Constraining the α-nucleus potential for α-decay calculation with nuclear rainbow scattering

Abstract

Introduction: The emission of a particles is a powerful probe for the α-cluster structure of heavy nuclei. The α-nucleus potential is a crucial ingredient in the a-decay calculation within the preformed cluster model. One of the most reliable ways to construct this potential is the double folding model, where an effective nucleon-nucleon interaction is folded with the nuclear densities. In the folding model calculation, there are many ambiguities in the choice of the nuclear densities of the daughter nucleus for α-decay. We propose to directly constrain the α-nucleus potential for α- decay and choose the daughter nuclear density using the nuclear rainbow scattering phenomenon.

Methods: The refractive rainbow pattern in the elastic scattering cross section within the optical model can probe deep into the interior region of the α-nucleus potential. We apply this method to investigate the reliability of the nuclear potential used in the α-decay of the 212Po nucleus leading to the 208Pb daughter nucleus by examining the elastic a scattering on 208Pb. In such an approach, we perform the double-folding calculation to construct the α-nucleus potential using several common parametrizations of the daughter nuclear densities. These parametrizations include the mean-field Hartree-Fock-Bogoliubov calculations with the BSk14 and D1S interactions, the independent particle model, and the 2-parameter Fermi distributions. The obtained nuclear potentials are applied to the optical model to calculate the elastic α-208Pb scattering cross sections that are compared with the experimental data. These nuclear potentials are further used in the preformed cluster model to study thea-decay half-life of 212Po.

Results: The nuclear densities from the Hartree-Fock-Bogoliubov calculations are shown to provide the best description for both the nuclear rainbow scattering anda-decay half-life. The results indicate a strong correspondence between the capabilities of the nuclear potential to reproduce the cross section ofa scattering and the α-decay half-life. The extracteda preformation factors from the semiclassical preformed cluster model with folding potentials are in good agreement with those from other studies.

Conclusion: The nuclear rainbow scattering phenomenon can be used to provide reliable a-nucleus potential
for α-decay studies within the preformed cluster model. The nuclear densities from the mean-field Hartree-Fock-Bogoliubov method with the BSk14 and D1S interactions are the appropriate choices for the DFM calculation used in the α-decay study.