A realistic density-dependent nucleon-nucleon ($NN$) interaction with a finite-range exchange part which produces the nuclear matter saturation curve and the energy dependence of the nucleon-nucleus optical model potential is used to calculate the microscopic $\alpha$-nucleus potential in the well-established double-folding model. The main effect of antisymmetrization under exchange of nucleons between the $\alpha$ and daughter nuclei has been included in the folding model through the finite-range exchange part of the $NN$ interaction. The $\alpha$-decay half-lives have been determined using a microscopic potential within the semiclassical Wentzel-Kramers-Brillouin approximation in combination with the Bohr-Sommerfeld quantization condition. We systematically studied the preformation probability, $S_{\alpha }$, for ten even-even and odd mass heavy nuclei from Po to No isotopes. We found that $S_{\alpha }$ has a regular behavior with $N$ if the $\alpha$ particle emitted from adjacent isotopes comes from the same energy levels or from a group of levels, assuming that the order of levels in this group is not changed. Sudden increase in $S_{\alpha }$ is found when protons and neutrons holes exist below the Fermi levels. Based on the similarity in the behavior of $S_{\alpha }$ with the neutron number for two adjacent nuclei, we try to determine the unknown or doubted nuclear spins and parities or at least correlate spins of adjacent nuclei.

• Received 23 September 2013

DOI:https://doi.org/10.1103/PhysRevC.88.054604