Effect of choosing the [formula omitted]-values and daughter density distributions on the magic numbers predicted by [formula omitted] decays

Abstract

We investigated the effects of choosing the α-decay energy (Qα) and particular density distributions of the daughter nuclei on predicting unknown magic numbers, or confirming some of them. The Qα values were calculated using three models, namely the finite-range droplet model (FRDM), the Weizsäcker–Skyrme (WS4) mass model, and a recent fitting formula. The α-decay half-lives (Tα) of superheavy nuclei of Z = 118–124 have been calculated within the generalized density-dependent cluster model. The double-folding α+core potential was determined based on the M3Y-Reid nucleon–nucleon interaction. We have used the two-parameter Fermi distribution to represent the nuclear density, with four sets of parameters that were determined based on electron scattering data and different microscopic calculations. Upon investigating the relative stability of the mentioned superheavy isotopic chains, we found that the Qα-values deduced from FRDM and WS4 models predict different neutron magic numbers. The examined fitting formula failed to predict any magic number larger than N= 162. Under normalization to the proton and neutron (N) numbers, the different choices of the density distributions showed almost no effect on the general behavior of Tα with N, but changed its values up to one order of magnitude. Even though the maxima and minima of Tα clearly follow the characteristic minima and maxima of Qα, respectively, the results showed that precise density distribution and deformations, in addition to a correct preformation probability, are necessarily required for estimating an accurate value of the half-life.