Two-Dimensional Motion of a Slow Quantum Particle in the Field of a Central Long-Range Potential

We study the two-dimensional motion of a slow quantum particle in the field of a central long-range potential decaying in the limit of long distances r as the power r −β with the exponent β ∈ (1, 2). We find the low-temperature asymptotic behavior for all partial phases and the differential cross section of the particle scattering and derive a rather simple approximation for the weakly bound state energy.