Abstract
Abstract In this paper, we find analytically the first order solutions of the Bardeen, Cooper and Schrieffer (BCS) Hamiltonian with degenerated single-electron energy levels. The results are compared to the Richardson exact solutions calculated numerically, showing good agreement in the weak interaction limit. Using this first-order solution, we further calculate the number of pairs at the ground state as a function of temperature. In particular, the Bose–Einstein condensation (BEC) temperature is found when the population of ground-state pairs starts growing. This study provides a BEC analysis of the superconductivity for weak coupling regime, which traditionally belongs to the BCS side of the BCS–BEC crossover picture.
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