Exact Multiple-Scattering Analysis of Low-Energy ElasticK−−dScattering with Separable Potentials

Abstract

A calculation of the $K^{-}-d$ low-energy elastic-scattering cross sections is carried out with the intent of determining the importance of multiple scatterings. Under the assumption that the two-body interactioins are $S$-wave nonlocal separable potentials of the Yamaguchi form, an expression for the scattering amplitude in terms of a set of one-dimensional in tegral equations for each partial wave is derived. The derivation does not take into account Coulomb forces or the $n-p$ and $K^{-}-{\overline{K}}^0$ mass differences. A transformation from real to complex dummy variables that allows a rapid numerical computation of the solution to the integral equations for the scattering amplitude is presented and discussed. With the use of the Humphrey and Ross kaon-nucleon scattering lengths, the elastic angular distribution and cross section, as well as the total cross section, are calculated for incident kaon lab momenta of 105, 194, and 300 MeV/c. The results of the multiple-scattering calculation for the elastic cross section are two to three times smaller than the impulse approximation results throughout this momentum range. The multiple-scattering corrections to the impulse approximation for the total cross section are small (≲10%) only at the largest momentum used.