Improved empirical formula for α particle preformation factor * *Supported by the National Natural Science Foundation of China (11675066, 11665019, 11947229) and Fundamental Research Funds for the Central Universities (lzujbky-2017-ot04), and Feitian Scholar Project of Gansu province

Abstract

In this contribution, the preformation factors of 606 nuclei are extracted within the framework of the generalized liquid drop model (GLDM). Through the systematic analysis of the preformation factors of even-even Po-U isotopes, we found that there is a significant weakening of influence of shell closure in uranium, which is consistent with the results of a recent experiment [J. Khuyagbaatar et al., Phys. Rev. Lett. 115, 242502 (2015)], implying that may not be the magic number for U isotopes. Furthermore, we propose an improved formula with only 7 parameters to calculate preformation factors suitable for all types of -decay; it has fewer parameters than the original formula proposed by Zhang et al. [H. F. Zhang et al., Phys. Rev. C 80, 057301 (2009)] with higher precision. The standard deviation of the preformation factors calculated by our formula with extracted values for all 606 nuclei is 0.365 with a factor of 2.3, indicating that our improved formula can accurately reproduce the preformation factors. Encouraged by this, the -decay half-lives of actinide elements are predicted, which could be useful in future experiments. Notably, the predicted -decay half-lives of two new isotopes Np [Z. Y. Zhang, et al., Phys. Rev. Lett. 122, 192503 (2019)] and Np [H. B. Yang et al., Phys. Lett. B 777, 212 (2018)] are in good agreement with the experimental -decay half-lives.