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 nucle us into volume, surface, curvature and gauss curvature contributions h as been studied starting from a semi-classical energy density formalis m of extended Thomas Fermi type. A numerical procedure was used to obt ain 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 for ces. A transition to the liquid drop model type expansion in increasin g 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 nucle us. It is found that there is no inconsistency between the curvature c ontribution to the total energy in the leptodermous expansion and the A-1/3 term contribution in the liquid drop model expansion. It has bee n shown that the earlier apparent anomaly between the above two method s arises due to the use of semi-infinite approximation and the mass de pendence of the central density and the surface structure of finite nu clei.