Leptodermous expansion of nuclear ground state energies and the anomaly in the nuclear curvature energy

The leptodermous expansion of the total ground state energy of a nucleus into volume, surface, curvature and gauss curvature contributions has been studied starting from a semi-classical energy density formalism of extended Thomas Fermi type. A numerical procedure was used to obtain the surface energy and curvature energy contributions from surface moments of energy density profiles H(r) for a sequence of nuclei with N = Z and neglecting the coulomb interaction for the three Skyrme forces. A transition to the liquid drop model type expansion in increasing powers of A-1/3 is then made, taking into account the dependence of the central density and the surface structure on the mass of the nucleus. It is found that there is no inconsistency between the curvature contribution to the total energy in the leptodermous expansion and the A-1/3 term contribution in the liquid drop model expansion. It has been shown that the earlier apparent anomaly between the above two methods arises due to the use of semi-infinite approximation and the mass dependence of the central density and the surface structure of finite nuclei. (author). 12 refs., 8 figs., 4 tabs