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The problem of the determination of the nuclear surface and surface symmetryenergy is addressed in the framework of the Extended Thomas Fermi (ETF)approximation using Skyrme functionals. We propose an analytical model for thedensity profiles with variationally determined diffuseness parameters. For thecase of symmetric nuclei, the resulting ETF functional can be exactlyintegrated, leading to an analytical formula expressing the surface energy as afunction of the couplings of the energy functional. The importance of non-localterms is stressed, which cannot be simply deduced from the local part of thefunctional. In the case of asymmetric nuclei, we propose an approximateexpression for the diffuseness and the surface energy. These quantities areanalytically related to the parameters of the energy functional. In particular,the influence of the different equation of state parameters can be explicitlyquantified. Detailed analyses of the different energy components(local/non-local, isoscalar/isovector, surface/curvature and higher order) arealso performed. Our analytical solution of the ETF integral improves overprevious models and leads to a precision better than 200 keV per nucleon in thedetermination of the nuclear binding energy for dripline nuclei.

Analytical mass formula and nuclear surface properties in the ETF approximation