Low-energy potential scattering in two and three dimensions
arXiv:0812.4054 · doi:10.1063/1.3167803
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.
19 pages, pdflatex, 3 figures, refs. added, typos corrected, to appear in JMP