On the theory of slow-particle scattering in the two-dimensional case

A solution to the problem of elastic scattering of low-energy particles on a “weak” potential U is given. An expression for the amplitude of s-wave scattering is found in this approximation, and it is shown that, for U < 0, it has a pole at the energy E ₀ of the corresponding loosely bound state. An explicit expression in terms of the potential U is obtained for the preexponential factor, which refines the known order-of-magnitude estimate for E ₀.