the γ rays belonging to 100In and the annihilation events. Incomparison to other γ-ray intensities, both 95- and 141-keV γ rays are likely M1transitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.32 Level schemes of 100In constructed from experimental results in the theoretical frame-works of two works: by Coraggio [15] and by Stone and Walters [16]. The dashedarrows and energy labels in red indicate predicted but experimentally unobserved γrays. The level scheme on the right assumes a fragmentation of the β-decay branchinto two final (1+) states, which satisfies the experimental results but requires a veryunlikely breakdown of the Z = 50 shells. . . . . . . . . . . . . . . . . . . . . . . . . . 964.33 Positron energy spectra of 100Sn β decays for different γ-ray gates, and their centroidenergies. A lower but not inconsistent centroid value is observed for the Qβ spectrumobtained by gating on the 2048-keV γ ray. . . . . . . . . . . . . . . . . . . . . . . . . 974.34 γ-ray spectrum following 101Sn β decay. The inset shows the amplitude of the 511-keV γ-ray peak, which is a relevant information in determining the ground-statespin of 101Sn. Red energy labels indicate unobserved γ-ray transitions that havebeen previously reported in Refs. [17, 18]. . . . . . . . . . . . . . . . . . . . . . . . . 994.35 Level scheme of 101In deduced from the observed β-delayed γ rays in Fig. 4.34 andthe predicted states from the SM calculations in the gds model space. Beside eachexperimentally deduced excited states, β-decay branching ratios and correspondinglog(ft) values are listed - all of which suggest allowed GT decays (∆J ≤ 1). . . . . . 100xivAcknowledgementsThis academic adventure would not have been possible without my research supervisor ReinerKru¨cken. His critical assessments and insightful suggestions throughout my research progress sharp-ened my ability to process the experimental results and discuss them with due rigor and clarity.I was greatly motivated by his profound knowledge and enthusiasm for nuclear structure physics,which has become a significant part of my career plan.Many thanks go to my analysis partner Daniel Lubos. Given the abundance of experimental datato be analyzed with a variety of challenges, I found regular discussions with him to be invaluablenot only for academic advancement, but also for sharing emotional burdens during stagnant times.His fluency in Japanese made my stays at RIKEN much more comfortable. I feel very fortunate tohave gained such a versatile friend.My mentor Mustafa Rajabali deserves a special recognition. Much of my hands-on expertisewith detectors for decay spectroscopy and and data acquisition systems was developed under hisguidance. He spared his valuable time to observe my research methods closely and offer quick andhelpful tips to move forward.This experiment has truly been an international effort, and here I cite only the key collaborators:Shunji Nishimura, Pieter Doornenbal and Giuseppe Lorusso from RIKEN; Roman Gernha¨user andThomas Faestermann from Technische Universita¨t Mu¨nchen; Bob Wadsworth and Paul Daviesfrom the University of York; and Igor Cˇelikovic´ from GANIL. Besides numerous other scientists,these individuals advanced key discussions on my experimental methods and results with theirprofessional experience.The colleagues at TRIUMF have provided me support as well. Theorist Jason Holt taught mehow to use the nuclear shell model calculation software NuShellX. PhD candidate friends SteffenCruz, Nikita Bernier, and Lee Evitts have offered me encouragements and made this journey muchmore enjoyable by simply participating in the race together.I thank my family, friends and acquaintances outside the academic environment for their un-wavering support through this endeavor. I was able to mature in other aspects of my life becausethey have reminded me about the intangible but precious values of social life, and the world outsideresearch laboratories.Most of all, I thank the triune God: the Father, Jesus the Son, and the Holy Spirit for bothcreating such an interesting universe and giving me the inspiration to study a small but intriguingpart of it. Awe belongs to God, and the delight of amazement belongs to me.xvChapter 1IntroductionAtomic nuclei are mesoscopic quantum many-body systems of protons and neutrons, which are twodistinct fermions. Each of the ∼3000 nuclides experimentally known so far is a unique combina-tion of Z protons and N neutrons bound by the strong force, resulting in its distinct properties.Advancements in particle/heavy ion accelerator facilities, detector systems, as well as experimentalmethods have allowed production and investigation of many unstable nuclei that could only havebeen made in the most exotic environments of the universe. Consequently, the properties of theseexotic nuclei then offer insights in two major disciplines of nuclear physics: nuclear astrophysicsand nuclear structure.In nuclear astrophysics, origins and production process paths of heavy elements beyond nickeland iron are a major focus. Knowing the half-lives and branching probabilities of particle emissionfollowing β decays of the unstable isotopes helps to determine the nucleosynthesis processes thatreproduce the experimentally observed elemental abundances. The properties of proton-rich nucleiare important input for understanding the rapid-proton-capture process (rp-process) [19].In nuclear structure, the robustness of the state-of-the-art theories are put to the test againstexperimental results of nuclei far away from stability. In particular, the scope of this thesis iscentered around the structure of nuclei in the vicinity of 10050Sn50: a nucleus on which many intriguingtopics converge. The sections below outline each of them in more detail.1.1 Shell model of atomic nucleiThe subsections below give brief overviews of the background information on the nuclear shellmodel (SM), and in this context 100Sn is a pivotal nucleus. Analogous to the concept of electronshells/orbitals in atomic physics, the SM has been very successful in describing the structure ofnuclei with nucleon numbers near 2, 8, 20, 28, 50, 82 and 126 (magic numbers), at which largeenergy gaps are present in the single-particle spectrum.One of the modern topics of nuclear structure, both experimental and theoretical, is the robust-ness of the aforementioned established magic numbers far away from stability. Being doubly magicbut extremely proton-rich, 100Sn and nuclei in its vicinity serve as good candidate nuclei to test therobustness of the SM involving only a few particles outside the closed shells or holes in the valenceorbitals. Basic principles of β and γ decays are described in Section 1.2.1 and Section 1.2.2, whichoffer insights into the structure of these unstable isotopes.11.1.1 Nuclear mean-field potential and the formation of N = Z = 50 shellsAn atomic nucleus is bound by the attractive nuclear force between protons and neutrons. Thefundamental principle of the nuclear force is quantum chromodynamics (QCD) of the quarks andgluons comprising each nucleon, but QCD is not invoked further in this thesis as the knowledgeof nuclear structure can be sufficiently described in terms of nucleon-nucleon (NN) interactions.The cumulative effect of NN interactions can be represented with a nuclear mean field potential,which corresponds to a net average potential acting on a bound nucleon. The mean field potentialconsists of several components: a central part, the spin-orbit coupling, the spin-spin and tensorinteractions, etc. The number of parameters needed to describe this potential can reach up to 18(see for example the AV18 potential [20, 21]).The central part of the nuclear potential has two major characteristics that are verified experi-mentally: saturation of the attractive force at the core which reflects the Pauli exclusion principle,and weak binding near the surface which reflects the short-range nature of the strong force. Amean field potential reflecting these characteristics is the Woods-Saxon potential [22]:V (r) = − V01 + exp( r−Ra ), (1.1)where V0 is the potential well depth, R = r0A1/3 (r0 = 1.2 fm) is the nuclear radius scaled bythe mass number A, and a is the surface thickness. More empirical potentials employ tuned V0and a, and/or introduce angular asymmetry r = r(θ, φ) to account for possible effects of nucleardeformation.Approximating the solution of the nuclear Hamiltonian with the Woods-Saxon potential is ahuge simplification, but it generates distinct orbitals with angular momenta l and large energygaps at certain nucleon numbers. However, the inclusion of the spin-orbit coupling (~l · ~s) [23, 24]is needed to reproduce the magic numbers by splitting a given l-orbital (only l > 0) into twoparts: spin aligned (j = l + s), and spin anti-aligned (j = l − s) where j is the total angularmomentum and s = 1/2 for protons and neutrons. This coupling is attractive for the spin-alignedcomponent, and its magnitude scales with l. The large spin-orbit splitting of the g(l = 4) orbitalcauses the spin-aligned g9/2 to be substantially lowered to an energy similar to that of the p1/2orbital. In addition to the 38 nucleons that can be placed in the lower orbitals, the p1/2 and theg9/2 orbitals can accommodate 12 more nucleons - leading to to the magic number 50. Additionalnucleons have to fill much higher-energy orbitals, which are g7/2, d5/2, d3/2, s1/2, and h11/2 before thenext magic number 82. Fig. 1.1 illustrates the locations of magic numbers and a general orderingof the orbitals from a Woods-Saxon potential, combined with the spin-orbit interaction. Beingdistinct fermions, protons and neutrons have similar but separate potentials whose depths differby a Coulomb repulsion energy. While neutrons are not charged, the isovector interaction betweenlike nucleons is repulsive. Therefore there are no bound states for an assembly of neutrons only,with the exception of neutron stars that are intact due to a massive gravitational attraction.For more quantitative analysis of the orbital energies, realistic mean-field potentials via Hartree-2Figure 1.1: Qualitative Woods-Saxon (WS) potential depth as a function of nuclear radii for ageneric nucleus from Eq. (1.1). The corresponding nuclear density, which is experimentally de-termined, is plotted above the x-axis. The orbitals and magic numbers generated from the WSpotential and spin-orbit coupling are listed within the potential. The quantum number n of theorbitals here begins at 1, while throughout the thesis n starts at 0. This figure is taken from Ref. [3].3Fock methods [25, 26] can be applied in solving the Hamiltonian. The proton and neutron orbitalsare denoted by prefixes pi and ν respectively, to distinguish between orbitals with identical totalangular momenta.1.1.2 Interacting shell modelThe SM described above can predict the energies and wavefunctions of single-particle states ratheraccurately. However, as the valence orbital is filled with nucleons, residual interactions of thevalence nucleons among themselves and those in lower orbitals must be taken into account. Inaddition, NN scattering can promote any constituent nucleon into a valence orbital or those aboveit, leaving vacancies in the inner orbitals. All of these configurations must be calculated for astate with its total spin J . Consequently, the number of required calculations usually exceeds theavailable computing power - certainly for a nucleus as heavy as 100Sn. Truncation in calculationis required on multiple levels: assumption of an inert core and inclusion of only relevant valenceorbitals (vertical truncation), and limitations on the occupation numbers for each orbital (horizontaltruncation). Table 1.1 shows the different models suitable for nuclei around 100Sn. Two elementsare required: effective single particle energies (SPEs) of the active valence orbitals and two-bodymatrix elements (TBMEs). For the calculations used in this work, both the SPEs and the TBMEsare empirical values which were extracted from a database of well-known nuclei.Table 1.1: SM model spaces employed for nuclei around 100Sn, available in the NuShellX software(see Section 1.1.3). The Core/Limit column refers to the inert core nucleus assumed in the modeland the heaviest nucleus calculable by the allowed valence space. For a more comprehensive list,see Table 3 in Ref. [1].Acronym Model space Core/Limit Refs.pg piν(1p1/2, 0g9/2)7638Sr50/10050Sn50 [27, 28]fpg piν(0f5/2, 1p, 0g9/2)5628Ni28/10050Sn50 [29, 30]fpgds piν(0f5/2, 1p, 0g, 1d, 2s)5628Ni28/14070Yb82 [31]gdsh piν(0g7/2, 1d, 2s, 0h11/2)10050Sn50/16482Pb82 [32]1.1.3 NuShellX: shell model calculation softwareOut of several computer codes to perform SM calculations, NuShellX has been chosen. Otheravailable codes include ANTOINE [33, 34], NATHAN [33, 34], and MSHELL [35] - each withunique features and Hamiltonian diagonalization schemes. However, the calculation outputs areexpected to be consistent with one another given the same input model space, truncations, SPEs andTBMEs. In addition to level schemes, calculated β- and γ-decay half-lives, branching ratios, decayenergies, and transition strengths are available outputs to be compared directly with experimentalvalues.41.2 Decay spectroscopyMuch of the structure of unstable isotopes is deduced from decay processes, a schematic scheme ofwhich is presented in Fig. 1.2. In order to capture as much experimental information as possible,both particle emission spectroscopy (β or p) and γ-ray spectroscopy need to be performed. Thefollowing sections describe each process and the underlying physics related to the investigation ofnuclear structure in this thesis.+/EC p     Sp QEC Ex  AZN A(Z N+1 A-1(Z N+1 T1/2 ( )  Figure 1.2: Decay processes of a hypothetical proton-rich nucleus with mass number A and protonnumber Z.1.2.1 β decay: Fermi and Gamow-Tellerβ decay is a weak interaction process where a nucleon in an atomic nucleus changes its type,releasing a β particle and either an electron neutrino νe (for β+ decay) or an electron antineutrinoν¯e (for β− decay). Electron capture (EC) is another decay mechanism available to proton-richnuclei. β particles and neutrinos are leptons, which are spin 1/2 particles unaffected by the stronginteraction. In this thesis, two types of β decays are relevant: positron (β+) emission and EC. Bothprocesses convert a proton in a proton-rich nucleus into a neutron to increase stability:β+ : p→ n+ e+ + νe, (1.2)EC : p+ e− → n+ νe. (1.3)5Comparisons of the two equations show that EC has a larger energy window compared to β+emission by approximately 2me, or 1.022 MeV (minus the binding energy of the captured electron).However, for a heavy and exotic proton-rich isotope the available decay energy is far larger than thisenergy window difference and the β+ decay branch becomes dominant (see Fig. 4.1.3 of Ref. [1]).For most of the nuclei in the 100Sn region, β+ decay dominates over EC. For the remainder of thethesis, β decays (without the superscript) refer to β+ decays.Experimental β decay information in this region of nuclides is not exhaustive. As a result, certainexcited states in the daughter nuclei, inaccessible through fusion-evaporation reactions or isomerspectroscopy after fragmentation reactions, may yet to be discovered. A non-comprehensive listof such nuclei (β-decay daughters) includes 89Tc, 90Ru, 92Rh, and 98,99Cd. Additional β-decayingisomeric states are predicted by theory and may be discovered.For the nuclei of interest, a β decay can be either a pure Fermi (F), a pure Gamow-Teller(GT), or an admixture of both. The properties and differences of the two decay modes are givenin Table 1.2.Table 1.2: Comparisons of the two β-decay modes. Only allowed transition properties are given.Decay mode Fermi (F) Gamow-Teller (GT)Lepton spins antiparallel (↑↓) parallel (↑↑)Isospin change ∆T 0 0, ±1Spin change ∆J 0 0 (not 0→ 0), ±1Parity change ∆pi 0 0The decay strengths of the two decay modes are related to the product of the phase spaceintegral f , which depends on the β-decay energy and the partial decay half-life t [36, 37]:ft =KG2VBF +G2ABGT,K =2pi3(ln 2)h¯7m5ec4, (1.4)where GV and GA are the vector and axial-vector weak coupling constants. It is common to quotethe log(ft) value of a β decay, which has been shown to reflect the decay selection rules [38]. Thetransition strengths BF and BGT correspond to the square of the matrix elements between theinitial state |ψi > and the final state |ψf >:BF = |MV |2 = |〈ψf |τˆ |ψi〉|2 ; (1.5)BGT = |MA|2 = |〈ψf |σˆτˆ |ψi〉|2 , (1.6)where σˆ is the Pauli spin matrix operator and τˆ is the isospin transition operator.6Fermi decayIn Fermi decays the leptons are emitted with antiparallel spins, and ∆T = ∆J = 0. Therefore, onlyisobaric analog states (IAS) are populated. The IAS are usually inaccessible in a β decay becausethe QEC value is lower than the Coulomb energy difference ∆EC between the IAS. However, for aproton-rich nucleus near the dripline, QEC > ∆EC and Fermi decay becomes a viable decay mode.For pure Fermi decays, the Fermi strength function BF is reduced to a isospin ladder operatoralgebra:BF = |〈ψf |τˆ |ψi〉|2 = |〈T, Tz + 1|τˆ+|T, Tz〉|2 = (T − Tz)(T + Tz + 1) (1.7)for β decays. The isospin T corresponds to half of the number of unpaired nucleons, and Tz =(N − Z)/2 of the parent nucleus is its projection. In view of Eq. (1.4), this implies that all pureFermi decays of the same isospin group must have a constant ft value. This is known as theconserved vector current (CVC) hypothesis, which requires additional corrections (radiative andisospin-symetry-breaking) on the order of 1% to before comparing different nuclei [39]. The ftvalues with corrections are noted as Ft.Candidate nuclei with significant or pure Fermi-decay components are very exotic Tz = −1/2and odd-odd Tz = 0 isotopes. The ground states of Tz = 0 nuclei undergo 0+ → 0+ superallowedFermi decays to isobaric analog states, the half-lives and Qβ (β-decay endpoint energy) values ofwhich can be used to test the CVC hypothesis. In particular, N = Z nuclei cease to be stableagainst proton emission beyond 100Sn, making 98In the heaviest superallowed 0+ → 0+ Fermi-decay candidate. With the highest Z and Qβ values, these nuclei are sensitive test cases of theconsistency of the corrected Ft value, which may be affected via the Fierz interference term [40].According to the present literature, precise half-lives with less than 1% relative uncertainties andQβ or mass measurements with δM/M < 0.1% are required in order to be relevant.If the CVC hypothesis holds, then the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM)quark-mixing matrix [41] could be tested with the average Ft value Ft. The unitarity of the CKMmatrix implies that all hadronic matter is composed of three generations of quarks (up/down,charm/strange, and top/bottom), and no other types of quarks are present in nature. The mixingbetween the up and the down quark |Vud| = GV /GF of the CKM matrix can be obtained from thefollowing relationship [37]:|Vud|2 = K2G2F (1 + ∆VR)Ft(1.8)=2915.64± 1.08Ft , (1.9)where the present literature has Vud = 0.97417(21).7Gamow-Teller decayIn GT decays, allowed transitions may change the isospin and change the spin of the final state byup to one unit. Due to their loose restraints on the selection rules, GT decays are ubiquitous inthe chart of nuclides. In general, the BGT value of a GT decay is fragmented across multiple finalstates and thus cannot be used to learn something about a unique transition. For a pure GT decaywith multiple final states, Eq. (1.4) is reduced toBGT =∑i3811.5 sfiti(1.10)after having evaluated the constants. fi and ti correspond to partial phase space integrals andhalf-lives, respectively. Experimentally, one must be aware of the pandemonium problem [42]which creates a bias in favor of dominant transitions. Under certain circumstances, however, adominant population of one final state may be assumed if other states are not easily accessibledue to energetics or selection rules. One example for this is 100Sn. In this case one may apply anextreme single particle estimate (ESPE) aided by the SM to predict the theoretical BGT [43]:BGT (ESPE) =4`2`+ 1(1− Nνg7/28)Npig9/2, (1.11)where ` = 4 for the g9/2 orbital, and Nνg7/2 = 0 and Npig9/2 = 10 are nucleon occupation numbersfor the parent nucleus 100Sn. In this approach, the ESPE BGT is 160/9 ' 17.8, much larger thanthe experimental value of 9.1+2.6−3.0 in Table 1.3. Among other causes that result in a lower BGT ,it is incorrect to neglect core excitations which would increase Nνg7/2 and decrease Npig9/2 in theabove formula. The phenomenon of the experimental BGT being systematically lower than theESPE across the nuclear chart is known as GT quenching. A universal quenching factor of 3/4 hasbeen applied to the GT operator to reproduce the experimental BGT values with relative success,which is a testament to the robustness of the SM. However, it would be interesting to increasethe knowledge of experimental BGT to validate theoretical interpretations of the GT quenchingdiscussed in Ref. [33].1.2.2 γ decay and electromagnetic transition strengthA β decay from a parent nucleus may populate the ground state of the daughter nucleus directly,or a set of excited states within the QEC window. Many excited states in nuclei are then de-excitedthrough γ-ray emission. With high-purity germanium detectors, a precise level scheme of a nucleusmay be determined with high-resolution γ-ray spectroscopy and γγ coincidence analysis. Withsufficient statistics, γγ angular correlation analyses may be performed to determine the spins andparities of the excited states.Similar to EC of the β decay, γ decay may compete with internal conversion (IC) where anatomic electron is emitted in place of the γ ray. In this case, the emitted electron energy is equal8to the transition energy minus the binding energy of the electron orbital. During this process,Auger electrons [44] may also be emitted. An IC branch becomes more viable as the transitionenergy decreases, and/or the minimum multipolarity of the γ-ray transition increases. This ratiois denoted by the IC coefficient α = λe/λγ , where λe and λγ are decay branching ratios of IC andγ-ray decays, respectively. For a 0→ 0 transition, only the electric monopole (E0) IC is possible.Isomeric γ-ray transitionsEvery state in atomic nuclei possesses its unique spin and parity Jpi, and a γ-ray transition from anexcited state must obey the selection rule: |Jf − Ji| ≤ ` ≤ Ji + Jf . γ-ray emission is hindered forlarge ` and small Eγ such that the half-life of an excited state may be orders of magnitude higherthan 10−12 s (see cases (c) and (d) of Fig. 1.4). With the exception of extreme hindrance for γrays which result in a dominant β-decay branch, γ-ray transitions with half-lives on the order of nsto µs are measurable with standard detectors. Then the electromagnetic transition strength B(σ`)of an isomeric γ-ray decay can be determined with the multipolarity σ`, the transition energy Eγ ,the half-life T1/2, and the branching ratio b. Experimental B(σ`) then can be used to test therobustness of SM calculations in various types of isomers and their γ-decay properties. A formulafor B(σ`) in terms of the multipolarity constant K(σ`) and the experimental observables is:B(σ`) = K(σ`)E−(2`+1)γ(ln 2T1/2)(b1 + α),K(σ`) =(h¯c)2`+1`[(2`+ 1)!!]2h¯8pi(`+ 1). (1.12)Electromagnetic transition strengths are usually represented in Weisskopf units (W.u.), whichis a coarse order-of-magnitude estimate of the nuclear collectivity involved in the transition. Twosimplifications are made to approximate the transition matrix element: setting the angular inte-gral to be one, and assuming a constant radial wavefunction for the radial integral. For electrictransitions from a nucleus with mass A, one W.u. corresponds toBW (E`) =14pi(3`+ 3)2e2R2`0 , (1.13)where R0 = A1/3r0 = (1.2)A1/3 fm is the average nuclear radius. For magnetic transitions,BW (M`) =10pi(3`+ 2)2µ2NR2`−20 , (1.14)where µN = eh¯/(2mp) is the nuclear magneton. More information on the electromagnetic transi-tions is found in Appendix B.1.2.3 Proton emissionBinding energy (or mass), one of the macroscopic properties of nuclei, may be investigated experi-mentally with spontaneous nucleon emission. Many proton-rich nuclei that were produced in this9experiment have proton separation energies Sp less than the β-decay Q-value and thus excited stateswith excitation energies Ex greater than Sp may be populated in the daughter nucleus as illustratedin Fig. 1.2. Consequently, β-delayed proton (βp) emission is possible. For certain states the Qpvalue exceeds the initial and the final state energy difference, enabling direct proton emission.1.3 Structure of 100Sn and nuclei in its vicinity100Sn is located far northwest of the stable isotope 102Pd in the Segre` chart of nuclides (see Fig. 1.3)and borders the predicted proton dripline. Suggested from the figure are several undiscoveredisotopes (empty squares below, or on the right side of the dripline) that may be stable againstspontaneous proton emission. Experimental information on nuclei in the 100Sn region are neededto confirm the dripline prediction and test the robustness of SM predictions in the most proton-richenvironment.Figure 1.3: Segre` chart of nuclides around 100Sn, displaying radioactive nuclei with known half-lives(yellow), half-lives and excited states (red), and stable 102Pd (black). A theoretical proton driplineis drawn in red dashed lines. This figure is taken from Ref. [1].101.3.1 Doubly magic nucleus 100Sn100Sn is the heaviest N = Z doubly magic nucleus, with Section 1.1.1 providing a basis for 50being a magic number. This nucleus plays a key role in understanding the nuclear structure inthe context of the shell model. Experimental and theoretical knowledge of 100Sn and nuclei in itsvicinity are discussed in the following sections.Superallowed Gamow-Teller decay of 100Sn100Sn is bound against proton emission and undergoes a superallowed GT decay which has thesmallest log(ft) value [14] in any nuclear β decay. In corollary, the GT-decay strength BGT is thelargest among thousands of known β decays. The underlying experimental values of the 100Sn aregiven in Table 1.3. This enables a unique opportunity to compare the experimental BGT value totheoretical predictions without much of the GT-decay strength being lost due to a finite β-decayenergy window QEC .Table 1.3: Average experimental values of 100Sn’s β decay compiled from previous experiments.Observable Average value Refs./notesT1/2 1.09(18) s [14, 45, 46]QEC − Ex 4.35+0.19−0.17 MeV [14, 46]BGT 9.3+2.3−3.0 all combined9.1+2.6−3.0 [14] aloneThe most significant experimental uncertainty of the BGT value comes from the uncertainty ofthe QEC value, where the phase space integral f mentioned in Eq. (1.10) depends on the 5th powerof QEC . To improve the precision of the QEC value, mass spectrometry or high-statistics β-decayspectroscopy measurements are required.Level scheme of 100InDetermining the correct level scheme of 100In, the β-decay daughter nucleus of 100Sn, is essentialfor 100Sn’s experimental log(ft) and BGT values. Three different level schemes have been proposedby independent models [15, 16, 47], and two of them hold reasonable validity according to thedissertation work by C. B. Hinke [48]. Of those two, the preferred level scheme is presented in [14].The ambiguity is caused by the non-observation of weak γ-ray transitions in one of the proposedlevel schemes, and is discussed in Section 4.4.7.Excited states of 100SnNo experimental information exists for the excited states of 100Sn, where the energies of the low-spin excited states would be valuable in addressing the discrepancies of theoretical predictions. Aseniority (nucleons not paired to spin 0; see the excited states of Fig. 1.4 (d)) isomer has been11predicted for the 6+ state in 100Sn among various models [49–51] with a half-life ranging from 90ns to 2.6 µs, which would help preserve the γ-ray transitions for delayed spectroscopy until the100Sn isotopes in an in-flight facility pass through the separators and identification detectors. Theresults of the search for an isomer in 100Sn are presented in Section 4.2.2.1.3.2 Proton-neutron interaction in the g9/2 orbitals100Sn and nuclei in its vicinity have equal or approximately the same numbers of protons andneutrons, and the ability to describe their structure depends heavily on the knowledge of isoscalar(T = 0) and isovector (T = 1) interactions among the nucleons in this region. An attractiveT = 0 interaction is available only to proton-neutron (pn) pairs with aligned spins, while T = 1interactions are present in all of pp, pn, and nn pairs with anti-aligned spins.In the g9/2 orbital, the pn interaction is most clearly demonstrated in N = Z nuclei due tothe closest overlap of the proton-neutron wavefunctions and the maximum number of pn pairsavailable for the valence nucleons. This is corroborated experimentally with high-spin isomers:(7+) and (21+) in 94Ag [52], and (16+) in 96Cd [8]. The (25/2+) isomer in 97Cd [53] can beunderstood as an unpaired g9/2 neutron with a spin projection K = 7/2 filling one of the two pnhole pairs generating the (16+) isomer in 96Cd. The T = 0 pn interaction is also responsible for anaccurate theoretical description of the experimental level scheme of a N = Z nucleus 92Pd [54], incontrast to the level scheme of a N = 50 magic nucleus 96Pd [55] where the dominant componentof the low-spin states’ wavefunctions is based on the T = 1 pp interaction. The current theories ofpn interactions near 100Sn can be examined more carefully with more robust experimental data.1.3.3 Limit of proton binding at Z ≤ 50Different mass models predict limits on proton binding of nuclei around 100Sn, but they have notbeen fully tested with experimental data. An overview of β-delayed proton emitters in the vicinityof 100Sn was presented in Ref. [56] with an impact on a certain scenario for the rp-process. Acontroversial report on the observation of direct two-proton emission in 94Ag [11] was challengedby Refs. [57, 58] on the basis of experimental apparatus and level scheme of the 2p daughter 92Rh,respectively. Another investigation of 94Ag isomers confirmed a 1p emission at Qp = 790(30) keV,but found neither the second 1p branch at Qp = 1010 keV nor the signature of 2p emission [59].It is of interest to confirm 94Ag as the first and only odd-Z 2p emitter. The results from thisexperiment are discussed in Section 4.3.5.Some of the most exotic nuclei are Tz = −1/2;N = Z−1 species, which for 40 < Z ≤ 50 are onthe edge of the proton dripline based on various mass predictions. From the literature on these nuclei[60–62], many odd-Z nuclei appear to be proton unbound based on their sub-microsecond half-lives.For even-Z nuclei, half-lives on the order of 10 ms are expected with ∆J = 0, mixed Fermi/GT βdecays to their daughter nuclei. Better half-life measurements would provide clearer borders of theproton dripline; Qβ measurements would be a more sensitive test of the mass calculations.121.3.4 N = 50 shell gap, single particle energiesThe spin-orbit coupling which brings down the g9/2 orbital close to the p1/2 orbital results inboth the formation of the shell gap at the magic number 50 and an increasing proximity of thetwo orbitals. ∆J = 4, a parity difference, and a small energy gap results in a hindrance of γdecays between these orbitals such that low-energy 1/2− states may be β-decaying isomers. Thesepredictions are elaborated in Refs. [13, 63].Two core-excited isomers in 98Cd [64] and 96Ag [65] reveal the closeness of the neutron g7/2and the d5/2 orbitals, which is the cause of hindered E2 transitions in parallel with E4 transitionsbridging the shell gap. In addition to the spin-gap isomers formed by the T = 0 pn interaction,other examples of isomers are exhibited in Fig. 1.4.101Sn has one extra neutron added to the 100Sn nucleus, and is an excellent probe to study theSPEs of the g7/2 and the d5/2 orbitals above the N = 50 shell gap. The ground state spin of101Snhas been a controversial topic due to the onset of degeneracy between the aforementioned orbitals.A study on the α-decay chain to 101Sn places the g7/2 orbital below the d5/2 orbital by 172(2)keV [66], in conflict with another experiment which proposed the reverse order [67]. It would beimportant to determine the order of the two orbitals for 101Sn to test the effects of the two-bodytensor force [68] that is evident in many exotic nuclei with unbalanced Z/A ratios.1.4 Thesis objectiveThis thesis presents results from a decay spectroscopy experiment aimed at establishing energy,spin and parity assignments of ground and excited states of nuclei around 100Sn, validating orchallenging SM predictions. Both β-decay and electromagnetic transition strengths determinedfrom this experiment allow for more stringent tests of transition matrix elements calculated fromSM models with different model spaces. Measured half-lives, decay Q-values and βp branchingratios are presented as valuable inputs for rp-process calculations and mass evaluations. The limitof the proton dripline in the Z ∼ 50 region is investigated with experimental data on the mostneutron-deficient isotopes.For the doubly magic 100Sn and its decay, more specific aims are covered in this thesis. First,improvements in the precision of T1/2 and Qβ of100Sn β decay are presented, which in turn establisha more sensitive test of the SM prediction on 100Sn’s BGT value. The literature level schemes of100Inare reviewed with higher-statistics γ-ray data, with emphasis on γ-ray intensities and unobservedtransitions that are essential to disambiguate the proposed level schemes. Finally, research on ahypothetical isomer in 100Sn is discussed in relation to the level scheme of the 100Sn itself.A parallel but independent analysis of this data has been carried out by D. Lubos [69] atTechnische Universita¨t Mu¨nchen, with varying degrees of emphasis on different topics to validatethe consistency of the results.13g9/2 M4 γ β+/EC M9 γ (1/2)− 9/2+ β+/EC (9+) (0+) 98In 95Rh p1/2 g7/2 (10+) (8+) 98Cd E2 γ (12+) g9/2 d5/2 E4 γ N = 50 (6+) 0+ 98Cd E2 γ (8+) ⁝ p1/2 g9/2 g9/2 ⁝ g9/2 g9/2 g9/2 9/2 7/2 9/2 3/2 ⁝ ― Protons (π) ― Neutrons (ν) (a) (b) (c) (d) 9/2 −9/2  Figure 1.4: Different types of isomers present in the nuclei of interest: (a) negative-parity isomerformed by a promotion of a proton from the p1/2 orbital into the g9/2 orbital; (b) spin-aligned pnpair with an attractive T = 0 interaction; (c) core-excited spin-gap isomer, where a neutron isexcited across the N = 50 shell gap; (d) lowest-energy spin states with a small transition energy.Hindered γ-ray transitions are labeled with their multipolarities. Each type of isomer has a ratherpure wavefunction, allowing unambiguous extractions of SPEs and TBMEs of nuclei in its vicinity.141.5 Outline of the thesisThe introduction is followed by the description of the experiment method in Chapter 2, includingthe isotope production mechanism, the particle identification (PID) scheme, the detector setup,and the data acquisition configuration. Chapter 3 is dedicated to the data analysis methods: ionimplantation-decay event reconstruction and correlation, silicon and germanium detector calibra-tions in time and energy, and strategies to determine key experimental quantities such as half-livesand β-decay endpoint energies. A comprehensive set of results are categorized and listed in Chap-ter 4, including relevant discussions of the results in comparison to theoretical predictions. Finalremarks and outlook on future experiments to enhance the understanding of nuclei in the 100Snregion are given in Chapter 5.15Chapter 2Experiment methodThe decay spectroscopy experiment was performed in June 2013 at RIKEN Nishina Center and itsRadioactive Isotope Beam Factory (RIBF) in Japan. This chapter is dedicated to the descriptionof RIBF, the experimental setup, and the detector/data acquisition systems.2.1 Isotope production and separation at RIBFCommissioned in March 2007, RIBF [70] at RIKEN employs in-flight production of radioactiveisotopes by projectile fragmentation of heavy ion beams. In comparison to other radioactive isotoperesearch facilities, RIBF’s high primary beam intensity enables the production of many exoticnuclei to be studied in detail for the first time in the world. Featuring also powerful separationand identification systems named BigRIPS and the ZeroDegree spectrometer, RIBF was an idealfacility to investigate the nuclei around 100Sn.2.1.1 Radioactive isotope productionA brief overview of the method to produce exotic radioactive isotopes in the vicinity of 100Sn atRIBF is given below. More details of the isotope production, including discussions of productioncross sections and comparisons to simulations, are found in Ref. [71].Primary beam accelerationThe lightest stable isotope of xenon, 12454Xe (T1/2 ≥ 1.6× 1014 years [72]) was chosen as the primarybeam in order to maximize the production cross section of neutron-deficient isotopes with Z ∼ 50.124Xe atoms in a gas were ionized with the 28-GHz superconducting electron cyclotron resonanceion source (SC-ECRIS [73]) up to the charge state 18+ (A/q ≈ 6.8) before being injected into theRIKEN Heavy-ion Linac 2 (RILAC2) commissioned in 2011.RIBF features a chain of cyclotrons which are operated in different modes depending on theprimary beam type (see Fig. 2.1). The 124Xe beam from the RILAC2 with an initial energyof 670 keV/u was accelerated through the RRC (RIKEN Ring Cyclotron), fRC (fixed-frequencyRing Cyclotron), IRC (Intermediate-state Ring Cyclotron), and the SRC (Superconducting RingCyclotron) up to 345 MeV/u. A sufficiently high charge state was required as the 124Xe ion beampassed through the cyclotrons, which was achieved by the helium-gas charge strippers between theacceleration stages. The final primary beam charge state was 52+.16Figure 2.1: Schematic layout of RIBF, featuring different acceleration modes. The 124Xe ion beamfrom SC-ECRIS was accelerated through RILAC2 and the four cyclotrons in the fixed-energy mode.ST3 and ST4 represent the locations of the charge strippers, which enable greater acceleration ofthe ion beam through the fRC and the IRC. This figure was taken from Ref. [4].Fragmentation reactionIn this experiment, the production of neutron-deficient Z ∼ 50 isotopes was achieved by fragmen-tation reactions of the 124Xe beam on a 4-mm 9Be target (thickness equivalent to 740 mg/cm2).Beryllium was chosen for its high production cross section and small energy loss/straggling dueto its low mass. While a thicker target would enable a higher production rate of the radioactiveisotopes, they would also introduce a poorer momentum resolution of the RI beam - leading to alower transmission efficiency. Thus the optimal thickness was determined with LISE++ simulations[74] and from tests with different thicknesses of the 9Be target before the main experiment [75].There is a distribution of charge states q for the fragmented isotopes, which is dependent on theprimary beam energy and the target’s properties. Since the magnetic rigidity depends on q and notthe nuclear charge Z, same isotopes with different charge states would have different trajectoriesthrough BigRIPS. For the 345-MeV/u primary beam and the 4-mm thick 9Be target, it was foundthat the majority of radioactive ions would be fully stripped of their electrons [75] such that q = Z.Due to the high RI beam intensity and the large beam acceptance required for a wide range ofZ, isotope separation and identification settings were set to accommodate only the fully ionizedspecies.2.1.2 Separation and identificationFragmentation reactions produce highly energetic radioactive isotopes with production cross sec-tions varying several orders of magnitude as a function of A and Z; the difficulty of producing exotic17nuclei scales with the imbalance of Z/A ratios. In order to conduct experiments on exotic nucleiproduced by the fragmentation method, the products of interest have to be separated from a largepool of unwanted, less exotic species and identified of their A and Z on an event-by-event basis.At RIBF, separation and identification of individual isotopes were performed by BigRIPS and theZeroDegree spectrometer [76, 77]. The sections below illustrate the basic principles of separationand identification of the RI beam. A schematic diagram illustrating the RI beam’s path through Bi-gRIPS and the ZeroDegree spectrometer before being implanted at the decay spectroscopy stationis shown in Fig. 2.2.Figure 2.2: Layout of BigRIPS in conjunction with the ZeroDegree spectrometer. This schematicdiagram of RIBF was taken from Ref. [5]. The decay spectrometers for the experiment were placedafter F11.Separation of unwanted speciesIn order to limit the rate at which the RI beam passes through the identification detectors andbecomes implanted at the decay station, only the species of interest must be transmitted throughBigRIPS and the ZeroDegree spectrometer. This was achieved by a two-stage isotope separationmethod [78, 79] using wedge degraders made of aluminum. The wedge degraders featured position-dependent thicknesses so that the radioactive isotopes with different position profiles incurreddifferent energy losses while traveling through the degraders. The energy loss was also proportionalto Z2 as described by Eq. (2.3). Therefore the nuclei with small ∆E were deflected at the subsequentdipole magnet with large bending radii due to their large momenta. In the opposite case of large∆E, the resulting bending radius was small. Compared to the isotopes of interest, the position18distributions of the other species were shifted further away from the reference path. Slits placedat the outer edges of a focal plane then stopped a significant fraction of the unwanted beam whilepreserving most of the isotopes worthy of investigation. The two-stage separation method effectivelyremoved contaminants due to changes in the charge state of the RI beam and the secondary reactionproducts generated after the first degrader. The first Al wedge degrader with a 3-mm maximumthickness was placed at the F1 focal plane in Fig. 2.2. The second Al wedge degrader was placedat F5, with a slightly lower maximum thickness at 2.2 mm.Particle identificationThe TOF-Bρ-∆E method and the instruments used to identify individual isotope’s A and Z arepresented below.Time-of-flight measurement The first intermediate quantity required to perform PID was thespeed of each ion: β = v/c. β was needed to determine both the mass-to-charge ratio A/q and thenuclear charge Z, and was deduced from the time-of-flight (TOF) measurement between two fixedlocations within BigRIPS with a known path length L:β =1cLTOF. (2.1)Two plastic scintillators coupled with photomultiplier tubes were placed at F3 and F7 of Fig. 2.2,acting as the start and the stop time measurement stations with a good timing resolution (δβ/β =0.017% for ions at 300 MeV/u, equivalent to β = 0.65 [76]). The path length between F3 and F7was 46.6 m.Determination of mass-to-charge ratio An ion with a mass number A and a charge stateq traveling through a dipole magnet with its field strength B is deflected by the Lorentz force,resulting in the following relationship:Aq= Bρcβγmu, (2.2)where γ = (1 − β2)−1 is the Lorentz factor and ρ is the bend radius. mu = 931.5 MeV/c2 is aconstant unit of atomic mass. Along with β from the TOF measurement, the magnetic rigidityBρ was determined experimentally from nuclear magnetic resonance probes to measure B andposition-sensitive parallel plate avalanche counters (PPACs) [80] to measure ρ. Two sets of PPACswere placed at each of F3, F5, and F7, allowing trajectory reconstructions [81–83] for ρ after eachbending section of BigRIPS. Combining the measurements at multiple focal planes allowed the A/qratio to be deduced with good resolution, where the relative uncertainty in A/q was less than 0.1%[75]. Isotopes with different Z but identical A/q ratios could not be distinguished with this methodalone, so the ∆E measurements were performed to determine Z.19Determination of nuclear charge Z In order to determine the radioactive isotopes’ Z, a multi-sampling ionization chamber (MUSIC) [84] was placed at F11, just in front of the decay station.The energy loss of a relativistic ion with nuclear charge Z in matter is governed by the Bethe-Blochformula [85]:−〈dEdx〉=4pie4Z2meβ2c2Nz[ln(2meβ2γ2c2I)− β2], (2.3)where z, N and I are the atomic number, the atomic density, and the mean ionization potentialenergy of the ionization material, respectively. The ionization material was a gas mixture of Ar-CH4(90% and 10% composition, respectively, for a > 99.99% purity). The geometric average of multiple∆E measurements from the MUSIC detector was combined with the velocity β obtained from theTOF measurement to calculate each isotope’s Z, culminating in an unambiguous identification ofthe RI beam’s species. The results of the isotope production and identification are presented inSection 4.1.2.2 Decay spectroscopy setupDescribed in this section are the detector systems deployed to perform decay spectroscopy mea-surements of the fully separated and identified isotopes. The specifications, characteristics, andmotivations of each system are discussed, followed by a description of the data acquisition scheme.2.2.1 WAS3ABi: ion, β particle and proton detectorsThe Wide-range Active Silicon-Strip Stopper Array for Beta and ion detection system (WAS3ABi)[5, 86] was used for multiple purposes. Being a semiconductor with a small band gap of 1.1 eVand electron-hole pair creation energy of 3.6 eV, silicon offers good energy resolution for low-energycharged particles (50 keV FWHM for E < 1 MeV) at an economic cost. Being reverse-biased atapproximately 250 V, they were maintained at 10◦C with a cool and dry nitrogen gas to reduceelectronic noise. Besides serving as an active implantation detector for the RI beam, it was usedto measure times and energies of the emitted particles from decays: β particles and protons.Experimental observables arising from WAS3ABi measurements were half-lives of the isotopes andparticle-decaying isomeric states, and proton/β-decay energies for Q-values of the decays. Internalconversion electron (ICE) energies and times were also measured with WAS3ABi, which were crucialin determining the transition strengths of isomeric states in 95Ag (see Section 4.2.1 for details).XY detectorThe XY detector was the most upstream Si detector with a 0.3-mm thickness and having 60 by 40strips in X and Y directions, respectively. The XY detector featured chains of discrete, position-dependent resistors in a grid formation to diagnose the incoming RI beam’s 2D position profile.20Double-sided silicon strip detectors (DSSSD)Three DSSSDs made by Canberra (Model PF-60CT-40CD-40*60) were used in this experiment.They were initially designed for the SIMBA detector [48] in the 100Sn experiment campaign at GSIHelmholtzzentrum fu¨r Schwerionenforschung in Germany. Si strips with 1-mm widths segmentedthe X and the Y sides of each DSSSD, defining a 60×40×1 mm3 implantation zone (1-mm thickness)for the incoming radioactive ions. The fine segmentation helped to reduce random backgroundspatial correlations of implanted ion events to decay events. As the ions with dozens of MeV/uarrived at WAS3ABi, they were stopped abruptly in one of the three DSSSDs. The kinematics of theRI beam was calculated in advance with LISE++ and moderated by supplementary Al degradersto control the implantation depth. All of the remaining kinetic energy of the ions was deposited inthe Si strips, whose energy profiles were clearly distinguishable from β-decay and proton emissionevents, whose ∆E were less than 10 MeV. The spacing between the DSSSDs was maintained at 0.5mm with metal washers.All the strip channels were connected to charge-sensitive preamplifiers (CS AMP-3), shapingamplifiers (CAEN 568B), and analog-to-digital converters (ADCs; CAEN V785) for energy mea-surements. The X-side strip channels were connected to a different ADC than the Y-side strips,and only the X-side strip channels were connected to the time-to-digital converter modules (TDC;CAEN V1190). The TDC readout values would later be used for precise determination of theimplantation position in the X-direction, described in Section 3.3.1.Single-sided silicon strip detectors (SSSSD)A stack of 10 SSSSDs was deployed downstream of the three DSSSDs for energy measurements ofβ-decay particles. The dimensions of the SSSSDs were identical to those of the DSSSDs, but theSSSSDs were segmented more coarsely. Unlike the DSSSDs which required fine position resolutionfor implantation-decay correlations, each SSSSD was segmented into 7 strips on the X-side only;the Y-side was not segmented. The same electronics mentioned in the previous section were usedto measure energy deposits in the SSSSD channels. The TDC modules were not connected to theSSSSD channels.Due to the finite kinetic energy of the RI beam, the SSSSDs could not be placed upstreamof the DSSSDs; this removed almost a 2pi solid angle coverage for proper β-decay calorimetrymeasurements. In addition, β particles deposit about 400-500 keV per mm in Si at Eβ < 10MeV with large scattering angles. High-energy β particles, even traveling downstream through theSSSSDs, may escape without depositing their full energies. To address the geometry limitationspreventing accurate energy measurements of β particles, methods using Geant4 simulations todetermine Qβ values are presented in Section 3.5.2. The WAS3ABi setup is shown in Fig. 2.3.21Figure 2.3: Left: model of WAS3ABi with the XY detector used in the Geant4 simulation. Onlyparts of the fully simulated geometry are shown for clarity. Right: photo of the actual WAS3ABidetector surrounded by the HPGe detectors of EURICA.2.2.2 EURICA: HPGe γ-ray detectorsEURICA is an acronym for Euroball-RIKEN Cluster Array, which was used to perform γ-rayspectroscopy measurements to study the excited states of the implanted radioactive isotopes andtheir decay daughter nuclei. For unpolarized radioactive isotopes stopped in the implantation zone,the γ-ray emission profile is isotropic. Hence EURICA surrounded WAS3ABi with a 4pi solid anglecoverage.The Euroball detector [6, 87], the progenitor of EURICA, features high-purity germanium(HPGe) cluster detectors in hexagonal tapered coaxial geometry (see Fig. 2.4). HPGe boasts inits excellent energy resolution, aided by its small band gap energy of 0.7 eV and electron-holepair creation energy of 2.9 eV. Featuring higher material density and number of electron-hole pairscreated per MeV than Si detectors, it is the ideal material to perform γ-ray spectroscopy on stoppedbeams. The RISING setup at GSI [48, 88], using the same Euroball detectors, conducted the latestspectroscopy experiments on 100Sn and the nearby isotopes. The HPGe clusters were then movedto RIKEN in 2011 for exotic decay spectroscopy experiment campaigns.Charge collection waveforms were analyzed online by the digital gamma finder (DGF; XiaDGF-4C) to determine the energy of the γ rays. Only 47 out of 84 mounted HPGe detectors werefully functional during the experiment, due to an unintended interruption of the periodic liquidnitrogen fills. As the detectors warmed up under the high-voltage bias, their leakage currents roseto sufficiently high levels such that many channels of the front-end electronics were permanentlydamaged. EURICA’s γ-ray detection efficiency loss negated some of the gains in statistics providedby the intense RI beam.22Figure 2.4: Left: front geometry of crystals in a Euroball cluster detector. Right: photograph ofthe first hexagonal tapered Ge detector. These figures were taken from Ref. [6].Time measurementIn order to determine half-lives of excited states decaying by γ-ray emission, the γ-ray times weremeasured in two separate streams within EURICA: one from the DGF, which also handled energymeasurement as mentioned above, and another from the TDC. The DGF time was provided fromthe looping clock with a 40-MHz frequency, leading to an intrinsic time step of 25 ns. The TDCswere tuned such that calibration slopes were less than 1 ns per channel, leading to a better timeresolution. However, the timing filter amplifier for TDC data performed poorly at low energiescompared to the DGF. Consequently, the detection efficiency decreased at low γ-ray energies if onerequested for meaningful TDC data in the offline analysis. Hence the two streams provided comple-mentary options for low-energy γ rays: high efficiency with poor timing resolution (DGF), or lowefficiency with good timing resolution (TDC). At sufficiently high energies (> 700 keV), however,no such compromise was needed as all the measured γ rays contained good TDC information. Theefficiency discrepancy between the two timing data streams as a function of γ-ray energy is shownin Fig. 3.7.2.2.3 Data acquisition triggering schemeSpecific trigger conditions, logic conditions and gates were necessary for the data acquisition (DAQ)system to collect relevant data from multiple detector systems. The connections are summarizedin a block diagram shown in Fig. 2.5. The master trigger was provided by the OR logic signal ofthe plastic scintillator at F11 (for incoming ion implantation) and any one of the DSSSDs (decayevent). The master trigger opened the gates for energy and time measurements, and it providedreference start times for the TDC modules of the DSSSD channels and the HPGe channels. The23TDCs recorded the time difference ∆T = Tstop − Tstart.BigRIPS HPGe DSSSD TDC TDC LUPO LUPO Master Trigger F11 plastic ADC SSSSD DGF WAS3ABi EURICA Clock LUPO E, Tstop Tstart OR Tstop Tstart Tstop Gate Gate Tstart E E Figure 2.5: Simplified block diagram of the DAQ systems for BigRIPS, WAS3ABi, and EURICA.A color scheme separates the detectors from other electronics. For simplicity, the DAQ electronicsfor other detectors of BigRIPS are not shown here. Each stream’s event timestamp was recordedby its own Logic Unit for Programmable Operation (LUPO), to be used in offline data merging.Logic conditions and physical quantities are labeled around the arrows. The clock to start the DGFtime measurement in EURICA operated at 40 MHz for a 25-ns time step. Other electronics, suchas delay modules, shaping amplifiers and discriminators are omitted in this diagram. For moredetailed block diagrams, the reader is referred to Figs. 2.10 and 2.14 of Ref. [7].In order to merge data from the three streams, each system recorded timestamps generated byits Logic Unit for Programmable Operation (LUPO) [89]. A sufficient time precision in steps of 10ns was achieved from the 100-MHz clocks inside the LUPOs. Barring clock resets, the timestampsgenerated by a physics event would have a constant difference between the streams. The results ofdata merging from the different detector streams are presented in Section 3.1.242.3 Summary of the experimentAn overview of the experiment status in terms of the primary beam rate and data collection ratesis presented below.2.3.1 Primary beam intensityThe average beam current for 124Xe was 29.6 particles nano-Ampere (pnA) during 203.2 hours ofbeam time, equivalent to 1.85× 1011 particles per second. The peak intensity of 38 pnA, a recordfor 124Xe beam, was achieved in the later part of the experiment. The average intensity exceededthe listed value of 20 pnA by approximately 50%. Approximately at 25% through the total beamtime, the SRC stopped operating due to cooling issues. After about 18 hours, the 124Xe beam wasrestored with an increased intensity.2.3.2 Data collection ratesDuring the experiment, the slit settings through BigRIPS and the ZeroDegree spectrometer wereadjusted to control the DAQ rate and the distribution of different isotopes for investigation. Anintense cocktail beam of radioactive nuclei resulted in a high implantation rate, which increasedthe rate of random background decay correlations. The rate of implantation and decay data as afunction of beam time during the experiment is shown in Fig. 2.6. During the first 75 hours, effortswere made to maximize the 100Sn transmission rate. During the later stages of the experiment,transmission of other nuclei (search for new and rare N < Z isotopes and N = Z nuclei, forinstance) were prioritized over the most abundantly produced N = 50 isotopes. From Fig. 2.6, onecould estimate the average implantation and decay rate per hour for different periods. The peakrates for implantation and decay data were 53 Hz and 97 Hz around Tbeam ∼ 20 hours respectively,and approximately 10 Hz and 20 Hz for later times. Naturally, isotopes with longer half-lives hadlower signal-to-background ratios in their decay correlations.25Figure 2.6: Data collection rates as a function of beam time over the course of the experiment. Thestoppage of data acquisition starting at around 55 hours occurred during the SRC troubleshootingperiod. The fluctuation of the rates were caused by the variation in the primary beam rate, anddifferent acceptance and transmission settings of BigRIPS and the ZeroDegree spectrometer.26Chapter 3Data analysisIn this chapter, analysis methods of the experimental data are presented. Event reconstruction,detector characterization and calibration are followed by the methods to obtain experimental half-lives, decay branching ratios, new transitions, and Qβ values using Geant4 simulations.3.1 Merging data from different detector systemsWith three independent data acquisition systems but without a global triggering system, the datafrom each of BigRIPS, WAS3ABi, and EURICA detectors had to be merged in the offline analysis.This was carried out by matching event timestamps that were generated from a global 100-MHzclock signal (each clock tick was thus generated in 10-ns steps) that was recorded by each datastream’s LUPO. As shown in Fig. 3.1, a proper merging of the data was achieved in a 100-200 nswindow for all three systems. The time discrepancy between the systems was caused by the cableswith different lengths, corresponding to unique signal delay times.Figure 3.1: Event timestamp difference distribution for three pairs of detector/event type combi-nations. The events shown in this histogram could be properly merged.273.2 Detector calibrationsThe following sections highlight the methods and results of offline calibrations for WAS3ABi andEURICA data.3.2.1 EURICA - energy, time and efficiency calibrationThe characterization and calibration of HPGe detectors of EURICA for energy, time, and efficiencyare described in the following sections.Energy calibrationStandard calibration sources such as 60Co and 152Eu were used to perform an energy calibrationof the HPGe detectors. The energies of β-delayed γ rays from the sources, ranging from 121 keVto 1400 keV, were used as calibration points. For each of the 47 HPGe channels, a first-orderpolynomial fit was performed to convert the DGF channel values into energies. The linearity of theslope was verified at 4207 keV, which was the γ-ray energy emitted from the known (12+) isomericstate in 98Cd [90]. The centroids of energy peaks of known isomeric transitions from segmenteddata sets were used to check for possible drifts in the calibration parameters over the course ofthe experiment. The results showed gain drifts less than 1% and offset shifts less than 0.2 keV forall 47 channels. The valid energy range of EURICA for this experiment was Emin = 35 keV andEmax = 6200 keV.Time calibrationThe time calibration of EURICA involved energy-dependent walk corrections (including WAS3ABitrigger walk for β-delayed γ rays) and a TDC channel-to-ns conversion.Walk and time zero correction Both the DGF and the TDC modules of EURICA exhibiteda time walk as a function of γ-ray energy. This phenomenon was caused by the energy-dependentsignal rise time in the electronics, combined with a leading-edge threshold trigger. As seen inFig. 3.2 for a TDC channel, low-energy γ rays resulted in extra delays of their time signals. Thiswas corrected by plotting the time versus energy distribution of the prompt γ rays and fitting thetime profile in energy slices. Then the raw TDC channel values were subtracted by the fit functionto set the zero times for the γ rays. The same method was applied to the DGF time data.Analogous to EURICA, WAS3ABi exhibited time walk as a function of energy deposited in eachstrip. Since EURICA also triggered on β-decay events triggered in WAS3ABi , the walk effect inWAS3ABi was carried over to the EURICA timing data. This effect is shown in Fig. 3.3, where theγ-ray times are systematically shifted in relation to the maximum energy deposited in any DSSSDstrip for a β event. A phenomenological function of the form A+B log(ESimax) +C log2(ESimax) wasapplied to correct both the walk and the zero offset for γ-ray times in β decay events.28Figure 3.2: TDC distribution as a function of prompt γ-ray energies for one EURICA channel. Afit of the centroids of the energy slices is shown as a black line, the function of which was used tocorrect for γ-ray energy-dependent time walk.Each individual DSSSD strip had its unique cable and trigger delays which affected the definitionof the start time. Beta particles in general deposited energy in multiple strips without clear hintsto the original position of the decay. Thus correcting for time zero on an event-by-event basisfor β decays was impossible. However, the offsets could be estimated by examining γ-ray timedistributions as a function of the strip number for single-strip β events. Fig. 3.4 shows systematicoffsets up to 20 ns caused by several X-side strips in the middle DSSSD. Consequently, all half-lifemeasurements of γ-decaying isomers populated by β decays were carried out with a delayed timegate.TDC channel-to-ns calibration After walk correction was performed for both the TDC andthe DGF modules, each crystal had its TDC channel plotted against the DGF time of the γ raysemitted from isomeric transitions in 96Ag, which was produced abundantly with the half-life of theisomer being 1.56(3) µs [65]. This half-life was long enough to generate enough statistics up to thefull range of 12 µs. First-order polynomial fits were applied in the range -500 to 11500 ns, and theresulting slopes were approximately 0.78 ns/ch for all channels.EURICA’s time resolution For half-life measurements of γ-decaying isomers, including thosewith limited statistics for maximum likelihood (MLH) analysis, a detailed characterization of EU-RICA’s timing modules was necessary. As already mentioned, the TDC modules provided a bettertiming resolution than the DGF modules at the cost of efficiency at low energies (see Fig. 3.7). In29Figure 3.3: γ-ray TDC time as a function of maximum DSSSD energy in β events. If the event’smaximum energy deposit in a DSSSD was low, the start trigger time in WAS3ABi became delayed;hence the difference between the WAS3ABi time and the γ-ray time was reduced. A fit function(black line) was used to correct the time walk for β-delayed γ rays.the half-life analysis, the tradeoff between the statistics and the time resolution was considered forindividual γ-decaying isomers. In addition, β-delayed γ rays had a greater time jitter than thosefrom ion implantation due to the additional jitter in WAS3ABi trigger time, as well as systematictime zero shifts among the different strips. These are shown in Fig. 3.5. The zero offset correc-tion was more accurate for the TDC than the DGF modules. For the DGF time data, the walkcorrection residuals were correlated with the γ-ray energy due to the limitations of the correctionfunction.Efficiency calibrationKnowing the energy-dependent γ-ray detection efficiency is crucial for decay spectroscopy experi-ments, for experimental quantities such as branching ratios and isomeric ratios depend on the inten-sities of the transitions. These are necessary for calculating electromagnetic transition strengths,and β-decay branching ratios, which provide important insight into the structure of excited statesand transition matrix elements. First, a method to improve the γ-ray detection efficiency knownas γ-ray addback is described below.Addback γ-rays interact with matter in one of three ways: photoabsorption, Compton scattering,or pair production. In a photoabsorption event, all of the γ-ray energy is deposited at a singleinteraction point. On the other hand, a γ ray that undergoes Compton scattering will either be30Figure 3.4: γ-ray TDC time distribution of β events with energy deposits in single DSSSD strips.Depending on the position of the β decay, systematic offsets of up to 20 ns are visible in the X-sidestrips. No such dependence is seen in the Y-side strips, except for a small shift at the last strip.fully absorbed with multiple interaction points, or escape the detector material with a fraction of itsoriginal energy. Pair production is possible only for Eγ > 2me = 1022 keV, and the γ ray produceselectron-positron pairs which share a part of the γ-ray energy. The positron will often deposit thefull kinetic energy in the detector before annihilating with an electron, producing two 511-keV γrays which undergo further photoabsorption or Compton scattering processes, unless they escape.The addback scheme attempts to reconstruct the full γ-ray energy that may have been frag-mented due to inter-crystal Compton scattering or pair production. In a given cluster, the energiesin adjacent crystals were added back if the time difference between the γ rays was less than 100 nsin DGF time. The energy-dependent walk correction described in Section 3.2.1 was applied beforeapplying the γ-ray addback scheme. It is possible that energies of multiple distinct γ rays thatdecay in a cascade be added back to a spurious summed energy; then the intensity of the energypeak under suspicion must compared against the non-addback spectrum.Efficiency data and fit While standard techniques of efficiency calibration using well-known ra-diation sources 60Co and 152Eu exist, the radiation geometry from such sources was quite differentthan the experimental radiation geometry governed by ion implantation distributions. Thus theabsolute efficiency of EURICA as a function of γ-ray energy was determined from the γγ coinci-dences of known isomeric transitions from 94,96Pd, 96Ag, and 98Cd obtained in the experiment data.31Figure 3.5: Left: mean centroid positions of prompt γ ray times as a function of energy followingion implantation events, after time walk correction. For β-delayed γ rays, the centroids of theprompt γ rays are poorly defined due to the strip-dependent time offsets, and are not reportedhere. Right: time resolution as a function of γ-ray energy in EURICA for the 4 types of events.32Figure 3.6: Black histogram: γ-ray spectrum of high-energy isomeric transitions in 98Cd withoutaddback. Red histogram: the same spectrum produced with addback. An improvement in countsat 4156 and 4207 keV is evident with the addback method that recovers the full energy of Compton-scattered γ rays, an example event of which is shown in the inset.Given two γ rays γ1 and γ2 that depopulate an excited state in a cascade, the absolute efficiency1 at the energy of γ1 can be determined as:1 =n12n2(1 + α1I1), (3.1)where n12 is the number of γ1-γ2 coincidence counts, and n2 is the number of γ2 singles counts.ICEs and branching into multiple states are taken into account by the IC coefficient α1 and therelative intensity I1. The subscripts 1 and 2 in Eq. (3.1) could be reversed to obtain 2.The efficiencies at each γ-ray energy are plotted in Fig. 3.7 with different fit functions. Empiricalfifth-order polynomials in ln(Eγ) were used:ln() = A+B ln(Eγ) + C[ln(Eγ)]2 +D[ln(Eγ)]3 + E[ln(Eγ)]4 + F [ln(Eγ)]5, (3.2)and projecting back the fit constants A to F in linear scales generated the fit curves as shownin Fig. 3.7. Even though the efficiency for γ rays with high-resolution TDC timing informationdecreased significantly at low energies due to higher energy thresholds, the improvement in thetime resolution had a higher merit in certain scenarios.33Figure 3.7: Absolute detection efficiency of EURICA as a function of γ-ray energy in four differentmodes. The addback scheme enhances efficiency at higher energies, but below 300 keV some lossin efficiency occurs due to false addback. High energy thresholds for the TDC modules, whichprovided better timing resolutions than the DGF modules, caused lower efficiencies at Eγ < 500keV.343.2.2 WAS3ABi - energy and time calibrationThe sections below highlight the methods for the energy calibration in all DSSSD and SSSSD strips,as well as the TDC calibration for DSSSD X-side strips to be used for ion implantation events.Energy calibrationThe energy calibration of the DSSSDs and the SSSSDs of WAS3ABi was done using γ rays froma 60Co source. For γ rays that Compton scattered once in the Si strips and deposited the rest ofthe energy in a HPGe detector of EURICA, the energy matrix Eγ(HPGe) vs Eγ(Si) (see Fig. 3.8)would show two diagonal bands that correspond to the total γ-ray energies: 1173 keV and 1332keV. Calibration constants from first-degree polynomial fits would then be algebraically solved toconvert the ADC channel values into physical energies.After calibrating the energies, minimum energy thresholds were applied to reject the low-energynoise. Emin of 100 keV was required for the DSSSD strips with a few exceptions: strip 5 (120 keV)and 49 (150 keV) in DSSSD A, X-side. For the SSSSDs, the threshold was 200 keV for all strips;their larger widths required higher thresholds, compared to the DSSSD strips.For the Y-side strips of the DSSSDs, high-energy calibrations in the 10-20 MeV range wasrequired for accurate determination of ion implantation position. This was carried out by plottingan E-versus-E matrix for adjacent Y-side strips and fitting a line which bisected the distributionsat the highest energies.Time calibrationAs mentioned in Section 2.2.1, only the DSSSD X-side strip channels recorded useful TDC informa-tion. Similar to EURICA, WAS3ABi time data was subject to an energy-dependent walk. However,the resolution of TDC time for WAS3ABi was too poor to merit proper walk correction. However,during ion implantation events, the time walk in WAS3ABi was negligible due to immense amountsof energy being deposited in each strip. The calibration of interest in this case was the time-zerooffset for ion implantation events.On the X-side of the DSSSDs, an incoming ion deposited energies beyond the ADC saturationthresholds (about 6000 keV) across multiple strips, rendering position determination via energymeasurements imprecise. On the other hand, the TDC time difference between the F11 triggerand a strip on the X-side allowed the ion implantation position to be deduced unambiguously(see Fig. 3.10), using the fact that signals with higher amplitudes produce waveforms with fasterleading edges. The time-zero calibration of the WAS3ABi TDCs involved fitting the minimum timedistribution of each strip’s TDC spectrum and centering the peak to zero.35Figure 3.8: γ-ray energies detected in EURICA versus the ADC channel values of one of the DSSSDstrips of WAS3ABi from a 60Co source. Two diagonal bands are visible, whose energy sums shouldbe 1173 and 1332 keV. Silicon strip energy calibration constants were obtained by fitting the energyprofiles selected along the diagonal bands.363.3 WAS3ABi event classificationWAS3ABi acts as both an implantation zone for heavy ions and a calorimeter for β particles andprotons. These different types of events were separated by analyzing the energy hit pattern in boththe DSSSDs and the SSSSDs. Low-mass charged particles constituting background events couldalso be rejected by applying separate rejection criteria.3.3.1 Ion implantationIon implantation events were accompanied by data from both the BigRIPS and the WAS3ABi datastreams. The sections below describe the analyses performed to determine the implanted ion’scharge and mass, as well as its position in the DSSSD for decay correlation.Isotope identification cutSelection cuts of the PID data from BigRIPS were made by examining the profiles of Z and A/qdistributions. For example, Fig. 3.9 shows the Z projection of a subset of the MUSIC data, cut onA/q = 2 events such that the identified isotopes were N = Z nuclei. For each isotope, projectioncuts were performed on both the A/q ratio and the Z-distribution profile to optimize the PID cutparameters. Contamination due to distribution overlaps from neighboring species was less than 1%for most isotopes. Gain and offset drifts in the PID data, due to slit setting changes, were observed.Hence the full dataset was divided into multiple subsets before applying the PID cuts.Position determinationThe implantation position was determined primarily on the basis of energy deposition in the DSSSD(see Fig. 3.10 as an example event). On the X-side, the saturation of the ADC modules meantimprecise position determination using the strip energies. Thus the strip with the minimum TDCtime was designated as the implantation strip. On the Y-side, the ADC modules were not saturatedby implantation events, and the strip with the highest energy deposit was chosen. The last DSSSDstack with ∆E > 10 MeV in at least one of the Y-side strips was interpreted as the depth of theion implantation.One could then plot the implantation position distribution for each isotope. For instance, acomparison between the exotic 95Cd ions and the abundantly produced 99Cd ions, illustrating cleardifferences in the centroid positions in the XY plane and implantation depth, is shown in Fig. 3.11.As evident from the XY position distribution plots, there were losses due to the finite size of theDSSSDs. The percentage loss varied from 7 to 15% for more abundantly produced nuclei, dependingon the isotope and the different separator settings which affected the rare isotope beam optics. Forall isotopes, the majority of the ions was implanted in the middle DSSSD.37Figure 3.9: Projection of Z for A/q = 2 for a subset of BigRIPS data, leading to the identificationof N = Z nuclei.3.3.2 β decay and proton emissionExcluding EC, proton-rich nuclei undergoing β decay and proton emission result in charged particlesdepositing energy in WAS3ABi. The sections below compare and describe the general characteris-tics of each type of decay, leading to a separation technique between the protons and positrons.Characteristics of β eventsIt was shown from simulations that β particles in the energy range 100 keV to 10 MeV producetracks with a wide range of scattering angles. The probability that a β particle travels in a straighttrajectory without gaps in strips was rather low, and it could scatter back and forth betweenthe stacks of both the DSSSD and the SSSSD. Initial attempts to build tracking algorithms wereabandoned to remove the possibility of systematic underestimation of the full β energy.Signature of proton emissionAs noted in Section 1.3.3, proton emission is possible from decays of several of the nuclei presentedin this thesis. In contrast to β particles, a proton usually deposits all of its kinetic energy in one Sipixel (one strip each in X and Y) due to its large mass and small β = v/c, leading to large 〈dE/dx〉in Eq. (2.3). This property was used to distinguish protons from β particles (see Fig. 3.12). Aminimum threshold of 1500 keV deposited in a pixel was the selection criterion for proton events.38Figure 3.10: Left: TDC values for a DSSSD’s X-side strips during an implantation event. Theminimum value is found at strip 33. Right: energies of the Y-side strips of the same DSSSD. Thestrip with the maximum value is 28, leading to the implantation position coordinates (33, 28) forthis event.39Figure 3.11: Implantation position and depth distributions of 95Cd (top) and 99Cd (bottom). Onlythe implantations into the middle DSSSD are shown. The differences in the distributions, causedby different A/q ratios and kinematics, are clearly visible.40Figure 3.12: Single-pixel energy spectrum of decay events following 97Cd implantation. Protonevents could be classified with E > 1500 keV unambiguously from β particles, whose ∆E per stripwas usually far less.Fig. 3.14 shows the detection efficiency of simulated protons as a function of the input protonenergy and the depth from the surface of the middle DSSSD. It is counterintuitive at first to seea valley in the detection efficiency profile as a function of the emission depth, but the explanationis the following: an escaping proton near the surface of the middle DSSSD deposits nearly all ofits remaining energy in the neighboring DSSSD, such that the energy deposited in the surroundingDSSSD can surpass the 1500-keV threshold for the proton signature. However, if the proton isemitted from a deeper depth in the middle DSSSD and escapes to the neighboring DSSSD, thenthe proton’s energy will be divided among the two DSSSDs so that neither of them may detectenergy deposits exceeding the 1500-keV threshold. This effect vanishes for proton energies greaterthan 2800 keV. The protons emitted in this isotopic region have energies between 2 and 4 MeV,and the weighted detection efficiency in this energy range is 97% for ions being implanted near thesurface (where ∆z < 0.05 mm from the surface of the DSSSD). The rate of such events is a feworders of magnitude lower than the deep implantation events; thus the proton detection efficiencywas assumed to be 100%.3.3.3 Background rejectionLight particles (mostly deuterons with A/q = 2) were a major source of background events inWAS3ABi. Such particles were ejected from the hot fragments at the Be target, traveling all theway through BigRIPS and the ZeroDegree spectrometer before penetrating the silicon detectorstacks. These events are characterized by a straight track through WAS3ABi with a fairly constant41Figure 3.13: Implantation depth distributions of several abundantly produced isotopes fromLISE++ calculations.0.550.60.650.70.750.80.850.90.951z-depth from surface of DSSSD (mm)0 0.01 0.02 0.03 0.04 0.05Proton energy (keV)1500200025003000Figure 3.14: Proton detection efficiency as a function of proton energy and implantation depthfrom the surface of a DSSSD as simulated in Geant4.42energy deposit between 600 to 1400 keV per strip. These were rejected by cutting on the number ofSSSSD stacks with energy deposits in the aforementioned energy range. Other background events,such as pileup implantation events, were removed from analysis using appropriate high-energy stripthreshold cuts.3.4 Implantation-decay correlationOnce an unstable isotope was implanted in a detector, it would undergo decays resulting in β and/orproton emission at the implantation position. Since the decay time is governed by the exponentialdecay probability density function (PDF), a decay event has to be correlated to an isotope in theoffline analysis with position and time gates. The text below describes the implantation-decaycorrelation scheme.3.4.1 Position correlation schemeIn spatial correlation, any β or proton event with an energy deposit above the minimum-energythreshold was correlated with the implanted isotope, if the decay event left energy signaturesinside a cross-shaped window in the X- and Y-directions centered around the implantation pixel (a3× 3 zone without the corners). The Z-direction correlation was limited to the same DSSSD. Theextensions in the XY directions was to accommodate certain events in which a β particle may havedeposited an energy below 100 keV in the starting pixel. On the other hand, decays accompaniedby proton emission yielded a unique position determination due to its high and complete energydeposit in a single pixel. Hence βp and proton events were correlated more cleanly.3.4.2 Correlation time windowThe correlation time window was adjusted according to the implanted isotope: from -5 s to 10 timesthe isotope’s literature half-life, up to a maximum of 20 s. Correlations with negative times wereevents that had deposited energy around the implantation zone before the isotope of interest wasimplanted, and they were used to estimate the random background correlations. The upper limit onthe time window was required to reduce computational time and remove from consideration decaysof long-lived species which are better known from literature and overwhelmed by the backgroundcorrelations. There was no limit to the number of decay correlations per isotope within the timewindow, for introducing a cutoff would introduce a bias for shorter half-lives. The significance ofthe bias would depend on both the random decay correlation rate and the actual half-life of theisotope.3.5 Techniques for experimental observablesThis section is devoted to the description of analysis strategies for processed experimental quantities,such as half-lives of isotopes/isomers and β-decay endpoint energies.433.5.1 Half-life associated with particle emissionThe nuclei of interest decaying via β+/EC, βp or direct proton emissions had half-lives on theorder of 10 ms to 10 s. The PDF describing this process is a simple exponential decay function:f(λ1, t) = λe−λt =ln 2T1/2(12)t/T1/2(3.3)However, the decay products in this experiment were unstable, and their subsequent decaycontribution to the time spectrum must be taken into account. Fig. 1.2 captures many possibledecay processes for an isotope of interest. Isomeric states are not included in the figure, which addmore contributions to the initially simple PDF. Two methods were used to measure the half-livesof nuclei and their isomers.Comprehensive fit without γ-ray gateThe first method is a fit with a comprehensive probability density function in the form of theBateman equation [91], which includes many parameters of the descendant isotopes’ decays. Thismethod requires an accurate and precise parametrization on all of the half-lives and decay branchingratios (β+, EC, βp, 1p, 2p) of generations of nuclei following the parent decay. It is crucial to notethat the correlation efficiency varies with each decay branch; EC events cannot be recorded withWAS3ABi, but decays accompanying proton emission can be assumed to be correlated 100% ofthe time. The β-decay correlation efficiency is lower than 100% due to a non-zero probability ofpositrons depositing energies below 100 keV in the pixels of the spatial correlation window, belowthe minimum energy threshold. The cutoff on the number of generations to be considered dependson the fit range, and the ratio between the parent isotope’s expected half-life and the descendantnuclei’s known half-life; the PDF of the descendant nuclei with significantly longer half-lives thanthe correlation time range and the half-life of the ancestors could be estimated as a constantbackground.The β decay process populates the daughter nucleus, while at the same time the unstabledaughter nucleus decays with a rate λ2. If the parent decay has additional branches (βp, 1p, or 2p),the daughter nuclei will be different with individual decay rates λβp2 , λ1p2 , and λ2p2 . Some instancesof the parent nucleus may be populated in its isomeric state with its own half-life. The EC branchdoes not contribute to the β-decay time distribution, but must be included in the normalizationcondition. ICEs from an excited state of the daughter nucleus may offset the losses from ECprocesses.With a finite time range to correlate implantation-decay events, the Bateman equation can betruncated to include only the components with T1/2 less than or comparable to the time range.As the amplitude of the PDF is inversely proportional to T1/2, contributions from isotopes andstates with significantly longer half-lives become negligible. In this region of nuclei, the decay ratedecreases by about an order of magnitude after each generation. Consequently, the granddaughter44decay component contributes to only 3% of the total β-decay counts, if the correlation time windowis 10 times the parent nucleus’ half-life.The probability density function in the case of a pure β+ decay has the form (constraining itto the daughter component)f(λ1, λ2, t) =λ1λ2λ2 − λ1 (e−λ1t − e−λ2t), (3.4)where λ2 is the decay rate of the daughter nucleus.Depending on the available statistics, the half-life was obtained either by χ2 minimization onbinned data, or the MLH analysis on unbinned data. The aim of the MLH method is to maximizethe log likelihood function ln[L(λ)] = ln[∏ni f(ti;λ)], where ti is the set of decay times of n eventsand λ is the decay rate. In the simplest case of a pure parent decay, this corresponds to:∂ ln[L(λ)]∂λ∣∣∣∣∣λ=λmax=∂∂λn∑iln(λe−λti) =n∑i1λ− ti = 0, (3.5)such that λmax =∑ni ti/n: the average value of the decay times. The uncertainty on this decayrate (and consequently the T1/2 value) is determined by locating λ< and λ> around the optimalλmax such that the log likelihood value increases by /2 from the minimum:ln[L(λ<)] = ln[L(λ>)] = ln[L(λmax)] + /2, (3.6)where the confidence level  = 1 is taken to mean 1σ uncertainties given by λ< and λ>. For adetailed description of the MLH method, the reader is referred to the thesis by C. B. Hinke [48]and citations therein.Fit of γ-ray gated time spectrumAs a second method, half-life determination using γ-ray gates takes advantage of the fact that aβ decay usually populates the daughter nucleus in an excited state, which then undergoes γ-rayemission. By fitting the β-decay time profile in coincidence with the known γ-ray transition energies,the half-life of the β-decaying state of interest can be obtained. In the case of low statistics, theγ-ray gated decay time distribution can be fitted by the normalized PDF fMLH :fMLH(λ, tmin < t < tmax) =λe−λt + C(t)∫ tmaxtmin(λe−λt + C(t))dt. (3.7)On the other hand, the decay time distribution with sufficient statistics can be fitted with a χ2method on binned data with an unnormalized PDF Fχ2 :Fχ2(λ, t) = Ne−λt + C. (3.8)45In both Eq. (3.7) and Eq. (3.8), the random background component is represented the parameterC (or C(t) for MLH). One should take caution to not gate on a transition whose energy peakcoincides with one of the descendants’ γ-ray energy, or from an isomeric state from the samenucleus with a different T1/2. For the MLH method, the inability to perform proper backgroundsubtraction with low statistics requires a parametrization of the random background time profile.This was done by gating on the side regions of the energy peak of interest and performing anempirical fit (usually an exponential with a constant background) - the fit function of which wouldthen be included in the overall MLH fit. The argument for a constant background in the χ2 fit isthe following: in this data set, half-lives obtained with low-statistics γ-ray gates are usually short-lived compared to those of abundant species. So only much longer-lived species will contribute tothe background, where a constant amplitude is a good approximation in a small time range fordecay correlations. On the other hand, caution is advised even with the background-subtractedχ2 method. Since the background subtraction is often not perfect, little variations in backgroundγ-ray gates may have a large effect on the background-subtracted time spectrum - especially in thecase of weak-intensity γ rays.3.5.2 β endpoint energy determinationThe β+ decay of an atomic nucleus is a three-body process, which results in an emission of apositron and an electron neutrino that share the total kinetic energy. In terms of the Lorentzfactor γ = Ek/mec2 +1 involving the positron’s kinetic energy Ek and the rest mass of the positronme = 511 keV/c2, the energy distribution function is:f(γ, γmax) ∝ γ√γ2 − 1(γmax − γ)2F (Z ′, γ), (3.9)where F (Z ′, γ) is the Fermi function. For non-relativistic β particles, an approximate form is used:F (Z ′, γ) ≈ 2piη1− e−2piη , η = ∓Z ′α√1− γ−2 for β±, (3.10)with the fine-structure constant α ≈ 1/137 and Z ′, the nuclear charge of the daughter nucleus. Theendpoint energy Qβ is the energy difference between the initial and the final states, and is used todetermine γmax.While this β decay energy distribution function is well known, the experimental energy spectrumis distorted by multiple factors: the minimum strip energy threshold cut, escape events (where theβ particle trajectory goes out of either the DSSSD or the SSSSD), Bremsstrahlung radiation, andin-flight annihilation of a positron and an electron. Many of these processes systematically shift theβ-decay energy distribution towards lower values. There is a possibility of a small positive shift inenergy due to ICEs following β decay, which has a large conversion coefficient for low-energy γ-raytransitions. To take these effects into account in determining the endpoint energy, the simulationsoftware Geant4 was used.46Geant4 simulationGeant4 [92], a simulation toolkit developed initially for high-energy physics, is now a multipurposesoftware with various interaction models and robust geometry. A geometry to model positroninteractions in the WAS3ABi setup had already been generated and checked for validity [93]. Adisplay of a few positron events in WAS3ABi is shown in Fig. 3.15.Figure 3.15: Geant4’s simulated event display of a few positrons in WAS3ABi. The XY detector,the 3 DSSSDs, and the 10 SSSSDs are visible. Positron tracks are drawn in blue, and 511-keVannihilation γ rays are the green lines. Large scattering angles of positrons inside WAS3ABi andescape events enforced a Qβ analysis using simulations.Aside from the details of the detector geometry, the main inputs to the simulation are: thedistribution of βs’ starting position in XY, as determined from the implantation position profile(see Fig. 3.11), and the β decay energy spectrum with a trial endpoint energy. The approach is tovary the trial endpoint energy and perform χ2 comparisons between the simulation output and theexperimental Qβ spectrum. For consistency, the output files from simulations were analyzed usingthe same conditions as with the experimental data. If the decay is suspected to populate multiplefinal states with comparable branching ratios and without a prospect of γ-ray gates to isolate asingle feeding, then multiple energy distributions with multiple endpoints are added. In that case,additional contributions to the endpoint energy spectrum must be constrained in both the energyand the branching ratios from prior knowledge (whether from literature or γ-ray gates). Fig. 3.16is an example of the Qβ determination of98Cd’s dominant decay to the 1691-keV level in 98Ag.47This Qβ value was corrected for internal conversion electron (ICE) energies originating from 61-keVM1 and 107-keV E2 transitions, the IC probabilities being 63% and 53% respectively. The sum ofthe expected energy contributions to the Qβ spectrum was 95 keV, which was subtracted from theraw Qβ value to yield Qβ(corrected) = 2735(30) keV. Then the QEC (ground-state to ground-stateenergy difference in a β decay) value, equal to the mass differences between the parent and theβ-decay daughter nucleus, was calculated by the following formula:QEC = ∆M(parent)−∆M(daughter) = Qβ + 2me + Ex, (3.11)where 2me and Ex is the excitation energy in the daughter nucleus. Combining Qβ = 2.735(30)MeV, 2me = 1.022 MeV and Ex = 1.691 MeV, The final QEC value for98Cd was 5.448(30) MeV -consistent with the literature value of 5.430(58) MeV [2].Energy (keV)0 1000 2000 3000Counts / 25 keV05001000 (keV)βQ2500 3000/ndf2 χ123 = 2830(30) keVβQ−107+61 keV Conv. eFigure 3.16: Qβ determination of98Cd’s most dominant GT-decay branch to a (1+) state in 98Agwith Geant4 simulation. The experimental energy spectrum (black) extracted with a 1176-keVγ-ray gate was compared with simulated spectra (red) at various trial energies. The χ2 evaluationrange is given by the arrow at the baseline, avoiding the energy range containing ICEs emittedduring EC. The inset shows the reduced χ2 results with a minimum at 2830(30) keV.3.5.3 Half-life associated with γ-ray emissionFor γ-decaying isomeric states, the γ rays with isomer half-lives on the order of 10 ns to 1 µs wereanalyzed by both χ2 and MLH fits, depending on the available statistics. In either case, the maincomponent of the fit function was an exponential decay function convoluted by a Gaussian, to48account for the non-negligible time jitter of the γ-ray detector and its electronics. The mean of theGaussian for the prompt time distribution was assumed to be zero after the time-walk correction.Then the PDF of the isomeric γ-ray decay time distribution is given by:f(t;σ, λ) =λ2eλ(λσ2−2t)/2erfc(λσ2 − t√2σ), (3.12)where erfc(x) is the complementary error function defined aserfc(x) = 1− erf(x) = 2√pi∫ ∞xe−t2dt, (3.13)and σ is the energy-dependent time jitter shown in Fig. 3.5. This PDF is commonly used infitting short half-lives of isomeric states from fast scintillator detectors such as cerium-doped LaBr3(see Fig. 5 in Ref. [94]). A large background of Bremsstrahlung radiation emitted during the ionimplantation was avoided by fitting only the γ-ray times with Tγ > 50 ns. Many isomers werepopulated directly during fragmentation, whose T1/2 could be obtained by simply fitting the gatedγ-ray time spectrum after implantation. If the isomeric state of interest had a parent state thatwas also isomeric with T1/2 comparable to the flight time through BigRIPS, the time differencespectrum between the feeding γ ray and the de-excitation γ ray was used in the analysis. Thiswould require γγ coincidence data.3.5.4 Isomeric ratiosAn isomeric ratio R is the percentage of radioactive isotopes populated in a long-lived excited state.This work follows the definition of an isomeric ratio as noted in Ref. [95] as the percentage of anisomeric state populated promptly during fragmentation, relative to the flight time through theseparator:R =YNimpFG, (3.14)where Y is the number of isomeric states deduced from WAS3ABi or EURICA data, Nimp is thenumber of implanted ions, F is the correction factor for isomeric decays during the flight time, andG is the correction factor for finite time correlation windows (β particles or γ rays). In the case ofan isomeric state fed by a higher-energy isomer in the same nucleus, the feeding contribution fromthe parent isomer was subtracted from Y . While isomeric ratios are dependent on many externalfactors (beam energy, beam/target nuclei, target thickness) before considering the structure ofthe radioactive nuclei, knowing them enables a prediction about the statistics required to performisomer decay spectroscopy in a neighboring region of nuclides.For β- and βp-decaying isomers, the half-lives are significantly longer than the ∼ 600 ns flighttime in BigRIPS and the ZeroDegree spectrometer. In this case the isomeric ratio is calculated basedon the number of decays observed divided by the number of implanted isotopes, combined withion-β correlation efficiency, WAS3ABi deadtime, and the finite correlation time window corrections.For γ-decaying isomers, the half-lives are comparable to the flight time through the separator and49must be taken into account when calculating the ratios. In addition, IC is blocked for bare nuclei(q = Z); the half-life of the isomeric state during flight is increased by the hindrance factor F :F =T ′1/2T1/2=∑i(1 + αi)bi, (3.15)where the summation includes all decay branches with individual IC coefficients and branchingratios. This is an additional correction required to determine R.3.5.5 Determination of deadtime lossThe deadtime loss corresponds to the percentage of unrecorded data due to multiple events occur-ring within a single data acquisition period. Given a Poisson process with a time-dependent eventfrequency λ (note Fig. 2.6), the loss was estimated as λτ , where τ is the WAS3ABi deadtime (600µs). It was important to include the low-energy events (E < 100 keV for all DSSSD strips) inthe deadtime calculation, which were removed from further analysis during the initial data sort.The deadtime loss correction was crucial for the βp branching ratio measurements, presented inSection 4.3.4.50Chapter 4Results and discussionThe results obtained from the experiment are presented in this chapter. Where appropriate, sup-plementary details of the analysis methods for individual nuclei are provided. Given the variety oftopics explored and the large number of nuclei investigated, the results were immediately followedby discussions based on comparisons to theoretical calculations.4.1 Isotope productionIsotopes which were successfully identified by the BigRIPS-ZeroDegree spectrometer are presentedin Fig. 4.1. Both Z and A/q shown in the figure are experimentally derived quantities, with slightdeviations in the centroids for each of the isotopes from theoretical values due to the inhomogeneousmagnetic field strengths of the dipole magnets and imperfect calibrations of the BigRIPS andZeroDegree spectrometer data. Nevertheless, the validity of this PID plot was confirmed withγ-ray transitions from previously known isomers.Figure 4.1: PID plot of the isotopes produced in this experiment. Events corresponding to 100Snare circled and labeled.51Multiple instances of N = Z − 2 isotopes were produced and identified for the first time: 90Pd,92Ag, 94Cd, and 96In [96]. A tentative identification of 98Sn and 86Ru is elaborated in Ref. [75]. Thelow counts for these most neutron-deficient isotopes are primarily because of low production crosssections. Due to insufficient statistics, N = Z − 2 nuclei are not discussed further in this thesis.On the other hand, not all of the identified nuclei could undergo decay spectroscopy (i.e. 87Ru)because they were deflected away from the WAS3ABi implantation zone at the last focal plane;the dispersion magnet settings were optimized for 100Sn and were not suited to accommodate 87Ruisotopes into the implantation area.4.1.1 Limits of proton stability: 89Rh, 93Ag, and 97InA more careful examination of the N = Z−1 nuclei statistics in Fig. 4.1 reveals a relative deficit ofcounts for 93Ag and 89Rh relative to the smooth trend expected for the production cross-sections.Half-life measurements, and proton separation energies were calculated based on a theory of protonemission [9] for these nuclei. A comprehensive analysis and discussion is provided in Ref. [96], whichconcludes that the proton dripline has been reached for Z = 45 and 47. Based on this analysis, thedripline does not appear to have been reached for Z = 49 as 97In did not show any loss in the PIDstatistics. Intriguing new decay spectroscopy results for 97In are discussed in Section 4.3.3.4.2 Isomeric γ-ray/internal conversion electron spectroscopyElement-preserving γ-ray and ICE transitions have been measured to determine their experimentalelectromagnetic transition strengths and isomeric ratios. A summary of the results is provided inSection 4.2.1. An overview of the isomeric ratios in comparison to theoretical predictions is givenin Section 4.2.2. Highlights of isomeric γ-ray spectroscopy results are presented and discussed inthe subsequent sections.4.2.1 Half-life and isomeric ratio measurementsA summary of individual half-life fit results obtained in this analysis is given in Fig. 4.2 andTable 4.1. The details of the γ-ray gates for each nucleus are provided in Appendix A. For someisomers, independent half-life measurements were not performed due to insufficient statistics, ortoo long half-lives compared to the 12-µs EURICA time window. Isomeric ratios were calculatedwith the method described in Section 3.5.4. In comparison to the literature values, all of themeasured half-lives were consistent within 2σ. Notable differences were found in 98Ag’s (3+) and98Cd’s (8+) isomers, and the T1/2 precision was significantly improved for98Cd’s (12+) isomer.New measurements involving several isomers are reported and discussed in the sections below.52s)µTime (2 4 6 8sµCounts / 0.40 110210)+Zr, (888sµ = 1.37(8) 1/2TTime (ns)2000 4000Counts / 400 ns01020 sµ = 0.93(17) 1/2T)+Tc, (492s)µTime (1 2 3 4sµCounts / 0.10 10210310)+Pd, (1494 = 495(7) ns1/2Ts)µTime (0.4 0.6 0.8 1 1.2sµCounts / 0.025 210310)+Ag, (398 = 161(8) ns1/2TTime (ns)1000 2000Counts / 200 ns0102030   = 415(67) ns1/2T)−Nb, (1190Time (ns)200 400 600Counts / 50 ns01020   = 89(18) ns1/2T)+Ru, (892s)µTime (5 10sµCounts / 0.05 10210310)+Pd, (896sµ = 1.79(1) 1/2Ts)µTime (0.5 1 1.5sµCounts / 0.05 110210)+Cd, (1298 = 214(6) ns1/2Ts)µTime (2 4 6sµCounts / 0.20 110210)+Mo, (890sµ = 1.11(6) 1/2Ts)µTime (5 10sµCounts / 0.40 10210)+Ru, (21/293sµ = 2.33(11) 1/2TTime (ns)200 400 600 800Counts / 100 ns01020  = 141(33) ns1/2T)+Ag, (1996Time (ns)200 400 600 800Counts / 50 ns02040 = 149(14) ns1/2T)+Cd, (898Time (ns)500 1000Counts / 100 ns01020  = 175(36) ns1/2T+Mo, 892Time (ns)500 1000Counts / 100 ns0102030  = 204(56) ns1/2T)−Pd, (1994s)µTime (5 10sµCounts / 0.20 10210310)+Ag, (1596sµ = 1.55(3) 1/2TTime (ns)50− 0 50 100Counts / 5 ns110210)+Cd, (698 = 11(1) ns1/2TFigure 4.2: Time distribution of isomeric γ-ray transitions and half-life fits. Half-lives obtainedwith ICE-γ coincidences in 95Ag and new γ-ray transitions in 96Cd are presented in Fig. 4.4 andFig. 4.7, respectively. For low-statistics data, unbinned MLH fits (data shown in linear scales witherror bars) were performed to determine T1/2. For sufficient statistics, χ2 fits were made on binnedhistograms in logarithmic Y-axis scales. See Section 4.2.1 for the half-life analysis of the (6+) isomerin 98Cd.53Table 4.1: γ-decaying isomers with measured half-lives. Isomeric decay information (excitationenergy Ex, isomeric state’s spin and parity Jpi, isomeric ratio R, transition multipolarity σ`, tran-sition energy Eγ , total IC coefficient α, and branching ratio b) is given. Literature T1/2 are shownfor comparisons, where the values are taken from the NuBASE2012 evaluation of nuclear properties[2]. Only α > 0.01 are tabulated.Nucleus Ex (keV) Jpi R (%) σ` Eγ (keV) α b (%) T1/2 (µs)This work Literature88Zr 2888 (8+) 69(5) E2 77 2.87(4) 1.37(8) 1.320(25)90Nb 1880 (11−) 11(3) E2 71 3.97(6) 27(6) 0.415(67) 0.472(13)M2 1067 73(6)91Nb 2034 (17/2−) 47(12) E2 50 13.9(2) 3.76(12)90Mo 2875 8+ 61(3) E2 63 6.30(9) 1.11(6) 1.12(5)92Mo 2760 8+ 48(10) E2 148 0.291(4) 0.175(36) 0.190(3)92Tc 270 (4+) 10(1) E2 56 9.8(1) 0.93(17) 1.03(7)93Tc 2185 (17/2−) 54(5) E1 0.31 8900 10.2(3)E2 40 33.9(6)M2/E3 75192Ru 2834 (8+) 32(33) E2 162 0.225(4) 0.089(18) 0.100(14)93Ru 2083 (21/2+) 53(2) E2 146 0.331(5) 2.33(11) 2.49(15)94Ru 2644 8+ 68(6) E2 146 0.331(5) 71(4)94Pd 7209 (19−) 7(3) E1 106 0.129(2) 80(4) 0.204(56) 0.197(22)E3 1651 20(4)4883 (14+) 30(1) E2 95 1.65(2) 0.495(7) 0.511(7)96Pd 2531 8+ 76(1) E2 106 1.11(2) 1.79(1) 1.81(1)95Ag 4859 (33/2+) 7.7(7) E3/M3 875 39(3)2531 (23/2+) 41(7) E3 428 0.031(1) 2.1(2) ms < 16 ms344 (1/2−) 2.9(8) E3 267 0.191(3) 90(18) ms < 500 ms96Ag 6952 (19+) 1.4(8) E2 98 1.55(2) 81(9) 0.141(33) 0.16(3)E4 4265 19(9)2647 (15+) 18.7(4) E2 44 27.9(4) 1.55(3) 1.54(3)2461 (13−) 12.4(13) M2/E3 486 ' 0.02 17(3) 100(10)E3 743 83(3)98Ag 168 (3+) 4.2(10) E2 107 1.13(2) 0.161(8) 0.22(2)96Cd (5605) (13−) 10(5) (E1) 0.199(26)98Cd 6635 (12+) 10(1) E2 50 18.9(3) 12(2) 0.214(6) 0.24(4)E4 4207 88(2)2428 (8+) 97(36) E2 147 0.377(6) 0.149(14) 0.189(19)2281 (6+) E2 198 0.133(2) 0.011(1) < 0.0254Discovery of 44-keV γ-ray transition in 96AgThe structure of 96Ag was investigated up to the core-excited (19+) isomer by Boutachkov et al.[65], who reported multiple γ-decaying isomeric states with a missing γ-ray energy emitted fromthe 2687-keV (15+) isomer due to its low transition energy. As shown in Fig. 4.3, this γ-ray energywas determined to be 43.7(2) keV with a half-life of 1.48(27) µs, consistent with the literature valueof 1.54(3) µs. Coincidence with the subsequent 667-keV γ ray was also confirmed, and α = 33(6)was deduced from the transition intensity analysis; this value agrees with the BrIcc [97] calculationof α(E2) = 27.9(4). An updated level scheme of 96Ag with this Eγ is shown in Fig. 4.24.Energy (keV)20 25 30 35 40 45 50Counts / 0.5 keV050100-ray singlesγ 15×Gated on 667 keV Time (ns)2000 4000 6000Counts / 500 ns050100sµ = 1.48(27) 1/2T43.7(2)Figure 4.3: γ-ray energy spectrum following 96Ag implantation. The black histogram correspondsto the time-delayed γ rays, and the red histogram is a scaled γγ-coincidence spectrum gated onthe 667-keV transition. The peak at 43.7(2) keV corresponds to the (15+) → (13+) E2 isomerictransition, where the inset shows the γ-ray time distribution of the low-energy peak with a consistenthalf-life for the (15+) state.Combining this new energy measurement with the T1/2 of the isomeric state resulted in B(E2) =3.0(1) W.u. This value is in excellent agreement with B(E2) = 3.0 calculated in the pg model spacewhile employing effective polarization charges of ep = 1.5e and en = 0.5e to account for non-zeropolarization of the core. The wavefunction of this isomer is a stretched pig−39/2νg−19/2 configuration asdiscussed in Ref. [65], the purity of which is supported by the agreement with the SM calculationswith valence space limited to the g9/2 orbital.55Half-life measurement of 98Cd’s (6+) stateThe 2281-keV (6+) state in 98Cd is a part of the pig−29/2 seniority scheme. Its half-life, previouslyconstrained as < 20 ns [90], was measured by fitting the γ-ray coincidence start-stop time differencespectra obtained from the 147-688 keV pair and the 147-1395 keV pair (see Fig. 4.28 for the levelscheme). The 147-198 keV γγ coincidence pair was not included in the analysis due to a highBremsstrahlung radiation background. The result is shown on the bottom right plot of Fig. 4.2,where the fit function reflects a time jitter of EURICA comparable to the measured half-life of11(1) ns. This measured half-life corresponds to B[E2; (6+) → (4+)] = 5.5(5) W.u. This valueis slightly greater than B(E2) = 3.63 W.u. calculated in the pg model space, and a much betteragreement is found with the value of 5.14 obtained in the gds model space [90] (see Section 1.1.2for details on the model space). Both calculations used polarization charges of +0.5e.Half-lives of long-lived isomeric states in 95Ag via ICE-γ spectroscopyThree γ-decaying spin-gap isomers in 95Ag have been reported with upper limits on half-lives upto 500 ms [98]. Given the fixed 12-µs time window for γ-ray spectroscopy data, these isomerictransitions were not observable with isomeric γ-ray data. However, internal conversion electronsfrom the two lower-energy states were detected with WAS3ABi. The detection of subsequent γ-ray transitions enabled half-life analyses of the isomers as if they were β-decaying states. Theresults are shown in Fig. 4.4. The half-lives of the isomers were 90(18) and 2.1(2) ms for the(1/2−) state and the (23/2+) state, respectively (see the insets of Fig. 4.4). The correspondingtransition strengths based on the suggested multipolarities are B[E3; (1/2−) → (7/2+)] = 0.22(4)W.u. and B[E3; (23/2+) → (17/2−)] = 0.37(3) W.u. These E3 transitions compare well toB(E3; 19− → 16+) = 0.28(3) W.u. in 94Pd and B(E3; 13− → 10+) = 0.18(2) W.u. in 96Ag. Theisomeric ratios for the states were calculated using the absolute γ-ray intensities and corrected forWAS3ABi deadtime loss and internal conversion coefficients.Moschner et al. [99] analyzed a separate dataset containing 95Ag isomers and assigned a 39(3)-µs half-life to the highest-energy isomeric state. Based on this half-life, they also suggest a changein the spin of the isomer to (33/2+) as well as the multipolarity to E3/M3. This half-life wouldbe too long for the EURICA time window and too short for WAS3ABi with its 600-µs deadtime.This value was adopted to calculate the (33/2+) state’s isomeric ratio.4.2.2 Isomeric ratios and the sharp cutoff modelThe isomeric ratios for γ-decaying isomers were combined with those from β-decaying isomerstabulated in Table 4.3 to be compared with theoretical predictions, similar to several works [95,100, 101] with fragmentation reactions performed at various primary beam energies and masses.Theoretical predictions of isomeric ratios involves the distribution of final angular momenta Jof the fragments. In addressing the statistical abrasion-ablation model [102] for fragmentation,56Energy (keV)0 200 400 600 800 1000 1200 1400Counts / 2 keV05010015020025030077164#428#823#511875936#1003#1117#1294Time (ms)0 5 10 15Counts / ms0100 (# gates) 1/2T= 2.1(2) msTime (ms)0 200 400Counts / 50 ms01020 (77 keV)1/2T = 90(18) msFigure 4.4: Black histogram: γ-ray energy spectrum with WAS3ABi total energy less than 500keV and in a time window between 0 and 20 ms after 95Ag implantation. Red histogram: γ-rayenergy spectrum gated on 267-keV ICE energies in WAS3ABi with a time window up to 500 ms.The insets show the half-lives of the two isomeric states obtained with the different γ-ray gates.Transitions at 875 and 1294 keV are γ rays emitted from the higher-spin isomer which are randomlycorrelated with ICE events.57Ref. [103] gives a simple analytical formula for the probability density function:PJ =2J + 12σ2fe−J(J+1)/2σ2f , (4.1)where σf is the spin-cutoff parameter of the final fragment:σ2f = 〈j2z 〉(Ap −Af )(νAp +Af )(ν + 1)2(Ap − 1) . (4.2)The first quantity 〈j2z 〉 - the average square of the angular momentum projection of a nucleon in thefragment - is calculated based on the semi-classical treatment of angular momentum distributionin the Woods-Saxon potential:〈j2z 〉 = 0.16A2/3p (1−23β), (4.3)where β is the quadrupole deformation parameter of the fragmented nucleus. Negligible deformationis expected for isotopes in the vicinity of a magic nucleus such as 100Sn, so β = 0 was assumed.Ap and Af are the mass numbers of the projectile (Ap = 124 for124Xe in this experiment) andthe fragment nucleus. The parameter ν is the mean number of evaporated nucleons per abrasionof one nucleon, which was varied among different works. In Refs. [95, 101] involving 750-MeV/u238U and 1-GeV/u 208Pb beams, ν = 2 was assumed; in Ref. [100] with a 60-MeV/u 92Mo beam,ν = 0.5 was chosen to calculate Rtheo. Since there is no quantitative determination of ν specific tothe 345-MeV 124Xe beam used in this experiment, it was left as a free parameter in this analysis.After having established the required relationships and ingredient quantities to calculate thedistribution of J , the sharp cutoff model was employed. For a given isomeric state with spin Jm,the sharp cutoff model assumes that J > Jm states populated after the fragmentation reactionpromptly undergo spin-decreasing γ-ray transitions until they are trapped at the isomer. Then thetheoretical isomeric ratio Rtheo is given byRtheo =∫ ∞JmPJdJ = e−Jm(Jm+1)/2σ2f . (4.4)The ratios Rexp/Rtheo are plotted as a function of J in Fig. 4.5 assuming ν = 0.5, which showsa relatively spin-independent agreement between the theoretical and the experimental ratios for allthe positive-parity isomers without N = 50 core excitation. The results were also independent ofthe decay mechanism (γ decay versus β decay), highlighting the consistency of the two very differentmethods described in Section 3.5.4 to determine experimental isomeric ratios. It was observed thatfor ν > 0.5, Rtheo was more severely underestimated with increasing spin; for ν < 0.5, Rexp/Rtheoapproached unity for J ≤ 16 but showed a systematic trend decreasing below 1 at higher spins.From Fig. 4.5 the limitations of the sharp cutoff model are exposed in three scenarios: negative-parity isomers, low-spin isomers with ∆J > 0, and N = 50 core-excited isomers. All of theseinvolve the details of the nuclear structure, and the explanations are provided below.Negative-parity isomers are wavefunctions with nucleon excitation from the p1/2 orbital; contri-58Spin (J)0 2 4 6 8 10 12 14 16 18 20 22theo/RexpR1−10110Positive parity isomersNegative parity isomers 4≤ mGround states where JN = 50 core-excited isomersFigure 4.5: Comparison of experimental isomeric ratios to the sharp cutoff model calculations.Isomeric ratios of both γ-decaying and β-decaying states presented in Table 4.1 and Table 4.3 arepresented.butions from the lower-energy f5/2 and p3/2 orbitals may also be present, but are generally small.Due to the large occupation number available for the positive-parity g9/2 orbital compared to thep1/2, the level densities at a given J are significantly higher for positive-parity states. Combinedwith the fact that parity-changing transitions are hindered, γ-ray branching ratios from higher-spinJ+ states to isomeric J− states must be limited. It is also crucial to note that both (13−) isomersfrom 96Ag and 96Cd have higher-spin positive parity isomers ((19+) and (15+) in 96Ag, and (16+)in 96Cd) which should introduce a spin cutoff in the integral of Eq. (4.4). In comparison, the exper-imental ratios for (17/2−) isomers in 91Nb and 93Tc are better reproduced by the model. For thesenuclei, N = 50 and the shell closure implies that the low-energy excitation scheme is solely drivenby protons in the p1/2 and the g9/2 orbitals. Without involving core excitations in the neutronorbitals, there are few positive-parity states with J > 17/2. The (19−) isomer in 94Pd is quite highin spin, where it is reasonable to expect little disparity between the number of possible nucleonconfigurations among positive and negative parity states; the only higher-spin, positive-parity stateavailable in 94Pd is (20+), which can only be constructed by maximally stretching both the protonand the neutron spin projections within the g9/2 orbital.Isomers with spin-increasing transitions violate the premise of the sharp cutoff model thatprompt transitions from higher-spin states will be funneled down to lower-spin isomers. This waspreviously observed based on the vastly different isomeric ratios of 90mMo and 92mTc populatedfrom fragmentation of a 58-MeV/u 112Sn primary beam [104]. A slight amendment to the model forthese isomers was to forgo the integral given by Eq. (4.4) and use the discrete probability density59function of Eq. (4.1) to calculate their Rtheo. The results of this modification on Jm ≤ 4 isomersare reflected in Fig. 4.5, which still have large deviations from experimental results. Thus thepopulation ratios of the ground states (Rg.s. = 1−∑iRi) were analyzed as if they were isomeric,and they were better reproduced by the model (blue triangles).Core excitation is another structure-driven effect that the sharp cutoff model fails to address.The ratios for 98Cd’s (12+) and 96Ag’s (19+) core-excited isomers were overestimated by approx-imately a factor of 3. In these configurations, one neutron is excited across the N = 50 shell gapby 4-5 MeV, leaving a hole in the g9/2 orbital (see Fig. 1.4(c)). This configuration requires anevaporation of a more deeply-bound g9/2 neutron at the cost of the shell gap energy while preserv-ing a neutron in one of the valence orbitals above N = 50, the rarity of which is reflected by thelow Rexp/Rtheo. This finding is relevant for the isomeric ratio estimation of the hypothetical (6+)core-excited isomer in 100Sn addressed in the next section.Discussion of the hypothetical 6+ isomer in 100SnNo delayed γ rays were found to be associated with 100Sn implantation events, in reference toSection 1.3.1. Thus upper limits on the half-life of the hypothetical 6+ isomeric state decaying byan E2 γ ray are proposed. The expression for the half-life upper limit is given by:T1/2 <ln(2)TFH[ln(NionR)− ln(NγH)] , (4.5)where TF is the flight time of100Sn ion through the separator,  is EURICA’s detection efficiency,Nion is the number of implanted100Sn isotopes, R is the isomeric ratio, Nγ is the number of availableγ-ray events for observation, and H = 1 + α is the hindrance factor for γ decays. The details ofR,Nγ and H are summarized below.From Fig. 4.5 and the sharp cutoff model, R(100mSn) can be estimated. Noting that the excitedstates of 100Sn must involve core excitations, the weighted average of Rexp/Rtheo from98Cd’s (12+)and 96Ag’s (19+) core-excited isomers was used to calculate the hypothetical R(6+) of 100mSn. Thisvalue was 25%. In order to reflect the crudeness of the sharp cutoff model and to visualize thedependence of T1/2 on R, two additional ratios of 12.5% and 50% were also assumed. From Poissonstatistics, 4 events could result in zero observations at the 2σ confidence limit; thus Nγ was setto 4. The origin of H comes from the physics of internal conversion. The IC branch, significantfor low-energy γ rays, is blocked for fully stripped isotopes during separation and identification.Therefore the apparent half-life of the γ-decaying isomer during 100Sn’s flight through the separatoris increased by the factor H. However, H appears twice in Eq. (4.5) because once the ions areimplanted in the Si detectors, the expected γ-ray counts is reduced by the factor H through theICE decay branch.Upper limits on T1/2 as a function of R and γ-ray energy are plotted on Fig. 4.6. In addition, aband corresponding to the theoretical B(E2) range of the isomeric transition is drawn, taken fromRefs. [49–51]. From the B(E2) band and the conservative assumption R = 12.5%, it is reasonable60-ray energy (keV)γ E2100 120 140 160 180 200 220 240 upper limit (ns)1/2T 210310Isomeric ratio = 12.5%Isomeric ratio = 25%Isomeric ratio = 50%) = 0.7 - 1.1 W.u.E2(BFigure 4.6: Upper limits on the half-life of a hypothetical 6+ isomer in 100Sn as a function ofγ-ray energy at different isomeric ratios. The dependence of the half-life based on the theoreticallypredicted B(E2) range of the isomeric transition is drawn as a red band.to suggest Eγ > 140 keV and T1/2 < 300 ns for the isomeric transition.4.2.3 Structure of 96Cd from isomeric γ-ray spectroscopyA total of 8 new and time-delayed γ rays were observed from 96Cd implantation events, as exhib-ited in Fig. 4.7. Individual half-lives and intensities (assuming negligible α) of these transitionswere consistent with one another within statistical uncertainties, and coincidence analysis resultssupported the suggestion of a γ-ray cascade from a single isomeric state. These results were con-firmed [105] by a separate experiment performed at RIKEN in 2012 by R. Wadsworth et al. Theirenergy spectrum showed hints of a 1562-keV γ ray, whose energy is a sum of 457- and 1105-keVγ rays; a parallel decay branch is suggested and supported by the comparatively low intensities ofthe 456/1105-keV γ rays given in Table 4.2.Table 4.2: Relative intensities of the γ rays in the isomeric decay of 96Cd, normalized to the mostintense 811-keV transition.Energy (keV) I (%) Energy (keV) I (%)307 67(+36−28) 811 100418 44(+28−21) 1025 66(+42−31)441 57(+33−25) 1041 76(+46−35)457 45(+29−21) 1105 58(+40−29)61Energy (keV)0 200 400 600 800 1000 1200Counts / 2 keV246810 307418441457811102510411105Energy (keV)0 200 400 600 800 1000 1200 (ns)1/2T100200300  = 199(26) ns1/2TFigure 4.7: Top: γ-ray energy spectrum following 96Cd implantation, where 50 < Tγ (ns) < 1200.Bottom: individual half-lives of the labeled transitions deduced with the MLH method. Thecombined half-life and its uncertainty are presented in both numerical values and the fit line witha 1σ band.62The discovery of the isomeric γ-ray transitions enables a quantitative investigation into theexcitation level scheme of the heaviest even-even N = Z nucleus, exceeding 92Pd [54]. However,due to limitations in statistics the structure 96Cd must be inferred by combining the experimentalinformation with the most plausible assumptions supported by SM predictions. Several theoreticallevel schemes generated with different model spaces are compared with the proposed experimentalscheme in Fig. 4.8. Good agreement was found between the proposed level scheme and the theoret-ical calculations, where the order of several transitions is ambiguous due to their similar energies.The experimental energies appear to be intermediate values of pg and gds results, which suggestsa noticeable wavefunction contribution from orbitals across the N = Z = 50 shell. Similar energyspacings of the first three excited states are found, consistent with the level scheme of 92Pd andquite different from the N = 50 seniority scheme. As noted in Ref. [8], the T = 0 pn interactionresponsible for the spin-gap (16+) isomer in this nucleus is manifested in low-spin states.Two possibilities arise for the precursor of the isomeric γ-ray cascade: a low-energy E2, ora parity-changing transition. From the number of γ rays observed and the calculated levels, a14+ → 12+ E2 transition emerges as a valid option. However, The energy gap is too smallcompared to any of the observed γ rays. The lowest-energy 307-keV γ ray with T1/2 = 199(26) nscorresponds to B(E2) = 0.04(1), which is 2-3 times smaller than the smallest B(E2) observed from93Ru’s (21/2+) isomer. In addition, the 14+ state would have a lesser likelihood of being isomericwith a prompt E2 decay branch to the spin-gap (16+) isomer. On the other hand, a parity-changingtransition could be E1,M2 or E3. Taking the three lowest-energy γ rays, the transition strengthsof each multipolarity are: B(E1) ∼ 10−8 W.u., B(M2) ∼ 0.1 W.u., and B(E3) ∼ 104 W.u. TheB(E3) value is unphysical, and the same can be said for B(M2) as experimental B(M2) < 10−4W.u. from negative-parity isomers in 90Nb, 93Tc, and 96Ag. In comparison to 94Pd’s (19−) isomerdecay with B(E1) = 2.5(5) × 10−7 W.u., the B(E1) value for 96Cd’s isomer is small but notunreasonable. Based on the number of γ rays observed, it is likely that Jpim = 12− or 13−.The disambiguation of the spin of the isomer must come from the details of the two wave-functions corresponding to the 12− and the 13− states. The main feature of the 13− state is theexcitation of a nucleon from the p1/2 orbital into the g9/2 orbital, and it contrasts with the 12+state which is entirely composed of unpaired nucleon holes in the g9/2 orbital. On the other hand,the 12− state is an admixture of both; it is reflected by the mean nucleon occupation number inthe p1/2 orbital of 1.5. An analogy is found between the (19−) isomer and the (18−) state in 94Pd.The small B(E1) value from the 96Cd’s isomer suggests little overlap between the initial and thefinal states mediated by the E1 operator. Therefore the spin of the isomer is more likely to be(13−). This argument is supported by the calculations in the fpg model space where the 12− stateis almost degenerate with the 12+ state. But the same reasoning cannot be applied in the pg modelspace. Another remaining issue is a possible E1 decay branch to the 14+ state which becomesavailable if Jpim = 13−. Accurate descriptions of the negative-parity states and their decay branchesare required.63Exp0 0+811 (2+ )1852 (4+ )2877 (6+ )3184 (8+ )4289 (9+ )4746 (10+ )5187 (12+ )5605 (12,13- )811104110253071105457(1562)441418pg0 0+906 2+1964 4+2955 6+3361 8+4595 9+4873 10+5298 16+5489 12+5576 14+5995 11+6071 12-6209 13-gds0 0+777 2+1784 4+2778 6+3239 8+4151 9+4646 10+4740 16+5040 12+5070 14+fpg0 0+901 2+1987 4+3021 6+3483 8+4704 9+4801 10+5021 16+5380 12+5385 14+5391 12-5916 13-Figure 4.8: Level schemes of 96Cd. The widths of the arrows on the proposed experimental levelscheme indicate relative γ-ray intensities. Negative-parity states are drawn in red, and the experi-mentally verified β-decaying (16+) isomer [8] is marked in blue for theoretical level schemes. Theacronyms of the calculated level schemes indicate model spaces listed in Table 1.1.644.3 Particle spectroscopy of β, βp, and proton decaysMany of the core objectives of this experiment were investigated with β-decay spectroscopy. Theresults are presented in two subsections: T1/2 measurements (Section 4.3.1), and Qβ measurements(Section 4.3.2). Due to the sheer length and breadth, β-delayed γ-ray spectroscopy results arepresented independently under (Section 4.4).4.3.1 Half-life measurementsHalf-life measurements were performed by fitting the β-decay time spectra with parent and daughterdecay components as described in Section 3.5.1. The experimental results are presented in Fig. 4.9and Table 4.3.Odd-odd N = Z nuclei: ground states and isomersThe half-life measurements of three odd-odd N = Z nuclei are presented: 90Rh, 94Ag and 98In. Inaddition to the superallowed Fermi decay of the (0+) ground states, all three of them have beenreported [61] to possess GT-decaying spin-gap isomers created by T = 0 attractive pn interactions.Due to the large difference between the half-lives, the decay time spectra were plotted and fittedin logarithmic time scales as prescribed in Ref. [106] to equalize effective binning for both decaychannels. The results are shown on the left side of Fig. 4.10.In each of the half-life fits, the constant background decay component becomes an exponentialin ln(t). The dark green dashed line corresponds to the β-decay daughter component. For 94Ag, the(21+) isomeric state was too scarcely populated in this experiment to merit an independent T1/2measurement. Thus this additional parent decay component (light green) was constructed withthe adoption of the literature half-life (0.40(4) s [2]). For 98In, significant βp branching of the (9+)isomeric state could not be ignored. While the βp decay channel did not directly contribute to thespectrum due to the maximum strip energy cut (E < 1500 keV), β decays from the βp daughter97Ag were included in the fit (light green dashed line). The obtained half-lives for both the fastsuperallowed Fermi component and the slow GT component were more precise than the previousliterature values by almost an order of magnitude.N = Z − 1 nucleiThe half-life measurements of the exotic N = Z−1 nuclei 91Pd, 95Cd, 97In, and 99Sn were performedfor the first time. MLH fits were used, and the decay curves and the T1/2 values are shown on theleft side of Fig. 4.11.Compared to the other N = Z− 1 isotopes, the initial fit result for 97In reported a significantlysmaller parent-decay amplitude; the number of decay events determined from the fit was only31(3)% of the number of 97In implantations, whereas the weighted average from 91Pd, 95Cd, and99Sn was 48(2)%. To resolve this mystery, it was postulated that a fraction of 97In isotopes wereproduced in a proton-emitting isomeric state with a half-life in the range of 3 to 140 µs. These events65Time (s)0 2 4 6 8 10Counts / 0.1 s11.522.53310×)+, (7/2βRh 91 = 1.59(10) s1/2TTime (s)0 2 4 6 8 10Counts / 0.1 s46310×)+, (9/2βPd 93 = 1.14(3) s1/2TTime (s)5 10 15Counts / 0.1 s34567310×)+, (9/2βAg 95 = 1.81(7) s1/2TTime (s)0 1 2 3 4 5Counts / 0.2 s204060 = 0.65(6) s1/2T)+, (16γβCd 96mTime (s)0 5 10 15 20Counts / 0.2 s200300400500 = 18.7(11) s1/2T)+, (5/2γβCd 99Time (s)0 5 10 15 20Counts / 0.2 s100200300 = 5.81(12) s1/2T)+, (6γβRh 92Time (s)0 5 10 15 20Counts / 0.1 s6.577.58310×+, 0βPd 94 = 8.5(2) s1/2TTime (s)0 5 10 15 20Counts / 0.1 s0.511.52310× = 4.42(4) s1/2T)+, (8γβAg 96Time (s)0 1 2 3 4 5Counts / 0.1 s50100 = 1.20(7) s1/2T)+, (9/2γβCd 97Time (s)0 5 10 15 20Counts / 0.1 s5678310×)+, (9/2βIn 99 = 3.35(11) s1/2TTime (s)0 5 10 15 20Counts / 0.2 s77.588.5310×)+, (9/2βRh 93 = 14.1(7) s1/2TTime (s)0 5 10 15 20Counts / 0.5 s200250300350 = 8.9(17) s1/2T)+, (9/2γβPd 95Time (s)0 5 10 15 20Counts / 0.1 s200400  = 5.6(6) s1/2T)+, (2γβAg 96mTime (s)0 5 10 15 20Counts / 0.1 s50100150 = 3.7(1) s1/2T)+, (25/2γβCd 97mTime (s)0 5 10 15 20Counts / 0.1 s1314151617310×)+, (6βIn 100 = 5.56(5) s1/2TTime (s)0 2 4 6 8Counts / 0.1 s200400600800+, 0βPd 92 = 1.17(4) s1/2TTime (s)0 5 10 15 20Counts / 0.2 s200400 = 12.9(4) s1/2T)+, (25/2γβPd 95mTime (s)0 1 2 3 4 5Counts / 0.2 s204060  = 1.08(9) s1/2T+, 0γβCd 96Time (s)0 5 10 15 20Counts / 0.05 s50100150 = 9.1(2) s1/2T+, 0γβCd 98Time (s)0 5 10 15 20Counts / 0.5 s11.21.41.61.8310×)+, (7/2βSn 101 = 2.09(18) s1/2TFigure 4.9: β-decay time distributions of isotopes and isomeric states. This list is not exhaustive.Spectra obtained with γ-ray gates are labeled as “βγ” beside isotope labels. χ2 and MLH fits wereperformed to obtain the half-lives.66Table 4.3: Properties of β-decaying isotopes and isomers (spin J , isomeric ratio R, T1/2 values,isomeric state energy Ex, and QEC values) with N ≥ Z ≥ 45 and T1/2 < 20 s obtained fromβ-decay data. Ex marked with & are NuShellX results, and those marked with # are extrapolatedpredictions taken from Ref. [2].Nucleus Jpi R (%) T1/2 (s) Ex (MeV) QEC (MeV)This work Literature This work Literature90Rh (0+) 0.0280(33) 0.015(7) 11.62(58) 12.9(4)90mRh (7+) 86(3) 0.52(2) 1.1(3) 0.500&91Rh (7/2+) 1.59(10) 1.60(15) 9.44(40)92Rh (6+) 5.81(12) 4.66(25) 11.302(5)92mRh (2+) 3.4(28) 2.54(44) 0.53(37) 0.05(10)#93Rh (9/2+) 14.1(7) 13.9(16) 8.205(3)92Pd 0+ 1.17(4) 1.1(3) 7.47(29) 7.93(50)93Pd (9/2+) 1.14(3) 1.15(5) 9.87(40)94Pd 0+ 8.5(2) 9.0(5) 6.807(5)95Pd (9/2+) 8.9(17) 7.5(5) 8.376(5)95mPd (21/2+) 77(11) 12.9(4) 13.3(3) 1.87594Ag (0+) 0.0277(15) 0.037(18) 12.45(47) 13.69(64)94mAg (7+) 77(3) 0.51(3) 0.55(6) 0.521&94nAg (21+) 2.4(3) 0.40(4) 6.35(50)#95Ag (9/2+) 1.81(7) 1.76(9) 10.36(40)96Ag (8+) 4.42(4) 4.44(4) 11.67(9)96mAg (2+) 22(3) 5.6(6) 6.9(6) 0.00(5)#96Cd 0+ 1.08(9) 0.88(9) 8.65(46) 8.94(41)96mCd (16+) 22(3) 0.65(6) 0.30(11) 5.3(20)#97Cd (9/2+) 1.20(7) 1.10(8) 10.38(32)97mCd (25/2+) 37(3) 3.7(1) 3.8(2) 1.5(5)#97nCd (1/2−) 5.3(10) 0.78(7)98Cd 0+ 9.1(2) 9.2(3) 5.448(30) 5.430(58)99Cd (5/2+) 18.7(11) 16(3) 6.781(6)98In (0+) 0.0290(12) 0.037(5) 12.76(37) 13.74(21)98mIn (9+) 59(2) 1.11(9) 1.03(13) 0.573&99In (9/2+) 3.35(11) 3.1(2) 8.55(20)100In (6+) 5.56(5) 5.85(16) 9.88(18)100Sn 0+ 1.19(10) 1.11(15) 7.16(19) 7.03(35)7.78(19)101Sn (7/2+) 2.09(18) 1.97(16) 8.30(42)67ln(t)8− 6− 4− 2− 0 2Counts110210310Rh90) = 28.0(33) ms+ (01/2T) = 0.52(2) s+ (71/2Tln(t)8− 6− 4− 2− 0 2Counts110210310Ag94) = 27.7(15) ms+ (01/2T) = 0.51(3) s+ (71/2Tln(t)8− 6− 4− 2− 0 2Counts110210In98) = 29.0(12) ms+ (01/2T) = 1.11(9) s+ (91/2TEnergy (keV)0 2000 4000 6000 8000Counts / 200 keV050Energy (MeV)10 11 12ν2 χ1.11.21.31.41.5 (MeV) = βQ10.60(58)Rh90Energy (keV)0 2000 4000 6000 8000Counts / 200 keV0200Energy (MeV)10 11 12 13ν2 χ1.21.41.61.8 (MeV) = βQ11.43(47)Ag94Energy (keV)0 2000 4000 6000 8000Counts / 200 keV0200Energy (MeV)11 12ν2 χ0.811.2 (MeV) = βQ11.74(37)In98Figure 4.10: Left: half-lives of ground and isomeric states of odd-odd N = Z nuclei; the parentdecay components are presented as solid lines, and background and daughter decay components areshown as dashed lines. Right: Qβ measurements of the same nuclei in reference to the ground-stateenergy; both the ground state and the isomeric state components were included.68Time (ms)0 100 200 300 400 500Counts / 10 ms110Pd] = 37(4) ms91[1/2TTime (ms)0 100 200 300 400 500Counts / 10 ms110Cd] = 31(3) ms95[1/2TTime (ms)0 100 200 300 400 500Counts / 10 ms110In] = 26(4) ms97[1/2TTime (ms)0 100 200 300 400 500Counts / 20 ms1−10110 Sn] = 27(5) ms99[1/2TEnergy (keV)0 2000 4000 6000 8000Counts / 500 keV050Energy (MeV)9 10 11 12ν2 χ1.151.2  (MeV) = βQ10.4(16)Pd91Energy (keV)0 2000 4000 6000 8000Counts / 500 keV050Energy (MeV)9 10 11 12 13ν2 χ1.21.31.4 (MeV) = βQ10.7(13)Cd95Energy (keV)0 2000 4000 6000 8000Counts / 500 keV020Energy (MeV)10 11 12ν2 χ0.70.75  (MeV) = βQ11.2(20)In97Energy (keV)0 2000 4000 6000 8000Counts / 500 keV01020Energy (MeV)10.5 11 11.5 12ν2 χ0.720.740.76  (MeV) = βQ11.7(14)Sn99Figure 4.11: Left: half-lives ofN = Z−1 nuclei obtained from experiment. MLH fits were performedwith separate components: parent decay (black), daughter decay (dashed blue), and background(magenta). For 97In, the relative deficit of the parent decay amplitude was compensated by aβ-decay component of 96Cd (dashed green) which would be populated by 1p emission from ahypothetical isomeric state. Right: Qβ analysis results of these nuclei.69would not be detected in WAS3ABi because of the 600-µs deadtime window immediately followingion implantation. A revised fit containing the 96Cd component (proton daughter of 97In, dashedgreen line in Fig. 4.11) reported 39(5)% population of the hypothetical isomer. The implicationsof two possible states in 97In are discussed in Section 4.3.3. A plot showing the systematics of thehalf-lives of N = Z − 1 nuclei from Z = 41 to 50 is shown in Fig. 4.12. Being near the protondripline, isotopes with odd-Z are highly susceptible to spontaneous one-proton emission and theirshort half-lives verify that the proton dripline has been reached. On the other hand, from the longβ-decay half-lives exceeding 10 ms, it is concluded that the even-Z isotopes are not yet susceptibleto direct proton emission.Z41 42 43 44 45 46 47 48 49 50 (s)1/2 T10log9−8−7−6−5−4−3−2−1−This workK. StraubI. Celikovic et al.K. Rykaczewski et al.H. Suzuki et al.P. Kienle et al.Rh89 Ag93Pd91 Cd95 In97 Sn99In97msµ140 sµ3 Figure 4.12: Half-life systematics of N = Z−1 nuclei with valence protons in the g9/2 orbital. Odd-Z nuclei are proton unbound and possess very short half-lives compared to even-Z counterparts.For 97In, a long-lived β-decaying state has been confirmed with better precision. Circumstantialevidence points to a short-lived proton-emitting state 97mIn with upper and lower limits on itshalf-life.4.3.2 Experimental Qβ and QEC valuesThe method using Geant4 simulations described in Section 3.5.2 was used to obtain experimentalQβ values. It was found in general that the Qβ results were more reliable for small correlationtime windows (t < 5 s) or with very clean γ-ray gates, where the signal-to-background ratios ofdecay events remain high. Besides 98Cd, few long-lived nuclei possessed dominant β-decay branchesaccompanied by a high-energy γ ray. Consequently only short-lived N ≤ Z isotopes were subjectedto Qβ analysis.70Qβ and QEC values of92Pd, 96Cd, and 100SnQβ of three even-even, N = Z isotopes92Pd, 96Cd, and 100Sn were measured with γ-ray gates.The Qβ measurement of92Pd was performed with the newly discovered 257-keV γ-ray shown inFig. 4.20 as a selection cut, and its result is shown in the top plot of Fig. 4.13. The conversion ofthe resulting Qβ = 6.27(29) MeV into the QEC value involves the addition of the 0.257-MeV γ-rayenergy, 2me = 1.022 MeV, as well as the (2+) isomer’s energy, which is listed as 0.05(10) MeV [2].The final value of QEC = 7.47(29) MeV was derived, which agrees with the theoretical predictionof 7.93(50) MeV listed in Table 4.3. Combined with T1/2 = 1.17(4) s, the resulting log(ft) valuewas 3.84(11) assuming 100% β-decay branching ratio to the yrast (lowest energy state for a givenspin and parity Jpi) (1+) state - a reasonable value for an allowed 0+ → 1+ GT decay.The Qβ measurement of the ground state of96Cd was performed after gating on the 421-keVγ ray shown in Fig. 4.22. The conversion of the resulting Qβ = 7.21(46) MeV into the QEC valueinvolves the addition of the 0.421-MeV γ-ray energy and 2me = 1.022 MeV. Unlike92Pd, thefinal (2+) state in 96Ag was considered degenerate with the (8+) ground state [2]. Thus for 96CdQEC = 8.65(46) MeV was deduced, also consistent with the theoretical prediction of 8.94(41) MeVlisted in Table 4.3. Combined with T1/2 = 1.16(8) s and assuming a 64(3)% β-decay branchingratio to the yrast (1+) state in 96Ag, the resulting log(ft) value was 4.35(15) - also reasonable foran allowed 0+ → 1+ GT decay.The experimental Qβ spectrum of100Sn was obtained by gating on the 100In γ rays shownin Fig. 4.31, except for the 2048-keV γ ray due to low statistics. The χ2 evaluation result isQβ = 4.04(18) MeV, which is higher than the 3.29(20) MeV reported in Ref. [14] but consistentwith 3.75(9) MeV reported in Ref. [69] within 2σ, based on an independent analysis of the samedataset. The low uncertainty in the result from Ref. [69] is due to higher statistics in the β-decay energy spectrum without applying the γ-ray gates. The QEC value of100Sn depends on thestructure of the daughter nucleus 100In, and is discussed in Section 4.4.7.Qβ and ft values of odd-odd N = Z nucleiOdd-odd N = Z nuclei 90Rh, 94Ag, and 98In undergo fast superallowed Fermi decays and possesslarge Qβ values. For these isotopes, β-decay energy spectra were generated from decay events within100 ms after implantation and corrected for background. Despite setting a short time window toimprove the purity of the clean Fermi decay, a significant fraction of the Qβ spectrum originatedfrom isomeric state decays due to the high population ratios (see Table 4.3). Therefore the isomericdecay channels were included in the Qβ evaluation.At each trial energy, a simulated Qβ spectrum was generated for each isomeric decay branchand scaled according to its β-decay branching ratio based on γ-ray intensities. The input Qβ valueof this spectrum was adjusted by the excitation energies of both the initial and the final state. Onemajor uncertainty arises from the excitation energy of the isomer. For 94Ag, E(7+) = 660 keV wasproposed from shell-model calculations [107] while NuBASE2012 reports a conservative estimate of1350(400) keV as the excitation energy.71Energy (keV)0 2000 4000 6000Counts / 200 keV050Energy (MeV)5.5 6 6.5 7ν2 χ1.11.21.31.4 (MeV) = βQ6.14(27)Pd92Energy (keV)0 2000 4000 6000Counts / 200 keV050Energy (MeV)6 7 8ν2 χ1.31.41.5  (MeV) = βQ7.21(46)Cd96Energy (keV)0 2000 4000 6000Counts / 400 keV02040Energy (MeV)3.5 4 4.5ν2 χ2345 (MeV) = βQ4.04(18)Sn100Figure 4.13: Qβ spectra of92Pd (top), 96Cd (middle), and 100Sn (bottom) obtained from γ-raygates and fitted with different trial Qβ energies.72The simulated Qβ histograms were added and compared to the experimental energy spectra.The results are shown on the right side of Fig. 4.10. Conversion of the ground-state to ground-state Qβ values into QEC requires just the addition of 2me = 1.022 MeV for β+ decays. Twoγ-ray transitions with noticeable internal conversion coefficients from the β-decay of 98mIn are 147and 198 keV, with ICE emission probability of 27.5(4)% and 11.8(2)% respectively. These effectsare visible in the first two bins of the Qβ spectrum of98In, The sum of the probability-weightedenergies is 64(1) keV, which is small compared to the systematic uncertainty of the energy of the(9+) isomer; this energy correction was not included in the QEC calculation.The log(ft) values of the 98mIn were were 4.8(4) for the decay into the 6585-keV (10+) statewith Iβ = 4.9+4.5−2.9% mentioned in Section 4.4.5, and 4.8(2) for the decay into the 2428-keV (8+)isomer. These are consistent with the known ∆J = 1 GT-decay log(ft) systematics. The raw ftvalues for the superallowed Fermi decays were 2.1(6)× 103 s for 90Rh, 3.2(7)× 103 s for 94Ag, and3.4(6) × 103 s for 98In. In comparison to the up-to-date corrected Ft value of 3072.27(62) [37]with corrections on the order of 1%, the preliminary ft measurements are consistent within thelarge statistical uncertainties caused by large δQβ. Much more precision in the mass measurementof these odd-odd N = Z nuclei is needed to include them in the quantitative discussion of theconsistency of the Ft value.N = Z − 1 nucleiThe N = Z − 1 nuclei 91Pd, 95Cd, 97In, and 99Sn undergo predominantly ground-state to ground-state Fermi decays with large Qβ values. The results are shown on the right side of Fig. 4.11.Combining the T1/2 and Qβ measurements assuming 100% ground-state to ground-state transitions(QEC = Qβ + 2me), the corresponding log(ft) values are calculated and tabulated in Table 4.4.These log(ft) values are quite small and consistent with ∆J = 0 allowed decays, as expected fromTz = −1/2 nuclei with a large energy window and the similarity of the initial and the final states.Table 4.4: Summary of β-decay information on 91Pd, 95Cd, 97In, and 99Sn, in reference to Fig. 4.11.100% ground-state to ground-state β-decay branching ratios were assumed in calculating the log(ft)values. T1/2 constraints for the proton-emitting (1/2−) isomer 97mIn are also presented.Nucleus Jpi T1/2 (ms) QEC (MeV) log(ft)This work Literature91Pd (7/2+) 37(4) > 1.5 µs [61] 11.4(16) 3.4(4)95Cd (9/2+) 31(3) 73+53−28 [18] 11.7(13) 3.4(3)97In (9/2+) 26(4) 26+47−10 [18] 12.2(20) 3.4(5)97mIn (1/2−) 3-140 µs99Sn (9/2+) 27(5) > 200 ns [18] 12.7(14) 3.5(3)73Masses of isotopes near the proton driplineFirst Qβ measurements for the heaviest N ≤ Z nuclei enable tests of different mass models atthe proton dripline near 100Sn. Four independent mass models were used to compare with exper-imental results: the finite-range droplet model (FRDM) [108], the Koura-Tachibana-Uno-Yamadamodel (KTUY05) [109], the Duflo-Zuker model (DZ) [110], and the Hartree-Fock-Bogoliubov model(HFB27) [111]. An additional comparison was provided by empirical extrapolations the atomicmass evaluation (AME2012) [112]. The comparisons to the experimental QEC values are shown inFig. 4.14. For the proton-unbound 93Ag nucleus, its Sp = −1060(30) keV [96] was used with themass of 92Pd to calculate its QECvalue.Rh90 Pd91 Pd92 Ag93 Ag94 Cd95 Cd96 In97 In98 Sn99 Sn100 (MeV)ECQ051015FRDMKTUY05AME2012DZHFB27ExpFigure 4.14: Comparison of experimental QEC values of the select N ≤ Z nuclei measured in thiswork to different mass models and extrapolated data (see text for references). For AME2012, the1σ-uncertainty band is drawn. For 100Sn, two QEC values inferred from the first two possible levelschemes shown in Fig. 4.32 are plotted.Several general remarks can be made. First, the trend of low QEC values of even-even, N = Znuclei is replicated by the models. These nuclei benefit maximally from pairing interactions andthe attractive pn interaction. Second, the experimental QEC values for odd-odd N = Z nuclei areconsistently lower than the predictions. Underestimation of the attractive T = 0 pn interaction inthese nuclei may be the cause. Third, it is ambiguous to rank the different mass models; KTUY05performs rather well for most of the nuclei except 98In, and HFB27 in general predicts poorly buthas the closest QEC value for98In. Lastly, large deviations of predicted QEC values are present for74odd-odd N = Z nuclei.4.3.3 Limits of proton binding in 97InUnlike the other odd-Z, T1 = −1/2 nuclei, 97In undergoes β decay with a T1/2 and Qβ similar toeven-Z counterparts. On the other hand, as elaborated in Section 4.3.1, missing decay correlationsfor 97In can be explained by suggesting another state which decays almost completely within thedeadtime of WAS3ABi of 600 µs. There is a 3-µs lower limit on this hypothetical state’s half-life,which is based on the perseverance of 97In isotopes through the separator [96]. The upper limiton the half-life of this isomer was determined by assuming less than 4 proton-emitting isomers tosurvive after 600 µs. The basis for choosing this number was based on Poisson statistics, where zeroobservations of protons lie outside of the 2σ confidence level with 1σ(4 samples) = 2. The derivedupper limit was 140 µs. Based on the trend illustrated in Fig. 4.12, this short-lived state is likelyto be a proton emitter. On the other hand, no single-pixel, proton-emission candidate events haveoccurred within the correlation time window. A conservative lower limit on the proton emissionT1/2 of the (9/2+) state was determined by taking the −2σ value of the β-decay T1/2 (18 ms) andmultiplying by the number of (9/2+) states (128) divided by 4 to yield 576 ms.A theoretical support for a coexistence of two states comes from a near-degeneracy of thep1/2 and the g9/2 orbitals for N ∼ Z nuclei approaching 100Sn. At the moment designation ofground and isomeric states is ambiguous. For the proton-emitting state, Qp values from variousmass models (using ground-state masses) are compared with estimates given by a simple theoryon proton emission [9], shown as the inset of Fig. 4.15. Two alternatives are proposed: protonemission with l = 1 from the p1/2 orbital and l = 4 from the g9/2 orbital. Due to the centrifugalbarrier, proton emission from the p1/2 is favored over the g9/2. The upper and lower limits on thehalf-lives can be translated into a range of the emitted proton energy Qp. The upper limit on theQp value from the g9/2 state is 0.65 MeV, which is less than the 0.66-0.76 MeV predicted for theemission with l = 1. Then 97In is suggested to have a ground state spin and parity of 9/2+, witha proton-emitting isomeric state with spin 1/2−. The energy difference between the two states isreflected in Fig. 4.15, which could be as large as, or greater than 760 keV if the (9/2+) state liesabove the Sp = 0 line. The Sp value of the (9/2+) could also be deduced with Qβ spectroscopy ormass measurements; the current experimental Qβ value is too imprecise to be useful.Different mass models diverge in their mass predictions up to 1 MeV for 97In, and the interpreta-tion from the experimental values happen to lie in between them. A decay spectroscopy experimentwhich is able to measure both the Qβ from the (9/2+) state and the energy of the proton emittedfrom the (1/2−) state would serve as a benchmark test of these mass models.4.3.4 βp branching ratiosBranching ratios and half-lives of β-delayed proton emission were measured by analyzing the βpdecay time distributions. Except for the most exotic isotopes where statistics are low, βp decaytime spectra are shown in Fig. 4.16. The number of βp events was determined from either counting75A95 96 97 98 99 (MeV)pS2−1−012AME2012KTUY05DZIn isotopesHFB27FRDM = 1 (bar)l = 4 (arrow)l (MeV)pQ0.5 0.6 0.7 0.8 0.9 (s)1/2 T10log8−6−4−2−02In97)9/2 = 4 (gl)1/2 = 1 (plsµ140 sµ3 576 ms< 0.65 MeV0.66 MeV 0.76 MeVFigure 4.15: Left: Qp values of97In based on the half-life limits for l = 1 and l = 4, correspondingto proton emissions from either the pip1/2 or the pig9/2 orbital. A theoretical description of theT1/2-Qp relationship is given in Ref. [9] and derived in Appendix C. Right: Sp values as a functionof mass number for In isotopes. The predictions diverge for 97In, and the Qp values deduced onthe left plot occur as intermediate values.76(for low-statistics data) or the integral of the parent fit function, corrected by a run-dependentWAS3ABi deadtime loss. For isotopes without isomeric states, the βp branching ratio bβp wassimply calculated as Nβp/Nion; if one or more isomeric states were present, biβp = Niβp/Ni wherei is the index for each state. The results and comparisons to literature values are tabulated inTable 4.5, where the half-lives between βp- and β-decay data agree with one another. For severalstates and isotopes with insufficient statistics, individual T1/2 measurements using βp data werenot performed due to contributions from isomeric states and daughter nuclei - complicating the bβpanalysis. The bβp values for these cases were obtained by adopting the β-decay half-lives in the βpdecay time analysis.For N = Z nuclei, βp emission from both the ground and isomeric states were analyzed in thesame way as the β-decay half-life analysis. The population of the (21+) isomer in 94Ag was toolow to merit an independent measurement of its half-life and bβp. So the literature values wereused in the half-life analysis to obtain T1/2 and bβp for the (0+) ground state and the (7+) isomer.The statistics were low for N = Z − 1 nuclei, and βp events from these isotopes were counted ina 200-ms correlation time window. The number of background βp events was determined with abackward-time correlation and subtracted from the t > 0 βp events to obtain bβp.For 96Ag, the half-lives of the two states were too similar within the finite correlation time rangeof 20 s to perform independent T1/2 measurements using βp data. Instead, the half-lives from β-decay data were adopted to determine the contributions to the βp time spectrum and subsequentlythe bβp values. The bβp analysis for96Cd was complicated by the fact that its β decay from theground state and the isomeric state populates both the (8+) and the (2+) states in 96Ag, each ofwhich has a non-negligible bβp. Rather than fitting the βp time spectrum, an alternative approachwas taken. The βp γ-ray half-life analysis concluded that all of the βp activity originates from the(16+) isomer. Then the intensity of the 691-keV γ ray to the isomeric (21/2+) state in 95Pd wasused to determine the bβp value of96mCd.4.3.5 Direct proton emission search in 94AgThere have been reports of direct 1p and 2p emission from 94Ag’s (21+) isomeric state [10, 11]. Basedon its low isomeric ratio, attempts to confirm proton emission from this state were challenging.Nevertheless, proton spectroscopy with WAS3ABi is immune from losses in statistics due to theβ-particle correlation efficiency, EC, and the EURICA efficiency. The result of the direct protonemission search from 94Ag is shown in Fig. 4.17.No evidence was found at the reported 1p proton energies. 5 counts were observed at 1900keV, consistent with the total energy of 2p emission. The half-life obtained from the 5 events was0.56+0.45−0.17 s, which is consistent with either isomeric state’s half-life. Note that this energy regionoverlaps with βp decays, which may generate single-pixel EC-induced proton events. Anotherpoint of contention is the branching ratio; for 1p decays, the branching ratios for 790(30) keV and1010(30) keV were 1.9(5)% and 2.2(4)% - about 4 times greater than 0.5(3)% for the 2p decay. Ifthe counts at 1900 keV are genuinely 2p events, approximately 20 counts should have been observed77Time (s)0 5 10Counts / 0.2 s204060 pβRu 89 = 1.5(2) s1/2TTime (s)0 5Counts / 0.5 s50100150pβPd 92 = 1.6(3) s1/2TTime (s)0 5 10Counts / 0.2 s200300400500 pβAg 95 = 1.97(11) s1/2Tln(t)5− 0Counts110210310pβIn 98): 26(7) ms+(0): 0.91(3) s+(9Time (s)0 5 10 15Counts / 0.5 s0100200300pβSn 101 = 2.33(10) s1/2TTime (s)0 2 4Counts / 0.5 s050100150pβRh 90 = 0.52(6) s1/2TTime (s)0 2 4Counts / 0.1 s100200300400500pβPd 93 = 1.16(4) s1/2TTime (s)0 10 20Counts / 0.5 s210310 pβAg 96: 4.42(4) sβ) +(8): 7.0(17) s+(2Time (s)0 5 10 15Counts / 1.0 s50100pβIn 99 = 4.5(6) s1/2TTime (s)0 5 10Counts / 1.0 s300350400450pβRh 91 = 1.6(5) s1/2TTime (s)0 10 20Counts / 1.0 s100150200250300pβPd 95 = 10.3(18) s1/2TTime (s)0 10 20Counts / 0.1 s210310): 1.13(7) s+(9/2): 3.8(2) s+(25/2pβCd 97Time (s)0 10 20Counts / 1.0 s22.53310×pβIn 100 = 5.4(4) s1/2TTime (s)0 10 20Counts / 0.5 s50100150200pβRh 92β fixed from 1/2T)+(6)+(2ln(t)5− 0Counts110210310pβAg 94): 29(13) ms+(0): 0.50(3) s+(7Time (s)0 10 20Counts / 1.0 s300350400450500pβCd 99 = 15(4) s1/2TTime (s)0 5 10Counts / 1.0 s0102030 pβSn 100 β fixed from 1/2TFigure 4.16: Time distribution of βp decays of isotopes and isomeric states. For 94Ag and 98In, thetime distributions were plotted and fitted in the same way as shown in Fig. 4.10. The amplitudesof the parent decay components were used to calculate bβp. For several states/isotopes, the T1/2values from β decays were adopted to determine bβp.78Table 4.5: Half-lives and βp branching ratios of isotopes with non-negligible bβp. Unless adoptedfrom β-decay measurements, the half-lives determined from βp events were compared to the β-decayhalf-lives for consistency checks. The bβp values are compared to those from literature [2].Nucleus Jpi T1/2 (s) bβp (%)β βp This work Literature89Ru (9/2+) 1.32(6) 1.5(2) 2.4(3) 3.1(18)90mRh (7+) 0.52(2) 0.52(6) 5.2(4)91Rh (9/2+) 1.59(10) 1.6(5) 0.65(13) 1.3(5)92Rh (6+) 5.81(12) 1.3(3) 1.9(1)92mRh (2+) 2.54(44) 12(11)91Pd (7/2+) 0.037(4) 0.031(+0.019−0.009) 1.7(+0.9−0.7)92Pd 0+ 1.17(4) 1.6(3) 1.7(3)93Pd (9/2+) 1.14(3) 1.16(4) 5.3(1) 7.5(5)95mPd (21/2+) 12.9(4) 10.3(18) 0.60(16) 0.93(15)94Ag (0+) 0.0277(15) 0.029(13) 1.3(6)94mAg (7+) 0.51(3) 0.50(3) 6.8(4) 2095Ag (9/2+) 1.81(7) 1.97(11) 2.6(1) 2.5(3)96Ag (8+) 4.42(4) 1.9(14) 6.9(7)96mAg (2+) 5.6(6) 7.0(17) 12.3(50) 15.1(26)95Cd (9/2+) 0.031(3) 0.051(+0.022−0.012) 2.2(+0.9−0.7)96mCd (16+) 0.65(6) 0.59(+0.12−0.07) 9.0(23) 5.5(40)97Cd (9/2+) 1.20(7) 1.13(7) 6.2(8) 11.8(20)97mCd (25/2+) 3.7(1) 3.8(2) 21.6(24) 25(4)99Cd (5/2+) 18.7(11) 15(4) 0.16(3) 0.21(8)97In (9/2+) 0.026(4) 0.004(+0.010−0.002) 0.6(+0.8−0.5)98In (0+) 0.0290(12) 0.026(7) 0.9(5) 5.6(3)98mIn (9+) 1.11(9) 0.91(3) 24.2(11) 19(2)99In (9/2+) 3.35(11) 4.5(6) 0.6(2) 0.9(4)100In (6+) 5.56(5) 5.4(4) 1.59(7) 1.64(24)99Sn (9/2+) 0.027(5) 0.011(+0.011−0.004) 5.2(+3.9−2.6)100Sn 0+ 1.19(10) 0.9(3) < 17101Sn (7/2+) 2.09(18) 2.33(10) 18.4(8) 21.0(7)19.6(1) [18]79Energy (keV)0 1000 2000 3000 4000Counts / 50 keV020Single pixel decayp decay, not single pixelβ790(30) 1p?1010(30) 1p?1900(100) 2p?Figure 4.17: WAS3ABi energy spectrum following 94Ag decay with background subtraction. Forclarity, a minimum of 1500 keV was required for βp decays. Previously reported Qp values [10, 11]are marked. The observation of 5 events at 1900 keV is discussed in the text.at 790 and 1010 keV each. Consequently, it was impossible to confirm direct proton emission in94Ag from this experiment.4.4 γ-ray spectroscopy following β and βp decaysγ-ray spectra and related analysis results from several selected nuclei’s β and βp decays are pre-sented, including those mentioned in Section 1.2.1 for which no literature exists for β-delayed γrays. The significance of each finding is discussed mostly in the context of the SM calculations.4.4.1 Low-spin structure of 90Ru and the spin of 90mRhThe excited states of 90Ru were populated from the β-decay of the N = Z = 45 nucleus 90mRh.The resulting γ-ray spectrum is shown in Fig. 4.18. Besides the known transitions obtained froma fusion-evaporation experiment [113], two new transitions at 1164 and 1316 keV were discovered.Relative intensities of the 886, 1164, and 1316-keV γ rays (normalized to the 738-keV γ ray)were 42(9)%, 21(6)% and 23(6)%, respectively. Based on the intensity analysis, these new γ-raytransitions feed the yrast (4+) state and the three proposed (6+) states are reproduced in thetheoretical calculations as shown in Fig. 4.19. In order to determine the feeding of the (8+) statewhich decays by a 512-keV γ ray, the intensity of the 511-keV annihilation peak was analyzed. Aftersubtracting the contributions from superallowed Fermi decays, decays to the three (6+) states and8090Ru β decays, it was found that the feeding of the (8+) was less than 6% at the 2σ confidencelevel.Energy (keV)0 500 1000 1500 2000Counts / 2 keV020406080738 9011164 1316886Tc)90154 (Energy (keV)0 500 1000 1500 2000225230511Time (s)0 1 2 3Counts / 0.2 s0204060 Rh)90m (1/2T = 0.58(4) sFigure 4.18: γ-ray spectrum of 90Rh decay within the decay correlation time window of 3 seconds.Two new transitions were found at 1164 and 1316 keV. The inset shows the half-life of the isomericstate obtained with the labeled γ-ray gates, which is consistent with 0.52(2) s listed in Table 4.3.The derived structure of 90Ru and the β-decay feeding supports the assignment of Jpim = (7+)for 90mRh, as it is predicted from the SM calculations with an excitation energy of 500 keV. Thisdecay scheme resembles the GT-decay of 94Ag’s (7+) isomer [52], which also feeds three (6+) states.4.4.2 Low-spin structure of 92RhThe low-spin structure of the daughter nucleus 92Rh was investigated with the γ rays following92Pd’s β decay. As seen in Fig. 4.20, only one γ ray at 257 keV belongs to 92Rh, as the 865-keV γ ray is the (2+) state energy of the granddaughter nucleus 92Ru as previous reported inRef. [114]. The 257-keV γ ray is understood from the spin selection rules of a GT decay as thetransition populating the (2+) isomer rather than the (6+) ground state of 92Rh; Fig. 4.21 showsthe SM calculations which reveals a low-lying 1+ state, and the excitation energy is experimentallyconfirmed as 257 keV above the (2+) state.Given the 100% population of 92mRh from the decay chain of 92Pd, the β-decay time profilewith the 865-keV γ-ray gate was used to determine the half-life of 92mRh. The input value ofT1/2(92Pd) = 1.17(4) s was varied at 2σ, and the resulting systematic uncertainties were includedin the overall uncertainty. The T1/2 obtained with this method (T1/2 = 2.54(44) s) is vastly differentfrom T1/2 = 0.53(37) s deduced from the overall92Rh β-decay half-life analysis in Ref. [114].8190 Rh0 (0+ )x (7+ )90 Ru0 0+738 (2+ )1639 (4+ )2525 (6+ )3037 (8+ )2803 (6+ )2955 (6+ )90 Ru pg0 0+830 2+1722 4+2447 61+2818 8+2556 62+2803 63+73890188651211641316Gamow-Teller βSuperallowed Fermi βFigure 4.19: Level scheme of 90Ru obtained from the β-decay of 90mRh. The widths of the arrowsindicate relative γ-ray intensities. The two new proposed (6+) states built by the 1164- and 1316-keV transitions are in agreement with the calculated 6+ states shown in “90Ru pg”.Energy (keV)0 200 400 600 800 1000Counts / keV0100200300400257511Ru)92865 (Time (s)0 5 10Counts / 0.5 s0204060 )]+Rh (292 [1/2T= 2.54(44) sFigure 4.20: γ-ray spectrum following 92Pd decay within 5 s of ion-β correlation. Only the 257-keVtransition is attributed to the 92Rh daughter nucleus, and it populates the (2+) isomeric state. Theinset shows the half-life determination of 92mRh using the time profile of the 865-keV γ ray in thegranddaughter nucleus 92Ru.8292 Pd0 0+257+y (1+ )92m Rhy (2+ )92 Rhx (6+ )235+x (8+ )92 Rh pg0 2+35 6+155 1+288 8+865 (2+ )92 Ru0 0+257865Figure 4.21: Schematic diagram of the 92Pd-92mRh decay chain, with the interpretation of thenewly discovered 257-keV γ ray being the (1+) → (2+) transition. The experimental low-energystates of 92Rh are reproduced in the SM calculations labeled “92Rh pg”.Another intriguing result is the comparison of the γ-ray intensities. In comparison to the 511-keV annihilation γ ray, relative intensities of 59(4)% and 40(3)% were obtained for the 257-keVand 865-keV γ rays in a correlation time window of 5 s. The ratios of the intensities were consistentwith the cumulative distribution calculation using the two half-lives and the finite time range. Thesum of relative intensities being consistent with 100% suggests very pure GT decays of both 92Pdand 92mRh (apart from βp emission) with no direct population of the ground states - in conflictwith the literature value of 77(23)% β-decay branch to the ground state of 92Ru from 92mRh [114].The current experimental results are better supported by the β-decay selection rules.4.4.3 β, βp-delayed γ rays of 96CdThe abundance of 96Cd isotopes produced in this experiment has enabled a more careful exam-ination of the structure of the daughter nuclei. Of the β-delayed γ rays shown in Fig. 4.22, sixtransitions were discovered at 489, 843, 1146, 1569, 3177, and 3691 keV. The relative intensities ofthese γ rays compared to the 421-keV γ ray ranged from 5 to 11%. From the βp-delayed γ raysshown in Fig. 4.23, transitions from high-spin states of 95Pd determined from a fusion-evaporationexperiment [12] are clearly visible. Thus there is now experimental evidence for βp decays from the(16+) isomer of 96Cd. The 681-keV transition, which depopulates the 33/2+ state in 95Pd, is mostlikely a 680-keV γ ray from 95Rh which was populated by the βp decay of 96Ag (see a differenttime profile of this γ ray in Fig. 4.23).The known γ-ray transitions from both β and βp decays serve as further experimental evidence83Energy (keV)0 500 1000 1500Counts / 2 keV050100150200250300421630 667257843Pd)961415 (15061146124915691607470489Energy (keV)0 500 1000 1500105011005113200 3400 3600051031773691Figure 4.22: γ rays following β decay of 96Cd. The black histogram corresponds to promptlyemitted γ rays assigned to the ground-state decay of 96Cd, and the red histogram shows delayed γrays emitted from the (15+) isomer of 96Ag populated by the β-decay of 96Cd’s (16+) isomer.Energy (keV)0 200 400 600 800 1000Counts / 2 keV01020304050130511681* 6911370 138001231375680 690Time (s)012345Figure 4.23: γ rays following βp decay of 96Cd, where the labeled transitions are known from thehigh-spin structure of 95Pd [12]. The left inset shows the time profile of the 681-keV transition,which shows a contamination of the 680-keV γ ray emitted after 96Ag’s βp decay into 95Rh.84of the (16+) spin-gap isomer of 96Cd, the excitation energy of which could be determined withγ-gated Qβ analysis. On the other hand, the new transitions are assumed to originate from thedecays of 1+ states populated by the ground-state decay of 96Cd; the half-life analysis result onthese γ rays was more consistent with T1/2(g.s.) = 1.08(9) s than the isomer half-life of 0.65(6) s.The calculated level scheme shown in Fig. 4.24 reveals excited 1+ states up to 3.7 MeV in the pgmodel space (no core excitations), which could accommodate γ-ray energies up to 3691 keV.The apparent fragmentation of the ground-state β-decay branch injects a systematic uncertaintyon the Qβ of96Cd, as one or more of these transitions could be in coincidence with the 421-keV γray used as the selection cut for the Qβ analysis. The sum of the intensities of the six new γ raysis about half of the intensity of the 421-keV γ ray. More statistics would allow a γγ coincidenceanalysis of these transitions to address this issue and develop the low-spin structure of 96Ag to becompared with calculations.4.4.4 Identification of negative-parity states in 97Cd and 97AgWhile β-delayed γ-ray spectroscopy has been performed for 97Cd revealing the (25/2+) isomer andis decay scheme [53], there have been predictions of a (1/2−) isomeric state for this nucleus [13, 63]which could be investigated with γ-ray transitions. In this work, three new transitions at 1245,1418 and 1673 keV were found as shown in Fig. 4.25. The half-life associated with these γ rays, was0.78(7) s, which differs from the ground-state half-life of 1.20(7) s by at least 5σ; therefore thesetransitions were attributed to the decay of the predicted (1/2−) isomer in 97Cd into three (3/2−)states in 97Ag.Schmidt et al. [13] note that 97Cd lies outside of the region of nuclei used in the fitting procedureto obtain empirical single-particle energies and two-body matrix elements by Refs. [27, 115, 116],which leads to large variances in the calculated properties of negative-parity states and their decays.One set of calculations appears to agree well with experimental results, which is elaborated here.Calculations by Ogawa [63] using the interaction derived by Gross and Frenkel [116] suggest the1/2− isomer to be approximately 800 keV above the ground state with a dominant GT-decaybranch over the M4 transition. The predicted half-life of this isomer was 0.65 s, which is quiteconsistent with the experimental value. The scenario of at least one γ ray emitted after the GTdecay is possible if Jpif of the β decay is 3/2−. SM calculations were done to include the f5/2 andp3/2 orbitals in addition to the pg model space, since the latter could generate only one 3/2− statein 97Ag. The calculation outputs are displayed in Fig. 4.26 for comparison with experimental data.Calculations show three 3/2− states with energy spacings consistent within 250 keV compared toexperimental γ-ray energies, with a small branching ratio to the intermediate 5/2− state. Betterstatistics would lead to a more definitive structure of low-spin, negative-parity states in both 97Cdand 97Ag, and even obtain decay information about the (1/2−) state in 97Ag.8596 Cd0 0+x (16+ )96 Ag0 (8+ )y (2+ )421+y (1+ )600844.51021.511731384.5600+1607/2600+3177/2600+3691/2470 (9+ )1719(10+ )1976 (11+ )2606(12+ )2643 (13+ )2687 (15+ )GT resonance95m Pd1876 21 /2+2567 23 /2+2697 25 /2+4072 29 /2+4753 33 /2+96 Ag pg0 2+25 8+245 11+692 12+1296 13+1912 14+2810 15+3542 16+366917+421 47012492571506630 6676911375681p489 84311461569160731773691Figure 4.24: Level schemes of 96Ag and 95Pd reproduced from the β/βp decay of 96Cd. It isunclear whether the βp decay populates the 33/2+ state in 95Pd. SM calculations of 1+ statesin 96Ag are shown on the right, in relation to the discovered but unassigned γ rays (dashed bluearrows, compressed energy scale).86Energy (keV)0 500 1000 1500 2000 2500 3000Counts / 2 keV0500100015002000290763129025722013 29091673124514181306716Pd)97686 (Energy (keV)0 500 1000 1500 2000 2500 300093509400 511Time (s)0 2 4Counts / 0.5 s50100150200 (1245, 1418, 1673)1/2T = 0.78(7) sFigure 4.25: γ-ray spectrum following 97Cd decay. Three new transitions at 1245, 1418 and 1673keV are reported, and the β-decay time profile of these γ rays exhibits a half-life of 0.78(7) s. Thishalf-life is incompatible with both the ground state and the isomeric state half-lives, but agreeswell with the predicted T1/2 = 0.65 s for the (1/2−) isomer [13].8797 Cd0 (9/2+ )x (1/2- )y (25/2+ )97 Ag0 (9/2+ )716 (7/2+ ) 1290(13/2+ )2053 (17/2+ )2343 (21/2+ )4915 (23/2+ )6221 (27/2+ )z (1/2- )1245+z (3/2- )1418+z (3/2- )1673+z (3/2- )97 Ag fpg0 9 /2+619 7 /2+1366 13 /2+2179 17 /2+2535 21 /2+658 1 /2-1745 3 /21-1901 3 /22-2566 3 /23-1589 5 /2-7161306257276312901245 14181673Figure 4.26: Level scheme of 97Ag obtained from the β-decay of 97Cd. The 1245-, 1418- and 1673-keV γ rays are considered to depopulate three (3/2−) states in 97Ag after the β decay of 97Cd’s(1/2−) isomer, in view of the SM calculations of low-energy states performed in the fpg modelspace shown on the right.884.4.5 β, βp-delayed γ rays of 98mInβ-delayed γ rays of the (9+) isomer of 98In into the excited states of 98Cd were analyzed. If thespin of the isomer is correct, then allowed GT β decays would populate states with spins between8+ and 10+. Indeed, the known γ-ray cascade from the (8+) seniority isomer in 98Cd was observedwith equal intensities. Furthermore, three counts were observed in an energy window of 4153-4160keV, which corresponds to the 4157-keV γ-ray energy from the core-excited (10+) state to the(8+) isomer [64]. The β-decay half-life extracted from these events was 0.7+0.9−0.2 s, consistent withT1/2 = 1.11(9) s as exhibited in Fig. 4.10. From γγ coincidence analysis, one coincidence eventwas observed at 147 and 198 keV each. From the intensity analysis, β feeding to the (10+) wascalculated to be 4.9+4.5−2.9%.In addition, the γ rays were from βp decays were analyzed. As shown in Fig. 4.27, the dominanttransitions at 290, 763, and 1290 keV were previously reported as part of the main seniority schemeof 97Ag in Ref. [117]. In addition, new transitions were found at the following energies: 281, 602,729, and 1417 keV. A βp decay from the (9+) state with l = 0 leads to final states with spins between15/2+ and 21/2+, and the new γ rays could be arranged in the way exhibited in Fig. 4.27 to forma separate γ-ray cascade from the 15/2+ state in 97Ag. The energies of the two proposed statesare in great agreement with the SM calculations of 11/2+ and 15/2+ states and their branchingratios. The 281-keV γ ray emitted with the βp decay may be depopulating a first-excited 9/2+state (shown in Fig. 4.28) into either the (11/2+) or the (13/2+) state, but the calculations suggesta dominant, high-energy decay branch to the ground state of 97Ag; therefore it was left unassigned.A second-excited 9/2+ state is predicted to lie between the (17/2+) and the (21/2+) states, butβp feeding to this state is expected to be much suppressed due to the centrifugal barrier. γγcoincidence results with higher statistics will allow a firm placement of this γ ray.4.4.6 Low-spin structure of 99CdThe β-delayed γ rays from 99In decays provide experimental information on the low-spin statesof N = 51 nucleus 99Cd. As seen in Fig. 4.29, nine new γ rays are assigned to the 99Cd witha combined decay time profile that is fully consistent with the ground state half-life of 99In. γγcoincidence relations and relative intensities of the labeled γ rays is found in Table 4.6. Assignmentof the new transitions to the current level scheme on 99Cd built on fusion-evaporation data [118]is presented in Fig. 4.30, using the gds model space to predict the single-particle states above theN = 50 shell.The construction of the level scheme of 99Cd was complicated by limited γγ coincidence in-formation and the abundance of low-spin states generated by a neutron above the N = 50 shell.Theoretical calculations report 48 distinct states with Jpi from 5/2+ to 13/2+ with Ex < 4.6 MeV.Thus the theoretical level scheme on the right of Fig. 4.30 was built by identifying the states withdominant decay branches to single final states, assuming that the GT decay from 99In’s (9/2+)ground state populates the 99Cd daughter states with spins between 7/2+ and 11/2+. The agree-ment with the experimental γ-ray energies is mixed; while the transitions satisfying the experimental89Energy (keV)0 500 1000 1500Counts / 1 keV05101520 29076312906021417281729Energy (keV)0 500 1000 1500545658511Figure 4.27: γ-ray spectrum following 98In’s βp decay. Three intense transitions at 290, 763 and1290 keV are known to belong to the γ-ray cascade in 97Ag, with the highest spin being (21/2+).The assignment of the new γ rays in 97Ag is discussed in the text.Table 4.6: γ-ray energies, coincidences and relative intensities following 99In β decay, where therelative intensities were normalized to the sum of the two yrast transitions 441 keV and 1224 keV.Newly observed γ-ray energies are given in parentheses.Eγ (keV) Coincidences Irel (%)(371) 607, 1224, (1473) 6.5(26)441 1234, (1340), (1534), (1786), (1986) 59(3)607 1224, (1473) 23(2)783 5.4(20)(1078) 6.5(26)1224 607, (1473), (1596) 41(3)1234 441 18(3)(1340) 441 5.7(23)(1473) (371), 607, 1224, 1234 8.3(17)(1534) 441 8.1(18)(1596) 1224 3.8(17)(1607) 4.4(13)(1786) 441, (1986) 2.8(13)(1986) 441, (1786) 8.0(14)9098 In0 (0+ )x (9+ )98 Cd0 0+1395 (2+ )2083 (4+ )2281 (6+ )2428 (8+ )2928 (10+ )GT resonance97 Ag0 (9/2+ )1290(13/2+ )2053(17/2+ )2343 (21/2+ )2019(15/2+ )1417(11/2+ )97 Ag pg0 9 /2+1415 13 /2+2242 17 /2+2581 21 /2+2254 15 /2+1525 11 /2+1830 9 /2+1395688198147415712907632907296021417pFermi βFigure 4.28: Level schemes of 98Cd and 97Ag reproduced from the β/βp decay of 98mIn. The threenew γ rays correspond to the transitions from the proposed (15/2+) and (11/2+) states in 97Ag,which are reproduced in the calculations.91Energy (keV)0 500 1000 1500 2000Counts / 2 keV0500100015002000250030004413717831224607 1234147313401078 15341596160719861786Ag)99343 (Energy (keV)0 500 1000 1500 20001210012150511Time (s)0 2 4 6 8 10Counts / s0100200300-ray gates)γ (blue 1/2T= 3.35(17) sFigure 4.29: γ-ray spectrum following 99In decay. Besides the known transitions in 99Cd (blacklabels), many new but weak transitions are present (blue labels). The half-life determined from theblue γ-ray gates are fully consistent with T1/2 = 3.35(11) s determined from the overall β-decay fit.92γγ coincidence relationships could be found, the deviation increased as a function of the excitationenergy. In addition, the 1473-371 keV cascade could not account for the whole relative intensityof the 607-keV γ ray from the 13/2+ state, which would not be directly populated by β decay;additional feeding to this state is required. A more robust dataset would identify the level schemeof 99Cd, which can solidify the understanding of the SPEs and the TBMEs in the g7/2, d5/2, d3/2,and s1/2 orbitals across the shell closure.99 Cd exp0 (5/2+ )441 (7/2+ )1078 (7/2+ )1607 (7/2+ )2820 (7/2+ )1224 (9/2+ )1781 (9/2+ )1975 (9/2+ )2427 (9/2+ )4213 (9/2+ )1675 (11/2+ )3675 (11/2+ )1831 (13/2+ )2202 (13/2+ )441107816071596122460737178314731234 134015341986178699 Cd gds0 (5/2+ )362 (7/2+ )1176 (7/2+ )2031 (7/2+ )3137 (7/2+ )984 (9/2+ )1580 (9/2+ )1943 (9/2+ )2376 (9/2+ )4488 (9/2+ )1342 (11/2+ )4483 (11/2+ )1721 (13/2+ )2108 (13/2+ )36211762031215398473738762123753799801217158020142112Figure 4.30: Proposed level scheme of 99Cd with J+ ≤ 13/2 from the β-delayed γ rays of 99In. Acalculated level scheme resembling the experimental results is drawn on the right for comparison.4.4.7 Structure of 100In, and 100Sn’s log(ft) and BGT valuesOne of the key objectives of the experiment was to construct an unambiguous level scheme of 100In,in order to determine the properties of the superallowed GT decay of 100Sn accurately. A detailedinvestigation of the GT decay of 100Sn from same dataset presented in this thesis was the centralaspect of an independent parallel analysis by D. Lubos [69]; therefore a comprehensive discussionof the results was not carried out here. The β-delayed γ ray spectrum following 100Sn is displayedin Fig. 4.31, with the absolute intensities of the known transitions.The half-life of 100Sn was determined with the MLH method from 100In’s γ-ray gates, yielding93Energy (keV)0 500 1000 1500 2000Counts / 2 keV02040608010095141435511Cd)100795(Cd)1001004( 12972048-ray singlesγ 3× coincidence γγTime (s)0 2 4Counts / 0.5 s050100Sn] = 1.19(10) s100 [1/2TEnergy (keV)0 500 1000 1500 2000Absolute intensity0500100015002000 annihilation−/e+eSn implantations100Number of 1297 and 2048 keV combinedM1E2Figure 4.31: Top: single and coincidence γ-ray spectra following 100Sn β decay within 5 s afterimplantation. No new γ ray has been found in comparison to Ref. [14], but the inset shows a moreprecise half-life determined from 100In’s γ-ray gates. Bottom: absolute intensities of the γ raysbelonging to 100In and the annihilation events. In comparison to other γ-ray intensities, both 95-and 141-keV γ rays are likely M1 transitions.94a value of 1.19(10) s. This result is consistent with T1/2 = 1.16(20) s reported by Hinke et al.[14], and is more precise. γγ coincidence relations were established among the 95/141/435/1297-keV γ rays, and one coincidence event of a 96-2048 γγ pair was found. Unfortunately, the totalcoincidence projections built by gating on all of the γ rays in 100In (red bins of Fig. 4.31) did notreveal a new transition. However, the intensity analysis has addressed certain questions. First,both the 95- and 141-keV transitions are likely M1 transitions; this was expected and assumed inthe literature. Second, the intensities of the 1297 and 2048 keV suggest a parallel branch whichfeeds a common excited state that hosts a cascade of the low-energy transitions. Two level schemesof 100In proposed in the frameworks of Coraggio [15], and Stone and Walters [16] are drawn withexperimental γ-ray energies in Fig. 4.32. Each level scheme is discussed below, in view of theexperimental information.The “Coraggio” [15] level scheme on the left of Fig. 4.32 proposes an isomeric 2+ state justabove the 6+ ground state, and places the 2048-keV as a side branch. Since the sum of the 95-141-435-1297 keV γ-ray energies is 1968 keV, the missing γ-ray energy must be at least 80 keV toensure that the ground state of 100In is 6+ as suggested by experimental data. There are threemain objections: first, the energy of the 2+ isomer is too low compared to 482 keV predicted by theSM calculation in the gds model space. Second, the isolation of the 2048-keV transition forces anagreement in intensity between the 1297 keV and the three low-energy γ rays in Fig. 4.31; the 1297-keV γ ray is weaker in intensity by approximately 2σ. Third, the minimum energy requirement ofthe missing transition raises the expected detection counts significantly, but the data shows no newγ ray.The “Stone and Walters” [16] level scheme, drawn in the middle of Fig. 4.32 also places the2048-keV γ ray in parallel with the 1297 keV, but the rest is more sophisticated. The yrast statesform a decay cascade of 95-141-435 keV with an unknown energy y, and the 2+ state populatedby the 1297-keV γ ray has three unobserved γ-ray branches; their energies are 751, ∼1000, and1186 keV. The validity of this level scheme depends heavily on the detection of the missing γ-rayenergies, and the best agreement with the experimental intensities of the known γ rays can beachieved if the 751-keV transition is the only decay branch. However, there were no counts within±2 keV of the 751-keV and the 1186-keV peaks in Fig. 4.31. In the search of an intermediate γ-rayenergy, the most prominent peak was found at 1040 keV with 6 counts - more than 3σ lower inintensity than the 1297-keV γ ray with 26(5) counts.The third alternative is to suggest a second β-decay branch to another 1+ state. Most of theγ-ray information provided in Fig. 4.31 is satisfied by the level scheme on the right of Fig. 4.32, withemphasis on resolving the relative intensities of the detected γ rays. The non-detection of a low-energy 5+ → 6+ γ ray is still assumed. The main contention for this level scheme is the populationof two different 1+ states. This would be reflected by distinct Qβ values, and the centroid of theQβ distribution gated on the 2048-keV γ ray is lower than those produced from other γ-ray gates(see Fig. 4.33). However, due to large uncertainties it is not a strong evidence for two 1+ states.Theoretically, the possibility of an energy difference of 2048− 1297 = 751 keV between the two 1+95100 In (Coraggio)0 (6+ )> 80 (5+ )(4+ )(3+ )x (2+ )(2+ )~2100 (1+ )100 In (Stone andWalters)0 (6+ )y (5+ )(4+ )(3+ )z (3+ )(2+ )1422+y (2+ )2719+y (1+ )100 In (decay to two 1+ states)0 (6+ )y (5+ )(4+ )(3+ )(2+ )1968+y (1+ )2719+y (1+ )4351297204820481297435751~1000 118612972048435Figure 4.32: Level schemes of 100In constructed from experimental results in the theoretical frame-works of two works: by Coraggio [15] and by Stone and Walters [16]. The dashed arrows andenergy labels in red indicate predicted but experimentally unobserved γ rays. The level scheme onthe right assumes a fragmentation of the β-decay branch into two final (1+) states, which satisfiesthe experimental results but requires a very unlikely breakdown of the Z = 50 shells.96states is very low. During the β decay, a proton from the g9/2 orbital below the Z = 50 shell gapis converted into a neutron in the g7/2 orbital above the N = 50 shell gap; a hypothetical, secondproton hole-neutron particle combination resulting in Jpi = 1+ is only possible for a pig7/2 or a pid5/2proton above the magic number 50 coupled to the νg7/2 neutron. In the current SM, promoting ag9/2 proton across the Z = 50 shell requires at least 4 MeV in excitation energy. Thus, bringingdown the second 1+ state to within 1 MeV of the yrast 1+ state in 100In requires a severe quenchingof the Z = 50 shell gap. This is contradicted by the agreement between the experimental BGTvalue and the theoretical calculations of the large scale shell model (LSSM) that assumes a robust100Sn core. The LSSM calculations are described in the Supplementary Information of Ref. [14].Energy (keV)0 1000 2000 3000 4000 5000Counts / 200 keV0510152025 = 1496(79) keVµ 435: ≤ = 1359(122) keVµ1297:  = 1077(226) keVµ2048: µµµFigure 4.33: Positron energy spectra of 100Sn β decays for different γ-ray gates, and their centroidenergies. A lower but not inconsistent centroid value is observed for the Qβ spectrum obtained bygating on the 2048-keV γ ray.Of the first two proposed level schemes of 100In, neither one satisfies the experimental resultscompletely. Considering the mass predictions for 100Sn, subtracting the Qβ and the 1.022-MeVannihilation energy from QEC results in Ex ranging from 2158 keV from AME2012 [112] to 2968keV from HFB27 [111]. Both level schemes’ (1+) energies fall close to these values. If the QECvalue and the excitation energy were scaled by identical energies, the log(ft) and the BGT valuesremain identical. Thus a single log(ft) and BGT value was evaluated, including the assumptionof the lowest excited state energy being at most 100 keV. A systematic uncertainty of this valuewas added to the calculations, yielding log(ft) = 3.01(12) and BGT = 3.7(10). The log(ft) valuehas increased from the value of 2.62+0.13−0.11 [14] but remains as the smallest in all of the known βdecays. The BGT value has decreased significantly from 9.1+2.6−3.0, owing to the greater Qβ evaluatedin Fig. 4.13. The log(ft) and BGT values agree with the empirically extrapolated values of log(ft)97= 2.87(5) and BGT = 5.21(60) [119] within 2σ. The experimental BGT value also agrees withBGT = 5.68 received by the yrast 1+ state in 100In from LSSM calculations.For the level scheme on the right with two β-decay branches, the branching ratios/log(ft) valuesof the two 1+ states based on relative γ-ray intensities are 63(11)%/3.21(14) and 37(11)%/3.06(19)for the 1297- and 2048-keV transitions, respectively. The partial BGT values and their sum are2.4(4) + 3.3(10) = 5.7(11). Herein lies another problem for this level scheme: the BGT value ishigher for the non-yrast 1+ state, which is strongly contradicted by the LSSM calculation thatpredicts 69% of the total BGT carried by the yrast 1+ state.4.4.8 Low-spin structure of 101In and the ground-state spin of 101SnThe ground state spin of the Z = 50, N = 51 nucleus 101Sn and the structure of the β-decaydaughter nucleus 101In was investigated with β-delayed γ rays. As mentioned in Section 1.3.4, theground state spin of 101Sn has been a controversial topic. The νg7/2 orbital above the N = 50 shellgap is expected to lie close in energy with the νd5/2 orbital, but multiple works [66, 67, 120] havediffered on the order of the two orbitals.One of the ways to determine the ground state spin of 101Sn was an analysis of the βp data.However, the results obtained in this experiment was similar in statistics and quality compared tothe results discussed in the thesis work by K. Straub [18], which did not yield a definitive statementon the spin of 101Sn. An alternative approach via the β-delayed γ-ray data analysis is thus presentedhere. As shown in Fig. 4.34, five γ rays have been found. This work finds no evidence of 352-keVand 1065-keV transitions reported in Ref. [17]. γ rays at 1347, 1500, and 1508 keV were firstobserved and noted in Ref. [18], where the 352/1065-keV γ rays were also absent. However, nosignificant γ-ray intensities at 252, 1281, or 1332 keV were observed, as reported in Straub’s work.The decay branching ratios and log(ft) values calculated using the literature QEC value of8.30(42) MeV are listed in Fig. 4.35, which also shows a comparison between the proposed levelscheme and the SM results. The SPEs and TBMEs used for this SM calculation result in a 7/2+ground state for 101Sn with a 52-keV energy difference to the yrast 5/2+ state. When taking intoaccount some energy scaling, the first three lowest-energy transitions are in agreement with thelevels with spins 5/2+, 7/2+, and 9/2+ from the SM calculations. Decay branches from thesestates to the yrast 11/2+ state are expected to be small; the transition energies to the ground stateare much larger than to the 11/2+, and the multipolarities of the transitions do not hinder theirdecays to the ground state of 101In. Based on the level spacing, the 1347-keV γ ray was assignedto depopulate the first (7/2+) state. Being nearly degenerate, the assignment of the state spins forthe 1500- and 1508-keV γ rays was left ambiguous between either a (5/2+) or a (9/2+) state. Inthis energy range, the number of available states for β-decay feeding matches the number of γ raysif the ground-state spin of 101Sn is 7/2+.For the two higher-energy γ rays discovered in this work, the SM predicts three near-degeneratestates with spins between 5/2+ and 9/2+. Here, it is more feasible to suggest 5/2+ as the ground-state spin of 101Sn as the β-decay branch to the third 9/2+ will be heavily suppressed. The number98Energy (keV)1200 1400 1600 1800 2000 2200Counts / 1.5 keV051013471500150821162157128113331065250 300 350 400 450 5000100200 511252 352Figure 4.34: γ-ray spectrum following 101Sn β decay. The inset shows the amplitude of the 511-keV γ-ray peak, which is a relevant information in determining the ground-state spin of 101Sn.Red energy labels indicate unobserved γ-ray transitions that have been previously reported inRefs. [17, 18].99of γ rays then matches the number of states fed by β decays. However, the probability that at leastone transition was unobserved is rather high due to the lack of statistics caused by a small β-decaybranch and a lower EURICA efficiency.101 Sn0 (5/2, 7/2+ )101 In0 (9/2+ )1347 (7/2+ )1500 (5/2, 9/2+ )1508 (5/2, 9/2+ )2116 (5/2-9/2+ )2157 (5/2-9/2+ )101 In gds0 9 /21+1432 11 /21+1518 7 /21+1661 9 /22+1712 5 /21+1972 11 /22+21779 /23+2226 7 /22+2286, 2290 11 /23, 5 /22+134715001508211621574.9(2) 33(6)%4.9(2) 15(4)%5.0(2) 11(4)%5.0(2) 8(3)%4.9(3) 6(3)%4.8(2) 9(3)%log ft I βFigure 4.35: Level scheme of 101In deduced from the observed β-delayed γ rays in Fig. 4.34 andthe predicted states from the SM calculations in the gds model space. Beside each experimentallydeduced excited states, β-decay branching ratios and corresponding log(ft) values are listed - allof which suggest allowed GT decays (∆J ≤ 1).One item of note is the significant β-decay branch to the ground state of 101In determinedfrom the analysis of the 511-keV γ-ray intensity. From the spin selection rules of the GT decay, βdecays from a 5/2+ state to a 9/2+ state are forbidden. However, the log(ft) value of the ground-state to ground-state decay is typical of a ∆J = 1 and parity-conserving transition, which is thedecisive evidence for the ground-state spin of 101Sn being 7/2+. If this supposition is true, then101Sn’s ground state becomes rather unique; even-Z, N = 51 isotones from Mo to Cd isotopes haveJpi = 5/2+ as the ground state, which is also true for odd-A Sn isotopes from A = 103 to 109. Theinversion of the order of the two states occurs in 111Sn [121]. The order of the near-degenerate g7/2100and d5/2 orbitals for101Sn is a sensitive probe of the strength of the two-body tensor force [68]which supports the (7/2+) ground-state assignment. From the tensor force effects, the repulsionbetween the negative-parity h11/2 orbital and the positive-parity g7/2 orbital causes the lowering ofthe g7/2 orbital below the d5/2 orbital in101Sn.101Chapter 5Summary and outlookThe decay spectroscopy experiment on 100Sn and nuclei in its vicinity has yielded many new andintriguing results. Many of these results are consistent with theoretical predictions, but several ofthem have raised new questions. International efforts to investigate these isotopes in greater detailin the future are mentioned.5.1 Highlights of the results and implicationsA summary of the results and discussions in Chapter 4 is reiterated here.5.1.1 Isomer γ-ray spectroscopy and isomeric ratiosHalf-lives of many isomers decaying by γ-ray emission were measured with consistent results com-pared to literature values. In addition, new half-life and energy measurements of several isomersin 95,96Ag and 98Cd led to new transition strengths that were consistent with theoretical calcula-tions. The sharp cutoff model was relatively successful in reproducing the relative isomeric ratios ofboth the γ-decaying isomers and β-decaying isomers, and its deficiencies were reasonably explainedby the structure effects. No isomeric states were found in 100Sn, and the decay properties of itshypothetical (6+) isomer were estimated: Eγ > 140 keV, and T1/2 < 300 ns.In 96Cd, a cascade of 8 new γ-ray transitions were found to be emitted from a single isomericstate with T1/2 = 199(26) ns. The γ-ray energies could be conveniently arranged to be consistentwith the energy gaps of the excited states predicted by SM calculations in the pg and the gds modelspaces. Based on the range estimate of the electromagnetic transition strength, the multipolarityof the isomeric transition was postulated to be E1. The spin and parity this isomer is likely to be(13−), but (12−) is not completely ruled out. 96Cd is now the heaviest even-even N = Z nucleuswith experimental information on its excited states, whose SPEs may be relevant for determiningthe wavefunction of the ground state of 100Sn.5.1.2 β, βp spectroscopy of N ∼ Z ∼ 50 nucleiHalf-lives and Qβ values of N ≤ Z ≤ 50 nuclei were either measured for the first time, or withgreater precision than literature values. The derived QEC values of these nuclei were generallylower than the predicted mass differences from various models. No model was able to predict all ofthe measured QEC values accurately. Furthermore, odd-odd N = Z nuclei are more bound than102the theoretical predictions. In relation to the current estimates, the attractive T = 1, Tz = 0 pninteraction contribution to the ground state may be greater in magnitude.Unlike other odd-Z, N = Z − 1 nuclei 89Rh and 93Ag, 97In has been shown to decay primarilyby β-decay. Nevertheless, circumstantial evidence for a near-degenerate proton-emitting isomericstate was also found. The spin of this isomer was postulated to be (1/2−), where overcoming thecentrifugal barrier for proton emission is easier from the p1/2 orbital (l = 1) than from the g9/2orbital (l = 4). The derived Sp (proton separation energy) values for the two states lie midwaybetween −1.2 and 0 MeV, the range given by the different mass models.5.1.3 β/βp-delayed γ-ray spectroscopyMany new results obtained from γ rays following β and βp decays revealed the low-spin structure ofnuclei around 100Sn, complimenting the high-spin structure of such nuclei previously investigatedby fusion-evaporation experiments.The decay properties 90mRh were analyzed in detail with γ rays known to belong in 90Ru.In addition, two newly observed γ rays are suggested to depopulate the non-yrast (6+) states,reinforcing the theoretical prediction of the spin of the isomer being (7+).From the β decay of 92Pd, the energy of the (1+) state in 92Rh was experimentally determinedto be 257 keV above the (2+) isomer. This was predicted by the SM with a ∼ 100 keV energydifference. In addition, the half-life and the decay of 92mRh were better measured compared toliterature.The measured γ rays following β and βp decay of 96Cd confirmed the previous level schemesof 96Ag and 95Pd, adding more evidence to the (16+) isomer formed by the T = 0 pn interaction.Unlike 92Pd, the β decay of the ground state of 96Cd appears fragmented into multiple 1+ statesin 96Ag, based on at least 7 new γ rays. More abundant γ ray statistics would be needed to verifythe accuracy of the SM predictions of 96Ag’s low-spin states up to 4 MeV in excitation energy.Three new γ rays have been measured from the β decay of 97Cd, and they are attributed to thedecay of the newly proposed (1/2−) isomer. This makes 97Cd a unique nucleus exhibiting both thespin-aligned isoscalar pn isomer and the spin-gap isomer formed by the excitation of a proton inthe p1/2 orbital. The γ-ray energies are consistent with the excitation energies of predicted (3/2−)states relative to the 1/2− state in 97Ag, and the half-life of 97Cd’s (1/2−) isomer agreed well witha theoretical prediction. While these results reinforce the robustness of the SM in the 100Sn region,the excitation energy of the isomer and the properties of the 1/2− state in 97Ag need to be knownto establish a solid understanding of negative-parity states in the nuclei around 100Sn.Evidence for the spin of 98mIn formed by the pn hole pair being (9+) was found with a γ-raycascade of the well-known seniority level scheme in 98Cd. In addition, signatures for this isomer’s βdecay into 98Cd’s core-excited (10+) state was also found. From new measurements of βp-delayedγ rays of the (9+) isomer, two states with spins (15/2+) and (11/2+) in 97Ag were revealed. Theenergies and the decay branches of these states are well reproduced in the SM.Many new γ rays were discovered from the β decay of 99In into the N = 51 nucleus 99Cd,103yielding a glimpse of many daughter states with expected spins from 7/2+ to 11/2+. Limited γγcoincidence relations of the weak transitions were used to establish a tentative level scheme up to5 MeV in excitation energy, but the disagreement with SM calculations of level energies was up to1 MeV. Sufficient statistics will be necessary to solidify the low-spin states of 99Cd and performsensitive tests of the single-particle energies of the neutron orbitals across the N = 50 shell forproton-rich nuclei.Despite higher statistics compared to any previous 100Sn experiment, the level scheme of 100Inremains undetermined. The intensities of the two highest-energy transitions suggest two parallel γ-ray decay branches, which ultimately feed a common state for the three low-energy γ rays. However,the non-observation of γ rays predicted by the SM and LSSM calculations has made the agreementbetween the experimental γ-ray spectrum and the proposed level schemes inconclusive. On theother hand, proposing two close-lying 1+ states to resolve the non-observation of new γ rays is onlypossible if the Z = 50 shell is heavily quenched to allow less than 1 MeV excitations into the g7/2and d5/2 orbitals. Based on the properties of nuclei and their decays studied in the SM framework,such an extreme breakdown of the Z = 50 shell is quite unreasonable. The experimental BGT valueof the superallowed GT decay of 100Sn was determined to be 3.7(10) assuming a 100% β-decaybranch to the yrast (1+) state in 100Sn, consistent with the experimental extrapolation and theLSSM calculations assuming robust N = Z = 50 shell closures for 100Sn. The interpretation ofthe GT decay of 100Sn and the structure of 100In still depend on sensitive measurements of boththe γ-ray data and β energies, requiring even higher statistics to address the discrepancy betweentheoretical and experimental results.The analysis of the β-delayed γ rays of 101Sn suggest its ground state spin to be (7/2+) ratherthan (5/2+), which implies the lowering of the neutron g7/2 orbital below the d5/2 for this nucleus.The primary basis of this argument lies with a 33(6)% direct β-decay branch to the (9/2+) groundstate of 101In, deduced from the γ-ray intensity of the 511-keV annihilation peak. The number ofother γ rays attributed to 101In is also more compatible with the (7/2+) assignment, where SMcalculations offer more available states with spins between (5/2+) and (9/2+). This spin assignmentis supported by the prediction of two-body tensor forces [68]. The spin of 101Sn’s ground state canbe further solidified by determining the exact low-spin structure of 101In with higher γ-ray statistics.5.2 Prospective experiments in the 100Sn regionEURICA has been operational at RIKEN for 5 years for many decay spectroscopy experimentcampaigns, but it has been relocated back to GSI. Hypothetically, a full EURICA array (abouttwice the γ-ray singles efficiency) combined with the current primary beam intensity of 124Xe being100 pnA (5 times more than this experiment) raises the amount of γ-ray statistics by an orderof magnitude, and approximately 20 times the γγ coincidence statistics. Two major potentialsetbacks would be the diminishing returns from high implantation rates (increased backgrounddecay correlations and deadtime losses), and the available beam time for a decay spectroscopy104experiment in the 100Sn region.A total absorption spectroscopy (TAS) experiment for N ∼ Z ∼ 50 isotopes is being proposedby A. Algora [122] at RIKEN. One advantage of this setup is the ability to capture the full energiesof β particles with large Qβ, which proved to be difficult with WAS3ABi. Improved precisionsin QEC measurements of nuclei near the proton dripline are expected. However, the TAS exper-iment is better complemented with high-statistics γ-ray data with sufficient γγ coincidences as aforeknowledge of the daughter nuclei’s structure and β-decay intensities.An intermediate-energy Coulomb excitation of 102Sn is being proposed by M. L. Corte´s [123] atRIKEN. The primary objective of the experiment is to probe the evolution of the B(E2; 0+ → 2+)trend in the Sn isotopes towards 100Sn, which yields a hint on the inertness of the Z = 50 core in100Sn. During the Coulomb excitation, Doppler-shifted γ rays from 102Sn’s yrast 2+ state will bemeasured with NaI crystals. From simulations of the γ-ray spectrum, the Coulomb excitation crosssection will be measured, which then can be translated into the B(E2) value.In the long term, GSI will be upgraded into FAIR (Facility for Antiproton and Ion Research)[124] with the DESPEC (DEcay SPECtroscopy) project [125, 126] in mind. In addition to meet-ing other major physics goals, FAIR will be capable of providing an intense beam of 100Sn andnuclei in its vicinity with the identical fragmentation-separation method at RIBF. Similar to theEURICA-WAS3ABi setup but with better overall capabilities, DEGAS (DEspec Germanium ArraySpectrometer) [127] and AIDA (Advanced Implantation Detector Array) are being developed. Thehigher kinetic energy of the radioactive isotopes produced at FAIR will enable a greater coverageof the implantation area for β-decay spectroscopy. On the other hand, FRIB (Facility for RareIsotope Beams) [128, 129] at Michigan State University is under construction. The proton-rich nu-clei produced from FRIB will be complemented with highly-efficient GRETA (Gamma-Ray EnergyTracking Array, which is the full 4pi solid angle coverage version of GRETINA [130]) to study thein-flight decays of 100Sn and nuclei near the proton dripline.105Bibliography[1] T. Faestermann, M. Go´rska, and H. Grawe. Prog. Part. Nucl. Phys., 69:85, 2013.[2] G. Audi et al. Chin. Phys. C, 36:1157, 2012.[3] R. Kru¨cken. Contemp. Phys., 52:101, 2011.[4] H. Okuno, N. Fukunishi, and O. Kamigaito. Prog. Theor. Exp. Phys., page 03C002, 2012.[5] S. Nishimura. Prog. Theor. Exp. Phys., page 03C006, 2012.[6] J. Eberth et al. Nucl. Phys. A, 520:669c, 1990.[7] Z. Y. Xu. PhD thesis, University of Tokyo, 2012.[8] B. S. Nara Singh et al. Phys. Rev. Lett., 107:172502, 2011.[9] D. S. Delion, R. J. Liotta, and R. Wyss. Phys. Rep., 424:113, 2006.[10] I. Mukha et al. Phys. Rev. Lett., 95:022501, 2005.[11] I. Mukha et al. Nature, 439:298, 2006.[12] R. Ma˘rginean et al. Phys. Rev. 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Gade, and I-Y. Lee. Ann. Rev. Nucl. Part. Sci., 66:321, 2016.111Appendix Aγ-ray gates for isomer T1/2determinationHalf-lives of γ-decaying isomers shown in Fig. 4.2 were obtained by applying γ-ray gates on thefollowing energies and fitting their time profiles:Table A.1: γ-ray gates used to obtain half-lives of isomeric states presented in Fig. 4.2.Nucleus Jpi γ ray gate energies (keV)88Zr 8+ 272, 399, 671, 1057, 108390Nb (11−) 813, 996, 106790Mo 8+ 810, 948, 105492Mo 8+ 148, 330, 773, 151092Tc (4+) 21492Ru (8+) 818, 866, 99193Ru (212+) 544, 139294Pd (19−) 1545, 165114+ 94, 324, 347, 660, 745, 814, 905, 994, 109296Pd (8+) 106, 325, 384, 141596Ag (19+) 4167, 4265(15+) 630, 66798Ag (3+) 10798Cd (12+) 4207, 3696, 3185 (511-keV escape peaks)(8+) 4207(start), 147 (stop)(6+) 147 (start)/688, 1395 (stop)112Appendix BElectromagnetic transition strengthsThe total electromagnetic transition rate λtot of an excited state, when converted from classicalelectromagnetic theory to quantum mechanics, isλtot =(Eγh¯c)2`+1 8pi(`+ 1)`[(2`+ 1)!!]2h¯B(σ`). (B.1)The total angular momentum difference (in h¯) is `. B(σ`) is the reduced transition strength:B(σ`) =12Ji + 1∣∣∣〈Ji|Mˆ(σ`)|Jf 〉∣∣∣2 , (B.2)where Mˆ(σ`) is the transition operator. The distinction between electric and magnetic radiationis indicated by σ. By determining the transition rate from the data, the experimental transitionstrength can be obtained for comparison with theoretical calculations.The total transition rate λtot of the excited state must be scaled by the branching ratio b andthe total internal conversion coefficient αγ in the following manner:λγ = λtotb1 + αγ=ln 2T1/2· b1 + αγ. (B.3)Independent of the experimental quantities, the multipolarity constantK(σ`) =(h¯c)2`+1`[(2`+ 1)!!]2h¯8pi(`+ 1)(B.4)can be tabulated for each type of electric and magnetic radiation. The simplified formula for B(σ`)in terms of K(σ`) and the experimental observables is:B(σ`) = K(σ`)E−(2`+1)γ(ln 2T1/2)(b1 + αγ). (B.5)Numerical values for K(σ`), BW (E`) and BW (M`) up to ` = 6 are provided below:113Table B.1: Numerical values of electromagnetic transition parameters.E` K(E`) [in e2fm2`MeV2`+1s] BW (E`) [in e2fm2`]E1 1.590× 1015 6.446× 10−2A2/3E2 1.225× 109 5.940× 10−2A4/3E3 5.708× 102 5.940× 10−2A2E4 1.697× 10−4 6.285× 10−2A8/3E5 3.457× 10−11 6.929× 10−2A10/3E6 5.108× 10−18 7.884× 10−2A4M` K(M`) [in µ2N fm2`−2MeV2`+1s] BW (M`) [in µ2N fm2`−2]M1 1.758× 1013 1.790M2 1.355× 107 1.650A2/3M3 6.312 1.650A4/3M4 1.876× 10−6 1.746A2M5 3.823× 10−13 1.925A8/3M6 5.648× 10−20 2.190A10/3114Appendix CProton emission T1/2 as a function of `and QpThe equations and several constants are taken directly from Ref. [9]. Starting with the reducedhalf-life for proton emission TredTred =T1/2C2l, (C.1)where Cl is the centrifugal barrier functionCl(χ, ρ) = exp[l(l + 1)χtanα], cos2 α =QpV 0C(R). (C.2)The Coulomb potential V 0C(R) has the common formV 0C(R) =ZDe2R, (C.3)where ZD is the atomic number of the daughter nucleus after single proton emission and R =1.2(A1/3D + A1/3p ) fm is the matching radius. In Ref. [9], experimental data was used to obtain anempirical formula for Tred:log10 Tred = a(χ− 20) + b, (C.4)where a = 1.31 and b = −2.44 for Z < 68 nuclei, the atomic number where a sudden change indeformation occurs. For Z > 68, a = 1.25 and b = −4.71. The dimensionless Coulomb parameterχ isχ =2ZDe2h¯v(C.5)where v = h¯k/µ =√2Qp/µ is the velocity of the outgoing proton and µ = mDmp/(mD + mp) isthe reduced mass of the proton-daughter system.Putting the equations together, the T1/2 of proton emission as a function of Qp islog10 T1/2 =1ln 10[h¯ZDe2√2Qpµl(l + 1) tan(cos−1√QpRZDe2)]+a(2ZDe2h¯√µ2Qp− 20)+b. (C.6)115The values of the constants are:h¯ = 197.32697 MeV · fm (in units of h¯c); (C.7)e2 = 1.4399764 MeV · fm. (C.8)116

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