Analysis of nuclear structure in the nuclear chart and improvement to the gross theory of β decay

Abstract

The gross theory, a global method for the calculation of nuclear $\ensuremath{\beta}$ decay, is improved using single-particle treatment. We analyzed the $\ensuremath{\beta}$-decay channel for the entire region of nuclides and found that the allowed transition is suppressed systematically in the neighborhood of heavier doubly magic nuclei. This is mainly due to the shift of neutron and proton single-particle levels in one major shell, which leads to a change in the spin and parity between parent and daughter nuclei. Under this consideration, the nuclear matrix elements for the allowed transition in the gross theory are suppressed in the above condition. In the vicinity of the doubly magic numbers of neutron-rich nuclides, such as nuclei with $Z=50$ and 82, the calculated half-lives are longer than those reported in previous work, where only parity mismatch was considered. In superheavy neutron-rich nuclei with $N=184$, the half-lives are predicted to be longer due to the same mechanism.