α decay preformation probabilities across the N = 126 shell closure based on the single particle energy spectra

Abstract

We put forward a concise approach to calculate the α decay preformation probabilities by defining the microscopic valence nucleon and hole numbers based on the single particle energy spectra, which is obtained within the relativistic Hartree–Bogoliubov model. The residual interactions including neutron–neutron, proton–proton pairing and proton–neutron correlations could trigger the collective motions among the valence nucleons and holes, along with the independent particle motions under the mean field assumption. Therefore the more the number of valence nucleons and holes, the stronger the collective motions such as α particle clustering. We assume that the valence orbits locate around the Fermi surface obeying a Fermi–Dirac distribution, i.e. nucleons (holes) occupying the orbits with much lower (higher) energies away from the Fermi surface can not be considered as the valence nucleons (holes). The α decay preformation probabilities Pα are calculated within the Np Nn scheme in terms of the valence proton–neutron interaction. As an example, in the case of even–even polonium, radon, radium and thorium isotopes the extracted α decay preformation probabilities , which are obtained within the generalized liquid drop model, can be well reproduced by employing two different formulas to take into account the shell effect at N = 126 shell closure.