Correlation between α-particle preformation factor and α decay energy

α-particle preformation factors, one of the most significant quantities in α decay, are systematically investigated, which are extracted from the ratios between theoretical α-decay half-lives calculated by the generalized liquid drop model and experimental data. The results indicate that both α-particle preformation factors Pα and α decay energy Qα are important observed quantities for revealing the nuclear shell structure information. And a nice linear relationship exists between log10⁡Pα and Qα−1/2, which means the famous Geiger-Nuttall law can not only describe α decay half-lives but deal with α-particle preformation factors, as well as the nuclear shell effects play key roles in α-particle preformation. Furthermore, the results indicate that Z=82 and N=126 closed shells play more important roles than Z=50 and N=82 shell closures in which the shell effect of N=126 is stronger than that of Z=82 in the α decay process. Besides, the unpaired nucleons will inhibit the preformation of α-particle. After considering the above significant physical effects, a global analytic formula with only twelve parameters for α-particle preformation factors is proposed based on the direct observation quantity of the nuclear shell effect i.e., α decay energy. The outstanding precision of this formula in describing the α-particle preformation factors indicates that it can be used to perform accurate calculations for α decay half-lives as well as provide some general guidance for microscopic study on α-particle preformation factors and nuclear structure.