Angular momentum dependence of nuclear decay of radon isotopes by emission of \(^{14}\)C nuclei and branching ratio relative to \(\alpha \)-decay

Abstract

This study aims to provide new insights into the angular momentum dependence of \(^{14}\)C-decay. To achieve this, we perform a systematic analysis of the radioactive decay of radon isotopes via \(^{14}\)C cluster emission, employing the Wentzel–Kramers–Brillouin approximation and introducing the screened Kratzer–Morse potential as an innovative nuclear potential. While the \(^{14}\)C emission from radon isotopes has not yet been identified experimentally, our study extends the classical theory of \(\alpha \)-decay to predict half-lives and branching ratios for \(^{14}\)C-decay in radon isotopes \(^{216-223}\)Rn. The results of this work indicate that low angular momentum states favor \(^{14}\)C emission, and the predicted half-lives are consistent with previous theoretical studies. On the other hand, the calculation of branching ratio relative to \(\alpha -\)decay allowed us to quantify the probability of \(^{14}\)C-decay channel for different values of l. The branching ratios suggest that radon isotopes belonging to the naturally occurring radioactive series are the most favorable regarding \(^{14}\)C emission, especially the \(^{222}_{86}\)Rn, which is prime candidate for potential experimental detection of \(^{14}\)C emission. Due to limited experimental data on \(^{14}\)C emission from radon isotopes, to validate our model we extended our calculations to other cluster decays with available half-lives, including \(^{14}\)C, \(^{20}\)O, \(^{22,24,26}\)Ne, \(^{28,30}\)Mg, and \(^{32}\)Si emissions from heavy nuclei. Our predicted half-lives values for cluster emission are validated by experimental data, especially for low angular momentum values.