Energy density formalism and semiclassical nuclear properties

Abstract

The semiclassical nuclear properties have been studied in the framework of the energy density formalism by choosing two energy densities, one containing derivative terms up to second order and the other also containing fourth-order derivative terms. The surface energy density in each of the two cases can be suitably approximated so that the Euler-Lagrange equations in a semi-infinite nuclear medium (SINM) lead to a pure Fermi distribution (F-1) for the density. The importance of the inclusion of the fourth-order derivative terms in the energy density to reproduce the correct surface energy and the correct behaviour of the density in the outer part of the surface has been shown explicitly. The variations of the central density rho 0 and the surface thickness a with the size of the nucleus have been studied under the assumption that the departures in and lambda of these quantities from their respective SIMN values are small. The restricted simple nature of the surface energy density resulting from the imposition of an F-1 distribution of density in a SINM has the advantage of describing the variations in and lambda in terms of the small ratio alpha between the surface thickness and the half-density radius in a general way, independent of the characteristics of the energy density used. This study shows that the correct behaviour of the variations of in and lambda cannot be reproduced in an expansion in powers of alpha and retaining the first few terms. It is further observed that the lower-order terms in the energy in an expansion in powers of alpha are quite important for a correct description of the departures in and lambda , at least in the region alpha >or=0.1, although these lower-order terms are not so important as far as the total energy is concerned. A comparison of the variations of the surface thickness with the size of the nucleus for the two different energy densities shows that the variation lambda is much smaller for the fourth-order case, in conformity with the fact that the surface thickness is almost independent of the size of the nucleus and thereby favours an energy density containing derivative terms up to fourth order over an energy density having only second-order derivative terms.