Half-life of spherical $\alpha$ emitters and intrinsic properties of nuclei

The quantum mechanical effects are investigated on the half-life of $\alpha$ decay. To this aim the penetration probability in $\alpha$ decay of spherical isotopes of ${}^{146}\mathrm{Sm},{}^{148}\mathrm{Sm},{}^{148}\mathrm{Gd}$, and ${}^{224}\mathrm{Ra}$ is calculated by employing coupled channel formalism by considering the effects of surface vibrations in the daughter nucleus; the obtained results are compared with those calculated by the semiclassical WKB approximation using two versions of the proximity potential. It is shown that by including low-lying excitation states the results are modified, in better agreement with experimental data.

Figure 1

Comparison of the calculated penetration probabilities through coupled channel approach and WKB approximation as a function of decay energy. The value of penetration probability in the $Q$ value of ${}^{148}Gd \alpha$ decay is indicated by an arrow in this figure.