Phenomenological formula for alpha-decay half-lives

Abstract

A phenomenological formula is presented for the partial half-life from the Q value for α decay. It is constructed in a conventional way by considering the penetrability of a charged particle in a spherical Coulomb potential. Parameters in the formula are fixed because they are determined by physical constants except for the following three adjustable parameters: the product of the collision frequency of an α particle and the formation probability, N; the distance between the charge radius and the radius of an inner point of the Coulomb barrier, r 0; and the odd-mass hindrance, h 0. The values obtained for the three adjustable parameters are reasonable, in contrast with those of conventional models such as the Viola–Seaborg formula. The root-mean-square deviations from experimental partial half-lives for even–even, odd-A, and odd–odd nuclei are 0.344, 0.740, and 0.940 (in log10), respectively. The obtained formula gives half-lives that are two or three times longer than those obtained using the Viola–Seaborg formula in the superheavy nuclear mass region.