The Generalized Liquid Drop Model Alpha-Decay Formula: Predictability Analysis and Super-Heavy Element Alpha Half-Lives

Abstract

The predictive accuracy of the generalized liquid drop model (GLDM) formula for alpha decay half-lives has been investigated in a detailed manner and a variant of the formula with improved coefficients is proposed. The method employs the experimental alpha half-lives of the well-known alpha standards (REFERENCE) to obtain the coefficients of the analytical formula using the experimental Qalpha values (the DSR-E formula), as well as the finite range droplet model (FRDM) derived Qalpha values (the FRDMFRDM formula). The predictive accuracy of these formulae were checked against the experimental alpha half-lives of an independent set of nuclei (TEST) that span approximately the same Z,A region as the standards and possess reliable alpha spectroscopic data, and were found to yield good results for the DSR-E formula but not for the FRDM-FRDM formula. The two formulae were used to obtain the alpha half-lives of super-heavy (SHE) and heavy nuclides where the relative accuracy was found to markedly improve for the FRDM-FRDM, which corroborates the appropriateness of the FRDM masses and the GLDM prescription for high Z,A nuclides. Further improvement resulted, especially for the FRDM-FRDM formula, after a simple linear optimization over the calculated and experimental half-lives of TEST was used to re-calculate the half-lives of the SHE and heavy nuclides. The advantage of this optimization was that it required no recalculation of the coefficients of the basic DSR-E or FRDM-FRDM formulae. The halflives for 324 medium-mass to super-heavy alpha decaying nuclides, calculated using these formulae and the comparison with experimental half-lives, are presented.