Single universal curve for α decay derived from semi-microscopic calculations

A universal curve is one of the simple ways to get preliminary information about the $\ensuremath{\alpha}$-decay half-life times of heavy nuclei. We try to find parametrization for the universal curve of $\ensuremath{\alpha}$ decay based on semi-microscopic calculations starting from the realistic Michigan-three-Yukawa Reid nucleon-nucleon interaction. Within the deformed density-dependent cluster model, the penetration probability and the assault frequency are calculated using the Wentzel-Kramers-Brillouin approximation. The deformations of daughter nuclei and the ground-state spin and parity of the involved nuclei are considered. For all studied decays, we found that it is accurate enough to express the assault frequency either as a function of the mass number of the parent nuclei or as a constant average value. The average preformation probability of the $\ensuremath{\alpha}$ cluster inside four groups of 166 even- $(Z)$ -even $(N)$, 117 odd-even, 141 even-odd, and 72 odd-odd $\ensuremath{\alpha}$ emitters is obtained, individually. The effects of participating unpaired nucleons in the involved nuclei as well as the influence of any differences in their ground-state spin and/or parity appear in the obtained average values of the preformation probability. We suggested a single universal curve for $\ensuremath{\alpha}$ decay with only one parameter. This parameter varies according to the classified four groups. It includes the preformation probability and the average assault frequency in addition to the pairing contribution.