  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.
