BCS SUPERCONDUCTIVITY WITH FIXED NUMBER PARITY

We investigate superconductivity in a grand canonical ensemble with fi xed number parity (even or odd). In the low-temperature limit we find small corrections to the BCS gap equation and dispersion E(k). The eve n-odd free-energy difference in the same limit decreases linearly with temperature, in accordance with the behavior observed experimentally and previously arrived at from a quasiparticle model. The theory yield s deviations from the BCS predictions for the specific heat, ultrasoun d attenuation, nuclear spin-relaxation rate, and electromagnetic absor ption.