LAUSR

Shell structure effects on $\ensuremath{\alpha}$-cluster formation and decay are studied by using the quartetting wave function approach (QWFA). Both the intrinsic and center-of-mass (c.o.m.) motions of an $\ensuremath{\alpha}$ cluster inside a core nucleus are investigated with different contributing shell model wave functions. The overlap between intrinsic wave functions of four nucleons in the $\ensuremath{\alpha}$-like quartet state and in a free $\ensuremath{\alpha}$ particle is analyzed in detail. The change of the effective potential describing the c.o.m. motion of the quartet is explicitly shown for the major shell closures $Z=82$ and $N=126$. It is found that both the $\ensuremath{\alpha}$-cluster formation probability and the half-life are sensitive to the quartet shell model states. By extending the QWFA calculations from $^{212}\mathrm{Po}$ to $\ensuremath{\alpha}$ emitters with one or two extra nucleons, we show that the bound state and scattering wave functions of the $\ensuremath{\alpha}$ cluster are changed accordingly. The calculated $\ensuremath{\alpha}$-decay half-lives agree nicely with the experimental data.