On scattering of slow particles by a 'weak' 2D potential

摘要

The problem of elastic scattering of low-energy particles by a "weak" 2D potential U without an axial symmetry is considered. The expression for the scattering amplitude is found in this approximation, and it is shown that at U < 0 it has a pole at the energy E _0 of the corresponding weakly bound state. An explicit expression in terms of the potential U is derived for the factor refining the known order-of-magnitude estimate for E _0.