Correlation between<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>-particle preformation probability and the energy levels of parent nuclei

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 potential model is used to calculate the preformation probability, ${S}_{\ensuremath{\alpha}}$, of $\ensuremath{\alpha}$ decay from Po isotopes to superheavy nuclei. The variation of ${S}_{\ensuremath{\alpha}}$ with the neutron number for the isotopes of Po, Rn, Ra, Th, and U elements is studied below and above the magic neutron number $N=126$. We found a strong correlation between the behavior of ${S}_{\ensuremath{\alpha}}$ and the energy levels of the parent nucleus at and just below the Fermi level. ${S}_{\ensuremath{\alpha}}$ has a regular behavior with the neutron number if the neutron pair of $\ensuremath{\alpha}$ particles, emitted from adjacent isotopes, comes from the same energy level or from a group of levels, assuming that the order of levels in this group is not changed. Irregular behavior of ${S}_{\ensuremath{\alpha}}$ with the neutron number occurs if the levels of the adjacent isotopes change or holes are present in lower levels.