Systematic study of α-decay in neutron-deficient nuclei

The $\alpha$-decay half-lives of 266 neutron-deficient nuclei in the 52 $\le Z\le$ 118 range are calculated within the density-dependent cluster model. The realistic Michigan three-range Yukawa-Paris nucleon–nucleon interaction is used to calculate the $\alpha$-core interaction potential within the double-folding model (DFM) context. In addition to the double-folding model, four analytical formulas are employed to compute the half-life time for the neutron-deficient nuclei. The obtained results from the five theoretical approaches are compared to the most recent experimental data. The calculated results from the DFM and the universal decay law (UDL) were in good agreement with the experimental data. A universal curve for $\alpha$-decay of neutron-deficient nuclei has been analyzed, illustrating the correlation between the decimal logarithm of the experimental half-lives and the negative decimal logarithm of penetrability. We studied the variation of ${log}_{10}T$ with the neutron number of the daughter nuclei, $N_d$, for different neutron-deficient isotopes in the range 78 $\le Z\le$ 92. We attempt to predict the neutron energy levels for each isotope from the behavior of ${log}_{10}T$ against $N_d$. Moreover, the impact of higher-multipolarity deformations, up to hexacontratetrapole, on the behavior of $\alpha$-decay half-lives around the neutron shell closure $N=126$ is investigated, both with and without including octupole deformation.