Nuclear Pairing Energy vs Mean Field Energy: Do They Talk To Each Other For Searching The Energy Minimum?

TL;DR

This study investigates the relationship between pairing energy and mean field energy in nuclei, revealing their anti-symmetric deformation dependence and mutual influence on energy minima using advanced nuclear models.

Contribution

It demonstrates the correlated evolution of pairing and mean field energies across nuclear deformations using deformed relativistic and Skyrme Hartree-Fock models.

Findings

Pairing energy and mean field energy are strongly correlated.

Energy minimum corresponds to a large negative mean field energy.

Pairing energy shows anti-symmetric deformation dependence.

Abstract

We study the evolution of the total binding energy (TBE) and pairing energy of Pb, Hg and Ar isotopes, as a function of the nuclear deformation. As for the nuclear model, we exploit a deformed relativistic Hartree-Bogoliubov theory in the continuum (DRHBc), and a deformed Skyrme Hartree-Fock plus BCS model. It is found that the dependence of pairing energy on the deformation is strongly correlated to that of the mean field energy, which is obtained by subtracting the pairing energy from the TBE; in other words, the energy minimum characterized by a large negative mean field energy has a smaller negative pairing energy or, equivalently, a smaller positive pairing gap, while a stronger pairing energy is found in the region away from the minimum of the total energy. Consequently, the two energies show an anti-symmetric feature in their deformation dependence, although the energy scales are very different. Moreover, since the pairing energy has a negative sign with respect to to the pairing gap, the evolution of mean field energy follows closely that of the pairing gap. This implies that the pairing energy (or pairing gap) and the mean field energy talk to each other and work together along the potential energy curve to determine the energy minimum and/or the local minimum.