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Journal of Mathematical Physics 4
- Publisher
- American Physical Society (APS)
- Copyright
- Copyright © 2010 The American Physical Society
- ISSN
- 1094-1622
- DOI
- 10.1103/PhysRevA.81.044701
- Publisher site
- See Article on Publisher Site
Abstract
At long distances, interactions between neutral ground-state atoms can be described by the van der Waals potential. In the ultracold regime, atom-atom scattering is dominated by s -waves phase shifts given by an effective range expansion in terms of the scattering length α 0 and the effective range r 0 . We show that while the scattering length cannot be predicted for these potentials, the effective range is given by the universal low-energy theorem r 0 = A + B / α 0 + C / α 0 2 , where A , B , and C depend on the dispersion coefficients C n and the reduced diatom mass. We confront this formula to about 100 determinations of r 0 and α 0 and show why the result is dominated by the leading dispersion coefficient C 6 . Universality and scaling extend much beyond naive dimensional analysis estimates.
Journal
Physical Review A – American Physical Society (APS)
Published: Apr 1, 2010