Low-energy potential scattering in two and three 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.

19 pages, pdflatex, 3 figures, refs. added, typos corrected, to appear in JMP

References in corpus (4)

• Levinson theorem in two dimensions
• Universality of low-energy scattering in (2+1) dimensions
• Universality of Low-Energy Scattering in 2+1 Dimensions: The Non Symmetric Case
• Some Remarks on Effective Range Formula in Potential Scattering

Cited by in corpus (16)

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• Diffusion Monte Carlo study of strongly interacting two-dimensional Fermi gases
• The Unitary Gas and its Symmetry Properties
• The $s$-wave scattering length of a Gaussian potential
• Renormalization group study of Bose polarons
• Non-Universal Equation of State of the Two-Dimensional Bose Gas
• Core structure of two-dimensional Fermi gas vortices in the BEC-BCS crossover region
• On-shell approximation for the s-wave scattering theory
• Striped Ultradilute Liquid of Dipolar Bosons in Two Dimensions
• Fermions in Two Dimensions: Scattering and Many-Body Properties
• Dynamical formulation of low-frequency scattering in two and three dimensions
• Universal Properties of Anisotropic Dipolar Bosons in Two Dimensions
• Bose-Bose gases with nonuniversal corrections to the interactions: a droplet phase
• Dynamics in the presence of local symmetry-breaking impurities