Description of spatial characteristics of elastic processes within the formalism of the Wigner functions

Definition of the Wigner function is given and its application to a description of elastic scattering processes is analyzed. A new element of the well-known formalism is a choice of the phase space in which the Wigner function is assigned as a quasi-probability distribution. This is a 4-dimensional space of canonically conjugated quantities – transverse momentum of the scattered particle and the projection of the closest particle approach vector onto the plane perpendicular to the incident particle momentum. Exact expression for the average squared radius of the region of scattered particle production through the scattering amplitude is presented.