Studying temperature dependence of pairing gap parameter in a nucleus as a small superconducting system

Abstract

In this paper, we have taken the effect of small size of nucleus and static fluctuations into account in the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity calculations of [Formula: see text]Ti nucleus. Thermodynamic quantities of [Formula: see text]Ti have been extracted within the BCS model with the inclusion of the average value of the pairing gap square, extracted by the modified Ginzburg–Landau (MGL) method for small systems. Calculated values of the excitation energy and entropy within the MGL+BCS method improve the extracted results within the usual BCS model and show a smooth behavior around the critical temperature with a very good agreement with the semi-empirical values. The result of using MGL+BCS method for the heat capacity of [Formula: see text]Ti is compared with the corresponding semi-empirical values and the calculated values within the BCS, static path approximation (SPA) and Modified Pairing gap BCS (MPBCS) which is a method that was proposed in our previous publications. Both MGL+BCS and MPBCS avoid the discontinuity of the heat capacity curve, which is observed in the usual BCS method, and lead to an S-shaped curve with a good agreement with the semi-empirical results.