Low energy universality and scaling of Van der Waals forces

Abstract

At long distances interactions between neutral ground state atoms can be described by the Van der Waals potential V(r) =-C6/r^6-C8/r^8 - ... . In the ultra-cold regime atom-atom scattering is dominated by s-waves phase shifts given by an effective range expansion p cot d0 (p) = -1/a0 + r0 p^2/2 + ... in terms of the scattering length a0 and the effective range r0. We show that while for these potentials the scattering length cannot be predicted, the effective range is given by the universal low energy theorem r0 = A + B/a0+ C/a0^2 where A,B and C depend on the dispersion coefficients Cn and the reduced di-atom mass. We confront this formula to about a hundred determinations of r0 and a0 and show why the result is dominated by the leading dispersion coefficient C6. Universality and scaling extends much beyond naive dimensional analysis estimates.

4 pages, 3 figures

References in corpus (3)

• Analytic description of atomic interaction at ultracold temperatures: the case of a single channel
• The higher-order C_n dispersion coefficients for hydrogen
• S-wave and p-wave scattering in a cold gas of Na and Rb atoms

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• Les Houches Lectures on Effective Field Theories for Nuclear and (some) Atomic Physics
• Parameters for Cold Collisions of Lithium and Caesium Atoms
• Variational Calculations of Positronium Scattering with Hydrogen
• Universality in Ionic Three-body Systems Near an Ion-atom Feshbach Resonance
• Low Energy Continuum and Lattice Effective Field Theories
• Auxiliary counterterms and their role in effective field theory
• Universal low energy features of two-body systems