Cluster radioactivity from trans-tin to superheavy region using an improved empirical formula

Abstract

A simple relation $(a{Z}_c+b)(Z_d/Q{)}^{1/2}+(c{Z}_c+d)$ of estimation of the half-life of cluster emission is further improved for cluster and $\alpha$-decays, separately, by incorporating isospin of parent nucleus as well as angular momentum taken away by the emitted particle. This improved version is not only found robust in producing experimental half-lives belonging to the trans-tin and trans-lead regions but also elucidates cluster emission in superheavy nuclei over the usual $\alpha$-decay. Considering daughter nuclei around the doubly magic ${}^{100}$Sn and ${}^{208}$Pb nuclei for trans-tin and trans-lead (including superheavy) parents, respectively, a systematic and extensive study of 56$\le$Z$\le$120 isotopes is performed for the light and heavy cluster emissions. A fair competition among cluster emission, $\alpha$-decay, spontaneous fission, and $\beta$-decay is observed in this broad range resulting in a substantial probability of C to Sr clusters from several nuclei, which demonstrates the adequacy of shell effects. The present article proposes a single, improved, latest-fitted, and effective formula of cluster radioactivity that can be used to estimate precise half-lives for a wide range of the periodic chart from trans-tin to superheavy nuclei.

Comments: 12 pages, 2 Figures, 5 Tables, Accepted in European Physics Journal A