Theory of multiple scattering

Consideration is given to problems of obtaining exact and approximate solutions of kinetic equations in the multiple scattering problem. For cross sections which are rational functions of χ² (χ = 2sin(δ/2), δ is the scattering angle) exact solutions are obtained as a series in terms of Legendre polynomials. The limits of validity of the kinetic equation for the distribution function in terms of the variable q = 2sin(?/2) are refined 1] and the solutions of this equation are compared with the exact solutions of the Rutherford and Mott cross sections. The problem of convergence of approximate solutions in the form of a series in terms of Legendre polynomials and a series in powers of 1/B is solved. These approximations are obtained and their limits of validity are determined.