Complex Angular-Momentum Approximation To Hard-Core Scattering

The complex angular momentum (CAM) approximation for nonrelativistic quantum scattering by a hard sphere-a union of the recently developed CAM uniform approximation with a semiclassical WKB-like approximation valid at large angles-is shown to be remarkably accurate over the complete range of scattering angles, and down to size parameters (circumference to de Broglie wave-length ratios) of order unity. The best approximations previously derivable (Fock-type) cannot reach large scattering angles where semiclassical approximations are useful; even at angles where Fock-type approximations are valid, they are typically two or more orders of magnitude less accurate than CAM. The crucial new feature responsible for the high accuracy of the CAM approximation is the treatment of large-angle diffraction associated with (a) tunneling near the edge of the scatterer, and (b) anomalous reflection.