Properties of the wigner static function for systems of particles in the Woods-Saxon potential

The Wigner static quantum phase-space distribution function is calculated for particles bound in the spherical Woods-Saxon potential. It is shown that the momentum distribution is highly diffused at the nuclear surface and oscillates strongly in the nuclear interior. Averaging distribution function in the sense of the shell correction method does not smooth-out completely the oscillations, which proves that the semiclassical determination of the distribution function and the Strutinsky-smoothing of the corresponding quantum expreaasion are not equivalent