Particle number projected energies at finite temperature

In this work, the particle number projection at finite temperature is incorporated into self-consistent Skyrme density functional calculations. In particular, the energies of compound nuclei as a function of deformations are calculated rigorously based on projected densities. Results show that the even-odd staggering effect in partition function gradually diminishes as the system approaches the critical temperature. The obtained fission barriers are similar to that without projection at finite temperature, although projected energies are different. The nuclear level density at the ground state and the barrier are also studied using the projection method and the discrete Gaussian method.