Semiclassical theory of melting of shell effects in nuclei with temperature

The level density parameter is calculated on the basis of exact semiclassical 'trace formulae' for magic and semi-magic nuclei. This powerful formula entails the level density of a quantum system in terms of the detailed properties of periodic orbits of the underlying classical system. Keeping the description within the mean-field approximation of a many-body Fermionic system, we present the well-known dependence of the level density parameter a on the mass number A which summarizes the shell effects in nuclei. To understand the melting of shell effects with temperature, we present calculations leading us to the behaviour of a vs A at non-zero temperatures for nearly one hundred nuclei. We see all the points huddling together along to the $A/1$-line as the temperature increases. With no adjustable parameters, we also find that our results for a are within ten to fifteen percent of the values deduced from the experiments. (paper)