Hindrance factors of unfavored α decay transitions to duplicated daughter states of the same spin and parity

Abstract

We investigate the hindrance of the unfavored α-decay modes to the different daughter states, which have different spin than that of the parent nucleus but of the same parity. The duplicated daughter nucleus states of identical spin-parity (Jπ) are ascendingly ordered according to the sequence of their excitation energy. We found that the hindrance of the unfavored decay modes increases with increasing the difference in spin (ΔJ) between the parent and daughter states. This hindrance slightly increases when the daughter state has less spin than the parent. The preformation probability (Sα) decreases with ΔJ and the decay slows down. Furthermore, the increase of the order (n) of the state to which the decay takes place brings the decay intensity drop significantly and decrease. Consequently, the partial half-life strongly increases with n. The hindrance factor averagely drops from few tenths, for an unfavored decay mode to first appearing state of a certain Jπ, to about 10−9 for the decay mode to the identical excited state that appear for the sixth time. The associated half-lives accordingly increase with the reciprocal ratios. The value of the corresponding preformation probability drops about 3 orders of magnitude. Simple formulas are given to describe the hindrance of both the unfavored decay intensity and Sα as functions of ΔJ and n.