Multiple Scattering Corrections to the Impulse Approximation in the Two-Body System

Exact solutions for the scattering of a fast particle by two heavy scatterers are obtained and compared with the usual treatment of the impulse approximation in which multiple scattering is neglected. It is found that the multiple scattering qualitatively changes the solution except in the extreme Born approximation limit. The methods developed are applied to the isotopic spin dependent, but spin independent, scattering of mesons in the deuteron. It is found that if high energy scattering is assumed to be in the isotopic spin $\frac{3}{2}$ state, a considerable depression in the total cross section can be expected for phase shifts larger than 45 degrees.