Cluster radioactivity using various versions of nuclear proximity potentials

Abstract

The systematic study of doubly closed shell ${}^{208}\mathrm{Pb}$-daughter cluster radioactivity using different versions of proximity potentials within the preformed cluster-decay model is extended to daughter nuclei other than ${}^{208}\mathrm{Pb}$. The nuclear proximity potentials used in the calculation of total interaction potential cover a wide range of barrier characteristics. The decay half-life of the cluster changes significantly with the use of these different potentials because of the corresponding change in the preformation probability (${P}_{0}$) and penetration probability ($P$) of the cluster. The cluster radioactivity is worked out at touching as well as at an elongated neck configuration by taking the neck-length parameter $\ensuremath{\Delta}R=0.5$ fm. In order to observe the effect of deformation, the spherical fragmentation of clusters is also taken into account and the standard root-mean-square (rms) deviation is also compared for the various nuclear proximity potentials. It is observed that Prox 1977 reproduces the experimental half-lives very well at $\ensuremath{\Delta}R=0.5$ fm and further improves upon the value obtained in previous work. Thus Prox 1977 turns out to be a better option for studying the cluster decay of radioactive nuclei; however, the calculated half-lives of ${}^{14}\mathrm{C}$ clusters are still poor. With the use of mod-Prox 1988, having stronger isospin and asymmetry dependence, the comparison for ${}^{14}\mathrm{C}$ clusters improves significantly and the standard rms deviation from experimental half-lives comes out to be 1.01 and 1.46 for spherical and deformed choices of fragmentation, respectively. The standard rms deviation reported for various proximity potentials can be further improved if the precise experimental half-lives of 15, out of the 45 clusters used in present study, are made available. Till now only lower limits are available for these clusters. The barrier characteristics of various interaction potentials obtained using different nuclear proximity potentials are also explored in the context of ground-state cluster radioactivity. The new cases of ${}^{34}\mathrm{Si}$ decay of ${}^{238}\mathrm{U}$ and ${}^{14}\mathrm{C}$ and ${}^{15}\mathrm{N}$ decays of ${}^{223}\mathrm{Ac}$ are also included in the present study of 45 clusters. Predictions of half-lives of possible cluster decays in the trans-lead region are also made using Prox 1977. The deformation effect is included with optimum cold orientations.