Systematic study on $$\alpha $$-decay half-lives: a new dependency of effective sharp radius on $$\alpha $$-decay energy

Abstract

Within the framework of the proximity formalism, we present a systematic study to analyze the effects of the $$\alpha $$ -decay energy through the effective sharp radius parameter on the $$\alpha $$ -decay half-lives of 227 nuclei in the range $$61 \le Z \le 99$$ . Wentzel-Kramers-Brillouin (WKB) calculations with the proximity potential Zhang 2013 are carried out to obtain the theoretical values of the $$\alpha $$ -decay half-lives. In this work, we introduce a new $$Q_{\alpha }$$ -dependent (QD) form of the effective sharp radius which significantly reduces the standard deviation of estimated half-lives using the Zhang 2013 model in comparison with the corresponding experimental data in our selected mass range. We evaluate the validity of this simple formula using the Geiger-Nuttall (G-N) plots and semi-empirical formulas. The modified form of the Zhang 2013 model is also found to work well in $$\alpha $$ -decay studies of superheavy nuclei (SHN) with $$Z=117-120$$ . Our results reveal that the calculated half-lives for the use of new proposed form of the effective sharp radius in the proximity potential can reproduce the closed-shell effects at neutron magic number $$N=126$$ and $$N=184$$ .