A Study of β-decay and Delayed Neutron of Odd Nuclei Including Core Polarization Effect*

There are various theoretical works based on mean-field theory + quasiparticle random phase approximation (QRPA) calculating β-decay half-lives of nuclei. For the moment, they are the only approaches that are based on a microscopic theory applicable for the systematic calculation in the nuclear chart. A special attention is needed when calculating odd nuclei because of the presence of core polarization effect (CPE). However, the systematic calculation of aforementioned microscopic theories has approximated the calculation of odd nuclei in a simple way. This may cause a problem when predicting unmeasured half-lives, delayed neutron (DN) emission probabilities, etc. 

Under this background, the CPE on β-decay and DN are investigated. We assume that odd nucleus consists of active even-even nucleus and valence particle(s), and use a perturbation theory to estimate the CPE. Core phonon states to be excited are calculated by HFB + QRPA. We found the CPE mitigates an odd-even straggling of half-lives found in no CPE calculations, which is consistent with experiments.