α preformation factors of medium-mass nuclei and the structural effects in the region of crossing the Z=82 shell

The a preformation factors of medium-mass nuclei as well as their behavior in the vicinity of Z = 82 shell closure are systematically investigated by using the cluster-formation model (CFM). The recently proposed CFM was proven to be effective in the evaluation of a preformation factors in the heavy-mass region, and we find that it is also valid for medium-mass nuclei because it reproduces reasonable features of the variation of a preformation probability, especially the Z = 82 shell effects which are made evident in a recent experiment. A total of 363 nuclides (including even-even, odd-A and odd-odd nuclei) with 72 <= Z <= 88 and 84 <= N <= 117 are included in our calculation. Through a comparison between Z = 82 and N = 126 shell effects, the structural effects inside the observed different behavior of preformation factors are discussed in detail. As an extended application to medium-mass nuclei, the CFM provides a convenient and effective way to extract nuclear structure information from the a preformation factor. The results in this work can be a useful reference for future analysis in the microscopic calculation of a decay.