Correlated finite temperature BCS approximation in finite systems

Abstract

We examine the solutions of a correlated finite temperature BCS approximation within the context of a general pairing Hamiltonian. It is shown that a new class of superconducting solutions, characterized by equal absolute values of the BCS transformation parameters u and v in a finite region around the Fermi surface exists at all temperatures. Furthermore, solutions of this type may provide a lower free energy than the ordinary normal solution above the BCS transition temperature for sufficiently strongly coupled finite systems. Comparison with the exact results in a particular finite case is made.