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

We present a microscopic calculation of α-cluster formation in heavy nuclei Te104 (α+Sn100), Po212 (α+Pb208), and their neighbors Sn102,Te102,Pb210, and Po210 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 α-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 α cluster in the Gurvitz approach. Striking shell effects on the α-cluster formation probabilities are analyzed for magic numbers 50, 82, and 126. The computed α-decay half-lives of these special nuclei are compared with the newest experimental data.