Elastic scattering in short-range potentials

Elastic scattering in short-range potentials is formulated in terms of the theory of the potential, and the scattering amplitude is obtained by constructing an approximate representation of the solution of the equation of the potential (Born scattering). The basic features of the scattering amplitude are identified on this representation of the solution. The solution is exact for δ-potentials. The effective-range theory of scattering is obtained (Fermi scattering length), and the resonance scattering is derived, both for high bound states and low virtual levels (Wigner formula). The resonance scattering on 'quasi-discrete' levels is derived (Wigner-Breit formula). The quasi-classical solution for high-energy scattering is presented. (author)