In the present work, we systematically study the α decay preformation factors Pα within the cluster-formation model and α decay half-lives by the proximity potential 1977 formalism for nuclei around Z=82,N=126 closed shells. The calculations show that the realistic Pα 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., Phys. Rev. C 96, 024318 (2017)], in which Pα are model dependent and extracted...
