Scattering length for Lennard-Jones potentials

We present an exact procedure that allows one to calculate the scattering lenth for any potential expressed as an algebraic sum of inverse powers of the interatomic distance. We apply it to (12, $s$) Lennard-Jones potentials, with different values of $s$. The procedure is suitable for a very precise determination of the intensities of the potential corresponding to zeros or poles of the scattering length.