Low-energy potential scattering in two and three dimensions
N. N. Khuri (Rockefeller), Andre Martin (CERN), Jean-Marc Richard, (Grenoble), Tai Tsun Wu (Harvard)
TL;DR
This paper investigates the conditions under which low-energy scattering parameters like scattering length and effective range exist for central potentials in two and three dimensions, and analyzes phase-shift behavior for long-range potentials.
Contribution
It establishes conditions for the existence of scattering length and effective range in low-energy expansions in 2D and 3D, and derives phase-shift behavior for long-range potentials.
Findings
Conditions for scattering length and effective range existence are established.
Phase-shift behavior for long-range power-law potentials is derived.
Analysis extends understanding of low-energy scattering in different dimensions.
Abstract
Conditions are established for the existence of a scattering length and an effective range in the low-energy expansion of the S-wave phase-shift of a central potential in two and three dimensions. The behavior of the phase-shift as a function of the momentum is also derived for longer-range power-law potentials which do not fulfill these conditions.
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