The extended Thomas-Fermi (ETF) model is used to express the average kinetic energy density ~'(r) of a system of independent particles in terms of the average nucleon density ~(r). Numerical tests made using Strutinsky-averaged densities from a local Woods-Saxon potential indicated that using terms up to and including the Weizs/icker term is not sufficiently accurate. However, if the next order terms are included, the average kinetic energy of a large nucleus is reproduced to within 2-5 MeV. The expansion is not very useful for the exact densities as it leaves out all shell effects. We have also expanded the ETF approximation to include the effects of nonlocalities in the potential; in particular the effective mass and spin-orbit contributions to the kinetic energy are given.The considerable success of recent Hartree-Fock (HF) calculations of nuclear binding and deformation energies [1,2] is largely due to the simplicity of the effective interactions of the Skyrme type [3,1 ]. For these interactions (as well as for more general ones, if the density-matrix expansion [4] is used), the total energy of a finite nucleus can be written in terms of an energy density e(r) which depends in a simple way on the kinetic energy densities ~-n,p(r), the nucleon densities Pn,p(r) and their gradients:Eto t = re(r) d3r = fe ['r n, Tp, Pn, Pp, VPn, Vpp .... ]d3r,As the constrained HF calculations for heavy deformed nuclei [5] require large amounts of computer time it is of practical interest to find faster ways of obtaining deformation energies from a given effective interaction. It has been shown recently [6] that it is sufficient to solve the self-consistency problem on the average, using statistically smoothed densities ~ and ~, and to add the shell effects perturbatively with Strutinsky's method [7]. In this way one can not only obtain liquid drop like deformation energies microscopically, but also very accurately reproduce the exact HF results by adding the first order shell-correction.In order to calculate selfconsistent average binding energies, one may thus use semiclassical models [8]. One essential step is to express the kinetic energy density r(r) as a functional of the density p (r) in order to avoid the explicit use of single particle wave functions* x. One way of doing this is to use semiclassical expressions for r (r) and O (r) in terms of the one body potential V(r) and then to eliminate V(r) to obtain ~-(r) in terms of p(r) [9].The results of this procedure is: * t The subscripts n, p will be suppressed in the following; r(r) and O (r) denote the densities of one kind of nucleus.

Using the extended Thomas-Fermi model, we calculate average nuclear binding energies with Skyrme type effective interactions. The total energy is minimized with respect to variations of the nucleon densities without the use of wave functions or adjustable parameters. We obtain binding energies only -2-7 MeV higher than selfconsistenly averaged Hartree-Fock energies. By least-square fits we determine the liquid drop parameters of different effective interactions very accurately. Shell effects are added perturbatively and lead to total energies within 5-10 MeV of the exact Hartree-Fock results.The use of effective nucleon-nucleon interactions as proposed by Skyrme where f(r) is the ratio of the free nucleon mass m to the effective mass m*(r) and S(r) the spin-orbit form factor, the explicit extended Thomas-Fermi (ETF) exprepons for T and J which we presented in ref. [5] are : TETF +,2)2/3 $513 t; +/, t&F +lVf.VP

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