Nuclear pairing energy versus mean field energy: Examination of their relationship and interdependence in reaching the energy minimum

We study the evolution of total binding energy (TBE), mean field energy, 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 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 antisymmetric 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.