Tensor force improved shell-model effective interaction for P And PF-shell nuclei

Abstract

Nuclear shell-model is a theoretical framework which has been extensively used for understanding the nuclear structure properties. Its success mainly depends on the choice of effective interaction. In recent years, however, attention has been shifted towards the individual components of the effective interaction, namely the central, spin-orbit, and tensor forces, due to their role in understanding shell evolution and shell gaps. Except for the spin-orbit force, the central and tensor force components possess systematic properties in shell-model effective interactions. Particularly, the tensor force monopole matrix elements originating from the bare tensor force are observed to retain systematic properties in shell-model effective interactions, and hardly change against the various renormalization procedures. However, in our observation, we found that some widely used shell-model effective interactions do not share these systematic properties. The deviations in the systematic properties may originate from the imprecise normalization of the contribution of higher-order in-medium terms and many-body force, particularly the three-body, to their initial two-body matrix elements, and/or the empirical modification based on the experimental observables. The objective of this thesis is to determine the deviations in the known systematics of the individual force components of effective interaction, and try to incorporate the missing features back into the original interaction. In our study, the spin-tensor decomposition method was used to investigate the known systematic features of the central, spin-orbit, and tensor force components of the effective interaction. The calculations in our study were carried out using a large-scale shell model framework. In our study, we found that seven out of ten T = 1 tensor force monopole matrix elements of widely used GX-interactions of pf -shell do not share the systematic properties as reported. We ameliorate this disparity by making use of Yukawa-type tensor force. The revised interaction has been tested from Ca to Ge isotopes with various physics viewpoints. The results are found to be satisfactory with respect to the experimental data. We have attempted and succeeded in incorporating the systematic properties of tensor forces to a good extent. Despite the changes to the interaction on a very large scale, we still obtained reasonable results as compared to the experimental data. Further, we have extended our theoretical investigations for p-shell. For p-shell effective interaction CK(8-16), we found that Isospin T = 0 tensor force monopole matrix elements do not share these systematic. We correct the discrepancies present in CK(8-16) interaction, and the revised interaction CKN has been tested for the calculations of excitation spectra, electromagnetic moments, and electromagnetic and Gamow-Teller (GT) transitions of p-shell nuclei of normal parity states. The results achieved using interaction CKN agree well with the experimental data and are found to improve the previously predicted theoretical results. Furthermore, our use of the analytical expression of the tensor force to improve the disparities in p and pf -shell effective interactions motivates us to apply it to higher shells, where conventional studies based on spin tensor decomposition are not feasible due to the mathematical restrictions. We have used this approach to study the significance of tensor force in the p f5g9-region, particular focus on the most visible monopole migration of p1p3=2 and p0 f5=2 orbitals when n0g9=2 orbital is filled with neutrons. The results obtained in our study from various physics viewpoints are consistent with what is stated in the literature.