Alpha Decay to Doubly Magic Core in Quartetting Wave Function Approach

Abstract

We present a microscopic calculation of $\alpha$-cluster formation in heavy nuclei ${}^{104}$Te ($\alpha$+${}^{100}$Sn), ${}^{212}$Po ($\alpha$+${}^{208}$Pb) and their neighbors ${}^{102}$Sn, ${}^{102}$Te, ${}^{210}$Pb and ${}^{210}$Po by using the quartetting wave function approach. Improving the local density approximation, the shell structure of the core nucleus is considered, and the center-of-mass (c.o.m.) effective potential for the quartet is obtained self-consistently from the shell model wavefunctions. The $\alpha$-cluster formation and decay probabilities are obtained by solving the bound-state of the c.o.m. motion of the quartet and the scattering state of the formed $\alpha$-cluster in the Gurvitz approach. Striking shell effects on the $\alpha$-cluster formation probabilities are analyzed for magic numbers 50, 82 and 126. The computed $\alpha$-decay half-lives of these special nuclei are compared with the newest experimental data.

16 pages, 4 figures

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