The interaction between atoms behaves as Ϫ␣/r n at large distances and, owing to the large reduced mass of the collision pair, allows a semiclassical treatment within the potential well. As a result, the low-energy scattering is governed by two large parameters: the asymptotic parameter ␥ϭͱ2␣/បӷa 0 (nϪ2)/2 ͑a 0 is the Bohr radius͒ and the semiclassical zero-energy phase ⌽ӷ1. In our previous work ͓Phys. Rev. A 48, 546 ͑1993͔͒ we obtained an analytical expression for the scattering length a,

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... showed that it has 75% preference for positive values for nϭ6, characteristic of collisions between ground-state neutral atoms. In this paper we calculate the effective range and show that it is a function of a, r e ϭF n ϪG n /aϩH n /a 2 , where F n , G n , and H n depend only on ␥. Thus, we know the s-phase shift at low momenta kӶ␥ Ϫ2/(nϪ2) from the expansion k cot ␦ 0 ӍϪ1/aϩ 1 2 r e k 2 . At kӷ␥ Ϫ2/(nϪ2) the phase shift is obtained semiclassically as ␦ 0 ϭ⌽ ϩ/4ϪI n ␥ 2/n k (nϪ2)/n , where I n ϭ͓n/(nϪ2)͔⌫"(nϪ1)/n...⌫"(nϩ2)/2n.../ͱ. Therefore, ␥ and ⌽ determine the s-wave atomic scattering in a wide range of momenta, as well as the positions of upper bound states of the diatomic molecule.