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

A simple relation $(aZ_{c} + b)(Z_{d}/Q)^{1/2} + (cZ_{c} + d)$ 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$\leq$Z$\leq$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.