Effect of correlations on the relation between excitation energy and temperature

Formulae for the excitation energy of a nucleus as a function of its temperature are derived in the framework of the random phase approximation (RPA). Two methods are investigated. We first calculate the energy as the derivative of the grand potential obtained in random phase approximation. We also calculate the energy as the thermal average of the Hamiltonian operator using RPA Green functions at finite temperature. The two methods are compared by analyzing their content in terms of diagrams. We also discuss the effect of correlations on the relation between chemical potential and particle number.