The variation after projection approach is applied for the first time to the Richardson pairing Hamiltonian to describe the thermodynamics of small superconductors with a fixed number of particles. The minimization of the free energy is made by a direct diagonalization of the entropy. The variation after projection applied at finite temperature provides a perfect reproduction of the exact canonical properties of odd or even systems from very low to high temperatures.

• Received 10 February 2012

DOI:https://doi.org/10.1103/PhysRevC.85.044321