Systematic study of α decay of nuclei around the Z=82, N=126 shell closures within the cluster-formation model and proximity potential 1977 formalism

In the present work, we systematically study the a decay preformation factors P-alpha within the cluster-formation model and alpha decay half-lives by the proximity potential 1977 formalism for nuclei around Z = 82, N = 126 closed shells. The calculations show that the realistic P-alpha is linearly dependent on the product of valance protons (holes) and valance neutrons (holes) NpNn. It is consistent with our previous works [Sun et al., Phys. Rev. C 94, 024338 (2016); Deng et al., ibid. 96, 024318 (2017)], in which P-alpha are model dependent and extracted from the ratios of calculated alpha half-lives to experimental data. Combining with our previous works, we confirm that the valance proton-neutron interaction plays a key role in the a preformation for nuclei around Z = 82, N = 126 shell closures whether the P-alpha is model dependent or microcosmic. In addition, our calculated alpha decay half-lives by using the proximity potential 1977 formalism taking P-alpha evaluated by the cluster-formation model can well reproduce the experimental data and significantly reduce the errors.