α decay to a doubly magic core in the quartetting wave function approach

We present a microscopic calculation of a-cluster formation in heavy nuclei Te-104 (alpha + Sn-100), Po-212 (alpha + Pb-208), and their neighbors Sn-102, Te-102, Pb-210, and Po-210 by using the quartetting wave function approach. To improve the local density approximation, the shell structure of the core nucleus is considered, and the center-of-mass (c.m.) effective potential for the quartet is obtained self-consistently from the shell model wave functions. The alpha-cluster formation and decay probabilities are obtained by solving the bound-state of the c.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.