Test of a modified BCS theory performance in the Picket Fence Model

Analyses of a modified BCS (MBCS) theory performance at finite temperatures in the Picket Fence Model (PFM) for light and heavy systems are presented. Both symmetric, Ω=N (N particles on Ω doubly-degenerate levels), and asymmetric, Ω≠N, versions of the PFM are considered. Quantities determined exactly from particle–hole symmetry of the symmetric PFM are calculated in the MBCS. They are found in significant deviation from the exact values starting from far below the critical temperatures of the conventional BCS. Consequences of the MBCS prediction that heating generates a thermal constituent of the pairing gap, are discussed. The question of thermodynamical consistency of the MBCS is also addressed.