The preformation probability inside Alpha-emitters having different ground state spin-parity than daughters

TL;DR

This study investigates how differences in ground state spin-parity between parent and daughter nuclei affect alpha preformation probabilities in radioactive decays, revealing reduced probabilities in unfavored decays and proposing a modified formula.

Contribution

It provides a detailed analysis of the impact of spin-parity differences on alpha preformation probabilities and introduces a modified formula to account for this hindrance in unfavored decays.

Findings

Preformation probability decreases when parent and daughter have different ground state spin-parity.

Modified formula accounts for hindrance in unfavored alpha decays.

Angular momentum influences decay half-life and preformation probability.

Abstract

The ground-state spin and parity of a formed daughter in the radioactive Alpha-emitter is expected to influence the preformation probability of the Alpha and daughter clusters inside it. We investigate the Alpha and daughter preformation probability inside odd-A and doubly-odd radioactive nuclei when the daughter and parent are of different spin and/or parity. We consider only the ground-state to ground-state unfavored decays. This is to extract precise information about the effect of the difference in the ground states spin-parity of the involved nuclei far away any influences from the excitation energy if the decays are coming from isomeric states. The calculations are done for 161 Alpha-emitters, with Z=65-112 and N=84-173, in the framework of the extended cluster model, with WKB penetrability and assault frequency. We used a Hamiltonian energy density scheme based on Skyrme-SLy4 interaction to compute the interaction potential. The Alpha plus cluster preformation probability is extracted from the calculated decay width and the experimental half-life time. We discussed in detailed steps the effect of angular momentum of the emitted Alpha-particle on the various physical quantities involved in the unfavored decay process and how it is finally increases the half-life time. We found that if the ground states spin and/or parity of parent and daughter nuclei are different, then the preformation probability of the Alpha-cluster inside parent is less than it would be if they have similar spin-parity. We modified the formula that gives the Alpha preformation probability in terms of the numbers of protons and neutrons outside the shell closures of parent, to account for this hindrance in the preformation probability for the unfavored decays between ground states.