Scattering by a van der Waals Force in the Born Approximation

By using the Born approximation an analytic formula is derived for the phase shifts ${\delta }_l$ for scattering by a van der Waals $r^{-6\mathrm{}}$ potential. We find that at low energies $tan{\delta }_l$ varies as $k^{2l+1}$ for $s$ and $p$ waves, and $tan{\delta }_l$ varies as $k^4$ for all the higher partial waves. Comparison is made with available results from standard effective-range theory.