SHELL MODEL STUDY OF ALLOWED AND FORBIDDEN BETA DECAYS

Abstract

The aim of the present thesis is to streamline a theoretical formalism for the compu tation of the partial half-life and electron spectral shapes of rare β decay transitions for the different regions of the nuclear chart. In the case of 24Na and 59,60Fe, exper imental data for the electron spectra are not available, so our theoretical prediction strongly encourages future measurements of the electron spectral shapes. In the lead region, the study of the 207Tl has been done corresponding to recently avail able experimental data and given some predictions from the theoretical side where the experimental data are not available. Present thesis also includes a comprehen sive study of the allowed β− decay properties for the sd shell nuclei using effective interactions recently derived from ab initio approaches. Further, to access the more accurate results of the β decay from the theoretical side, we have included the next-to-leading-order corrections in the shape factor for the forbidden β decay. In the case of the second-forbidden nonunique β− decay of 60Fe, we have made a comparison between the leading-order and next-to-leading order contribution in the partial half-life and the electron spectral shapes. Also we have analyzed the spectrum-shape method (SSM) to extract the information of the value of the effective axial-vector coupling constants gA. In the SSM, we have computed an electron spectral shape as a function of gA and then compared it with the corresponding experimental shapes in order to find the effective value of gA for which the computed spectra shapes matches with the experimental one. Also we have enhanced the SSM by constraining the small vector nuclear matrix element by tuning this matrix element to reproduce known experimental partial half-life. More details about these four novel works are summarized below. We have reported a systematic study of the logft values, shape factors and electron spectra for the second-forbidden nonunique β− decays of 24Na(4+) →24Mg(2+) and 36Cl(2+) →36Ar(0+) transitions in the framework of the nuclear shell-model. We have performed the shell-model calculations in the sd model space, using more re cent microscopic effective interactions such as Daejeon16, chiral N3LO, and JISP16. These interactions are derived from the no-core shell-model wave functions using Okubo-Lee-Suzuki transformation. For comparison, we have also shown the re sults obtained from the phenomenological USDB interaction. To test the predictive power of these interactions first we have computed low-lying energy spectra of parent and daughter nuclei involved in these transitions. The computed results for energy spectra, nuclear matrix elements, logft values, shape factors, electron spectra and decomposition of the integrated shape factor are reported and compared with the available experimental data. Wepresent a theoretical study of the electron spectral shapes for the second-forbidden nonunique β−-decay transitions 59Fe(3/2−) → 59Co(7/2−) and 60Fe(0+) → 60Co(2+) in the framework of the nuclear shell-model. We have computed the involved wave functions by carrying out a complete 0ω calculation in the full fp model space using the KB3G and GXPF1A effective interactions. When compared with the available data, these interactions predict the low-energy spectra and electromagnetic proper ties of the involved nuclei quite successfully. This success paves the way for the com putations of the β-decay properties, and their comparison with the available data. We have computed the electron spectral shapes of the mentioned decay transitions as functions of the value of the weak axial coupling gA. By comparing these com puted shapes with the measured spectral shapes allows them to extract the effective value of gA for these decay transitions. This procedure, coined the spectrum-shape method (SSM) in several earlier studies, complements the method of determining the value of gA by reproducing the (partial) half-lives of decay transitions. Here we have enhanced the original SSM by constraining the value of the relativistic vector matrix element, V M(0) KK−11, using the conserved vector-current hypothesis (CVC) as a starting point. Our finding would be a strong incentive to measure the spectral shapes in the future. In the Pb region, we have performed large-scale shell-model calculations for the first forbidden β− decay of 207Hg into the one-proton-hole nucleus 207Tl corresponding to the recently available experimental data from ISOLDE-CERN. We have used the one-particle one-hole (1p-1h) truncation for both protons and neutrons simultane ously across the doubly-shell closure at 208Pb in the final states of 207Tl. In our calcu lations, we have also considered the effect of masonic enhancement mec = 2.01±0.05 in the rank-0 for the axial-charge matrix element γ5. Here, we have calculated the log ft values from the ground-state of 207Hg to the several excited states of 207Tl and obtained a good agreement between the calculations and the experimental data. In the experimental data spin and parity for some states are not yet confirmed, thus based on the shell-model results for the logft values we have given the prediction for these states. This is the first theoretical calculation for the logft values for these transitions. For the sd-shell nuclei, we evaluate the allowed β−- decay properties of nuclei with Z = 8−15 systematically under the framework of the nuclear shell-model with the use of the valence space Hamiltonians derived from modern ab intio methods, such as in-medium similarity renormalization group and coupled-cluster theory. For comparison we also show results obtained with fitted interaction derived from the chiral effective field theory and phenomenological USDB interaction. Theoretical results of B(GT), logft values and half-lives, are discussed and compared with the available experimental data.