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The limiting total excitation energy of the nucleus and Levinson's theorem

The limiting total excitation energy of 208Pb is calculated using the nuclear grand partition function. A temperature-dependent shell-model potential and an energy-dependent nucleon-nucleus optical potential are employed to generate the temperature-dependent bound single particle energies epsilon k and the continuum level density rho ( epsilon ) respectively. Levinson's theorem is used to make the relevant change in rho ( epsilon ) due to the T dependence of epsilon k(T). The calculated limiting total excitation energy is about half of the one recently obtained by Dean and Mosel (1985).