Theory of the optical potential for strongly interacting particles

Abstract

We use the insight gained from the study of analyticity and unitarity to suggest a new method for the construction of the optical potential for strongly interacting particles. The calculational procedures suggested in this work are such as to associate a distinct physical process with each term in our expansion of the optical potential. By starting with various decompositions of the A-body target wave function we can obtain theories of varying complexity. Introducing a decomposition with respect to states of the (A-1) -body system, we obtain a construction of the optical potential based upon the single-scattering approximation. If we introduce a decomposition of the target ground state with respect to states of the (A-2) -body system we obtain a more complex theory. In the extended theory, the first-order optical potential of the simpler model is readily extracted along with a second-order potential that depends on the detailed structure of the two-body density matrix of the target. The role of Pauli and short-range correlations in modifying the calculation of the second-order potential is discussed. The physical picture that emerges from this analysis is different from that obtained from multiple-scattering theory, although the two theories are in general agreement as to themore » nature of the first-order optical potential. When the fixed-scatterer approximation is used to simplify calculations based upon multiple-scattering theory, the second-order optical potential is found to depend on the two-body correlation function. In contrast, for the theory presented here, we find that the inclusion of Pauli and/or short-range correlations is a relatively minor aspect in the construction of the second-order potential. Indeed, we would obtain a second-order potential for an uncorrelated system.« less