THE SHAPE OF THE FERMI-SURFACE

We show that in the surface region, where the matter density falls off , the local momentum distribution of a many Fermion system becomes ani sotropic. The local Fermi surface has a predominantly prolate shape, w ith its long axis normal to the surface in both spherical and semi-inf inite many Fermion systems, We determine the dependence of the smooth and of the fluctuating contributions of the momentum anisotropy as fun ctions of particle number.