VALIDITY OF THE CLOSURE APPROXIMATION IN MULTIPLE-SCATTERING THEORY

The closure approximation is necessary for the evaluation of the double scattering term, for the reduction of the multiple scattering from a dynamic nuclear system to the scattering from fixed scattering centers, and for the derivation of the Glauber formalism from the Watson multiple scattering formalism. If closure is valid, there should be no double scattering term in the optical potential for an uncorrelated target nucleus. A simple Gaussian model, in which the intermediate nuclear states are scattering states, is used to calculate the binary scattering term in the optical potential for such a nucleus. The nonlocal binary potential is used, together with the local single-scattering potential, to predict the differential scattering cross section of 1 GeV protons incident on He4 and Ca40. The results confirm the validity of the closure approximation for the heavier nucleus at all scattering angles. The results for the lighter nucleus confirm its use for small scattering angles but cast doubt on its use in the region of the first diffraction minimum. In the case of He4, the results also show that double scattering may improve the optical model fits to the scattering data. NUCLEAR REACTIONS Optical potential model, double scattering effects; relation to Watson, Glauber, theories. © 1979 The American Physical Society.