Refinement of the gross theory of β-decay for odd-odd nuclei

Abstract

Abstract The gross theory of nuclear β-decay is refined for decays of odd-odd nuclei. The main refinement is to take into account the selection rule for the transition to the ground state based on a statistical consideration. The effect of the transition to the first excited 2 + state, which has not explicitly been treated in the conventional gross theory, is also included explicitly if that transition is expected to predominate over the transition to the ground state. The refined theory at this stage gives half-lives in better agreement with experiment than those by the conventional gross theory except for the parents with spin-parity 1 − . The calculated half-lives of 1 − nuclei are generally shorter than the experimental data, and it is shown that the cause for this underestimation is hindrance of the transitions between 1 − ground states of odd-odd nuclei and 0 + ground states of even-even nuclei in actual nuclei. Therefore, the theory is further refined for 1 − parents by incorporating this hindrance in a phenomenological way. While this study has improved the gross theory for β-decays of odd-odd nuclei, it has also revealed a problem inherent in the gross theory, which is briefly discussed together with the problem of half-life prediction.