A microscopic model for inelastic (pp') scattering

The microscopic description of inelastic proton scattering is usually made in the DWBA approximation using an effective two-body force which acts between the incident nucleon and the excited particle in the target, and which is fitted to the experimental data. Such an approach leads however to poor angular distributions, except when using rather short range forces, and the effective strength has a tendency to increase for large spin transfer and to depend on energy. We take into account the exchange effects arising from antisymmetrization of the incident particle and target wave functions and also from the exchange nature of the nuclear forces. This model predicts the experimental magnitude of the cross-sections without any adjustable parameter for inelastic scattering when the bound state description is good. In particular, it explains the spin and energy dependence of the experimental cross-section strengths. We derive an expression for the T matrix in the DWBA approximation for antisymmetrized wave functions, taking into account the fact that the potential well for free particles is complex. The DWBA transition amplitude is expressed in terms of the antisymmetrized two-body matrix elements of the nucleon-nucleon interaction. We use the helicity formalism of J. Raynal, which leads to a great simplification in the geometrical coefficients. Considering nuclei with at least one closed shell, we discuss the most recent microscopic descriptions for the lowest excited collective states. The ground state is described in the BCS scheme and the excited states are made of one particle-one hole and two quasi-particle excitations in the Tamm-Dancoff or Random Phase approximations. We develop also some very simple models in order to discuss the physical features of the pp' excitations. The mechanisms by which the inelastic scattering occurs are demonstrated and the sensitivity of the results to only a few nucleon-nucleon parameters is explained. In order to test the validity of our model, we have chosen the excitation of the T = 0 collective states of doubly closed shell nuclei where good microscopic wave functions are available. Without any adjustable parameters, and using a force which fits free low energy nucleon-nucleon scattering, we are able to reproduce the magnitude of the experimental cross-sections to the excited states of 12C, 40Ca and 208Pb at several different energies. Exchange effects increase the cross-sections by a factor 2 to 10. Their strong energy and spin dependence is seen to be needed in order to explain the experimental results. The improvement of the angular distributions is however small. We have used this model as a spectroscopic tool for the nuclei with one open shell. The 3- states are found to be rather well described in the BCS + RPA approximation. Comparing pp' and ee' scattering we were able to show that both 2+ and 3- collective states are almost pure ΔT = 0 excitations, whereas all the available microscopic descriptions for the 2 states predict that the latter are mainly built with excitations of the particles in the open shell and have therefore a strong ΔT = 1 component. (author)