Thermal two-neutron separation energy in the case of Erbium isotopes

Abstract

We propose to study the thermal two-neutron separation energy in the case of Erbium isotopes: 80 ≤ N ≤ 108. In this aim, one used the finite temperature Bardeen Cooper Schrieffer (FTBCS) method where the statistical fluctuations are treated as a part of Landau prescription. The behavior of this quantity according to the neutron number and temperature provides indication about the nuclear shape transition, and disappearance of shell effects. The obtained results allow to show that the inclusion of statistical fluctuations in the calculation have a nonnegligible effect. Indeed, the fact that this kind of fluctuations effect is important at high temperatures induces a smooth decrease of pairing gap parameter. As a consequence, the persistence of pairing effect at high temperature leads a change on the shell effect. Indeed, when statistical fluctuations are considered, the shell effect persists at high temperature which is not the case of the usual FTBCS approach.