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Title: s-wave scattering for deep potentials with attractive tails falling off faster than -1/r{sup 2}

Abstract

For potentials with attractive tails, as occur in typical atomic interactions, we present a simple formula for the s-wave phase shift {delta}{sub 0}. It exposes a universal dependence of {delta}{sub 0}(E) on the potential tail and the influence of effects specific to a given potential, which enter via the scattering length a, or equivalently, the noninteger part {Delta}{sub th} of the threshold quantum number n{sub th}. The formula accurately reproduces {delta}{sub 0}(E) from threshold up to the semiclassical regime, far beyond the validity of the effective-range expansion. We derive the tail functions occurring in the formula for {delta}{sub 0}(E) and demonstrate the validity of the formula for attractive potential tails proportional to 1/r{sup 6} or to 1/r{sup 4}, and also for a mixed potential tail consisting of a 1/r{sup 4} term together with a non-negligible 1/r{sup 6} contribution.

Authors:
; ;  [1]
  1. Physik Department, Technische Universitaet Muenchen, D-85747 Garching (Germany)
Publication Date:
OSTI Identifier:
22068703
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 84; Journal Issue: 3; Other Information: (c) 2011 American Institute of Physics; Country of input: Syrian Arab Republic; Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; INTERACTIONS; PHASE SHIFT; POTENTIALS; S WAVES; SCATTERING; SCATTERING LENGTHS; SEMICLASSICAL APPROXIMATION

Citation Formats

Mueller, Tim-Oliver, Kaiser, Alexander, and Friedrich, Harald. s-wave scattering for deep potentials with attractive tails falling off faster than -1/r{sup 2}. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.84.032701.
Mueller, Tim-Oliver, Kaiser, Alexander, & Friedrich, Harald. s-wave scattering for deep potentials with attractive tails falling off faster than -1/r{sup 2}. United States. doi:10.1103/PHYSREVA.84.032701.
Mueller, Tim-Oliver, Kaiser, Alexander, and Friedrich, Harald. Thu . "s-wave scattering for deep potentials with attractive tails falling off faster than -1/r{sup 2}". United States. doi:10.1103/PHYSREVA.84.032701.
@article{osti_22068703,
title = {s-wave scattering for deep potentials with attractive tails falling off faster than -1/r{sup 2}},
author = {Mueller, Tim-Oliver and Kaiser, Alexander and Friedrich, Harald},
abstractNote = {For potentials with attractive tails, as occur in typical atomic interactions, we present a simple formula for the s-wave phase shift {delta}{sub 0}. It exposes a universal dependence of {delta}{sub 0}(E) on the potential tail and the influence of effects specific to a given potential, which enter via the scattering length a, or equivalently, the noninteger part {Delta}{sub th} of the threshold quantum number n{sub th}. The formula accurately reproduces {delta}{sub 0}(E) from threshold up to the semiclassical regime, far beyond the validity of the effective-range expansion. We derive the tail functions occurring in the formula for {delta}{sub 0}(E) and demonstrate the validity of the formula for attractive potential tails proportional to 1/r{sup 6} or to 1/r{sup 4}, and also for a mixed potential tail consisting of a 1/r{sup 4} term together with a non-negligible 1/r{sup 6} contribution.},
doi = {10.1103/PHYSREVA.84.032701},
journal = {Physical Review. A},
issn = {1050-2947},
number = 3,
volume = 84,
place = {United States},
year = {2011},
month = {9}
}