s-wave scattering for deep potentials with attractive tails falling off faster than -1/r{sup 2}
- Physik Department, Technische Universitaet Muenchen, D-85747 Garching (Germany)
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.
- OSTI ID:
- 22068703
- Journal Information:
- Physical Review. A, Vol. 84, Issue 3; Other Information: (c) 2011 American Institute of Physics; Country of input: Syrian Arab Republic; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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