Thermodynamical properties of a paired nucleus with a fixed number of quasi-particles

Abstract

The general formalism for the description of the properties of a paired system with fixed number of quasi-particles has been developed. The number of quasi-particles has been introduced into the pairing Hamiltonian by means of a Lagrange multiplier. The grand partition function and all the other thermodynamical functions have been derived. The formalism has been applied to the uniform model. The properties of the system in the limit of zero temperature have been obtained analytically. It has been found that for temperatures smaller than the critical temperature of the unrestricted system, a first order phase transition from the paired to the unpaired phase occurs when the quasi-particle number is increased isothermally. Above the critical temperature the transition becomes of the second order. The model also predicts that at a fixed quasi-particle number the pairing correlation increases with increasing temperature. In particular, at the highest excitation, and at small quasi-particle number, the pairing correlation is as strong as in the ground state. A rapid decrease and aa eventual disappearance of pairing occurs as the system is allowed to relax towards its equilibrium number of quasi-particles.