Relativistic multiple scattering theory and the relativistic impulse approximation

It is shown that a relativistic multiple scattering theory for hadron-nucleus scattering can be consistently formulated in four dimensions in the context of meson exchange. We give a multiple scattering series for the optical potential and discuss the differences between the relativistic and non-relativistic versions. We develop the relativistic multiple scattering series by separating out the one-boson exchange term from the rest of the Feynman series. However, this particular separation is not absolutely necessary and we discuss how to include other terms. We then show how to make a three-dimensional reduction for hadron-nucleus scattering calculations and we find that the relative energy prescription used in the elastic scattering equation should be consistent with that used in the free two-body t-matrix involved in the optical potential. We also discuss what assumptions are involved in making a Dirac relativistic impulse approximation (RIA)