EXPANSION OF THE STATIC WIGNER DISTRIBUTION FUNCTION IN HERMITE-POLYNOMIALS

A new representation of the Wigner distribution function, based on the expansion of the spectral function in a series in Hermite polynomials with the shifted arguments, is proposed. Taking into account only the first two terms of such an expansion leads to a distribution function that is smeared in the momentum space in the vicinity of the local Fe rmi momentum. An analytic expression (correct to h2BAR) connecting the parameter characterizing smearing of the Wigner function with the mea n field is obtained. The influence of averaging by the shell-correctio n method on the static distribution function is considered.