Exact scattering length for a potential of Lennard-Jones type

For a modified Lennard-Jones interaction potential of the form ∼(r₀/r)^2n-2-(r₀/r)ⁿ], an exact and simple expression for the s-wave scattering length is presented, and discussed in some detail. For heavy alkali atoms, which nowadays are routinely being employed to produce Bose-Einstein condensates, this potential is well compatible with known experimental data when n = 6.