THE SEMICLASSICAL DESCRIPTION OF THE NUCLEAR-SURFACE PROPERTIES IN THE ENERGY DENSITY FORMALISM

The semiclassical nuclear surface properties have been studied in the framework of the energy density formalism. The necessity of the inclusion of fourth-order derivative terms in the energy densities has been emphasized to remove the inadequacy of the energy densities containing only second-order derivative terms to reproduce simultaneously the correct surface energy and the correct shape of the density in the tail region. Emphasis has also been given to choose the fourth-order derivative term in a suitable simple form to obtain analytical relations for the various surface characteristics of semi-infinite nuclear matter with the aid of the resulting Euler-Lagrange equations. The justification of using parametrized densities of generalized Fermi shape (F - v) has been shown explicitly by choosing the fourth-order derivative term in the energy density in a convenient form to give exponential behaviour for the density in the extreme interior and exterior parts of the nuclear surface. Simple relations for various surface properties have also been obtained for a number of Skyrme-type interactions for these parametrized densities and these results compare very well with those obtained directly by using the Euler-Lagrange equations.