Preformation probability inside α emitters having different ground state spin-parity than their daughters

Abstract

The ground state spin and parity of a daughter formed in a radioactive $\ensuremath{\alpha}$ emitter are expected to influence the preformation probability of the $\ensuremath{\alpha}$ and daughter clusters inside it. We investigate the $\ensuremath{\alpha}$ 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 spin-parity of the ground states of the involved nuclei far away from any influence from the excitation energy, if the decays are coming from isomeric states. The calculations are done for $161\ensuremath{\alpha}$ emitters, with $65\ensuremath{\le}Z\ensuremath{\le}112$ and $84\ensuremath{\le}N\ensuremath{\le}173$, in the framework of the extended cluster model, with the Wentzel-Kramers-Brillouin penetrability and assault frequency. We used a Hamiltonian energy density scheme based on the Skyrme SLy4 interaction to compute the interaction potential. The $\ensuremath{\alpha}$-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 the angular momentum of the emitted $\ensuremath{\alpha}$ particle on the various physical quantities involved in the unfavored decay process and how it finally increases the half-life time. We found that if the ground state spin and/or parity of parent and daughter nuclei are different, then the preformation probability of the $\ensuremath{\alpha}$ cluster inside the parent is less than it would be if they had similar spin-parity. We modified the formula that gives the $\ensuremath{\alpha}$ preformation probability in terms of the numbers of protons and neutrons outside the shell closures of the parent, to account for this hindrance in the preformation probability for the unfavored decays between ground states.