Prediction of nuclear spin based on the behavior of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>-particle preformation probability

Abstract

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 $\ensuremath{\alpha}$-nucleus potential in the well-established double-folding model. The main effect of antisymmetrization under exchange of nucleons between the $\ensuremath{\alpha}$ and daughter nuclei has been included in the folding model through the finite-range exchange part of the $NN$ interaction. The $\ensuremath{\alpha}$-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, ${S}_{\ensuremath{\alpha}}$, for ten even-even and odd mass heavy nuclei from Po to No isotopes. We found that ${S}_{\ensuremath{\alpha}}$ has a regular behavior with $N$ if the $\ensuremath{\alpha}$ 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 ${S}_{\ensuremath{\alpha}}$ is found when protons and neutrons holes exist below the Fermi levels. Based on the similarity in the behavior of ${S}_{\ensuremath{\alpha}}$ 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.