# Inelastic scattering microscopic calculations with second order Born approximation, link with quantum pre-equilibrium models

**Marc Dupuis**

CEA Bruyeres-le-Chatel, France

In a collision between a nucleon and a target nucleus at medium incident energy, several reactions occur, among them elastic and inelastic scatterings, particles emissions, nucleon transfer, knock-out... In order to describe or predict the observables associated with these reactions, different kind of reaction processes are involved, such as direct, preequilibrium reactions, and compound nucleus formation and decay. Our goal is to describe elastic and inelastic scattering off double-magic nuclei coming from direct and preequilibrium processes by avoiding phenomenological ingredients. For direct processes, we will review our previous results obtained from fully microscopic optical model potential (OMP) calculations. This OMP is constructed from the Melbourne-g matrix taken as the two-body interaction between the projectile and target nucleons and a RPA (Random Phase Approximation) description of the target nucleus, including correlated ground state. Inelastic scattering is then calculated using RPA description of the target excited states, within the DWBA framework. The results are in fair agreement with experimental data. This allows us to go further and use these ingredients to describe processes beyond the scope of direct reactions. Among such processes, inelastic scattering with high energy transfer cannot been described using only DWBA calculations. We will focus on inelastic scattering calculations using the Born expansion of the transition amplitude up to the second order and its link with theoretical approaches of pre-equilibrium reactions such as the FKK (Feshbach, Kerman, Koonin) model, the TUL (Tamura, Udagawa, Lenske) model and the NWY (Nishioka, Weindenmüller, Yoshida). These three approaches involve several kind of approximations of the Born expansion of the transition amplitude which have not yet been tested. For instance, the FKK and the TUL models use some statistical approximations which allow to get rid of interference terms present in the second order cross-section. Moreover, the FKK model is usually applied with a modified closure relation which is not well justified. Finally, these three models use the on-shell approximation. Comparisons between exact second order calculations and the same calculations using one of the three approximations mentioned above allow us to test them. Our results allow us to discuss on the validity of these three quantum pre-equilibrium models and give some directions to improve them.