Comparison of methods of scattering from two potentials

Several approximations to multiple scattering are compared with an exact calculation. The model chosen for comparison is scattering from two Gaussian potentials of range 0.5 fm and depth 16 ${\mathrm{fm}}^{-2\mathrm{}}$. Particular attention is paid to the case of overlapping potentials. It is shown that, of all approximations considered, only the separable potential method is capable of giving good agreement in this region. It is demonstrated that a separable potential can always be chosen to give the exact answer for multiple scattering in the case in which the (spherically symmetric) interaction regions are nonoverlapping as well as when the interaction regions are concentric.