Systematic study of various proximity potentials in208Pb-daughter cluster radioactivity

Abstract

Various types of nuclear proximity potentials are employed to study the cluster decay of radioactive nuclei, particularly those decaying to a doubly closed shell ${}^{208}$Pb-daughter nucleus using the preformed cluster-decay model (PCM). The deformation effect is included up to quadrupole (${\ensuremath{\beta}}_{2}$) with ``optimum'' cold orientations. The use of different proximity potentials modifies the potential barrier characteristics (i.e., barrier height, position, and frequency), which in turn change the preformation probability ${P}_{0}$ and tunneling probability $P$, and hence the decay half-life considerably. The analysis of ${}^{208}$Pb-daughter 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. A wide range of barrier characteristics is covered by using various nuclear proximity potentials. We observe that Prox 1977 and Prox 1988 can reproduce the experimental half-lives very well at $\ensuremath{\Delta}R=0.5$ fm; however, the use of the mod-Prox 1988 potential seems more reliable for ${}^{14}$C cluster decay. The relevance of barrier characteristics of other nuclear proximity potentials is also explored in the context of ${}^{208}$Pb cluster radioactivity.