Bound state densities and the Helmholtz free energy

Bohr's conception of the compound nucleus is based on the idea of ‘longlived’ nuclear states in which all single particles are bound. We briefly discuss the properties of the density of bound states and then use two prescriptions, that of Brack and Quentin and that of Bonche, Levit e Vautherin to calculate the equivalent temperaturedependent quantity – the Helmholtz free energy.We compare the temperature dependence of the latter, as well as that of the excitation energy and entropy, obtained using the two prescriptions in self-consistent calculations within the relativistic Hartree and Skyrme models. We then discuss the extended, temperature-dependent liquid-drop approximation to the excitation and free energies obtained from fits to the self-consistent calculations over a wide range of charge and mass numbers.