Recent Results on Elastic and Inelastic Scattering

¹ CEA/DSM/DAPNIA/SPhN Saclay, 91191 Gif-sur-Yvette Cedex, France
² GANIL (DSM/CEA, IN2P3/CNRS), BP. 5027, 14021 Caen Cedex, France

Abstract

In this review article, which corresponds to lectures given by one of us (N.A) at the third "Euroschool on Exotic Beams" held in Leuven in September 1995, we present experimental results and theoretical developments in heavy-ion elastic and inelastic scattering and Giant Resonance excitation. The paper contains a short review of the field with special emphasis on more recent results and problems. We start by recalling the theoretical situation concerning the description of nucleon-nucleus elastic scattering. We show that in the framework of the local density approximation, complex potentials derived from fundamental effective nucleon-nucleon interactions, describe successfully the data. However, the main part of the discussion on elastic scattering, is dedicated to the description of intermediate energy heavy-ion elastic scattering. We present different folding models for the calculation of the real part of the nucleus-nucleus optical potential, M3Y, DDM3Y, .... The theoretical predictions are compared to experimental data mainly obtained at GANIL (20-100  Mev per nucleon). We show that a new density dependent interaction which reproduces the equilibrium density and the binding energy of normal nuclear matter, leads also to a satisfactory description of heavy-ion elastic scattering angular distributions. This interaction reproduces also the density and energy dependence of the nucleon optical potential. We present a new simple effective interaction with a real and imaginary part for peripheral heavy-ion collisions at intermediate energies. Finally the effect of the isospin and spin terms of the effective nucleon-nucleon interaction on the nucleus-nucleus folded potentials is discussed. We introduce the deformed optical model potential which is the most frequently used model, to obtain inelastic scattering transition potentials. However the most direct approach to obtain transition potentials is from the folding of the transition densities with an effective nucleon-nucleon interaction and the ground state density of the nucleus which is not excited. We show that the predictions of the optical and folding model are very different, especially for transitions dominated by nuclear excitation. The difference between the cross sections estimated within the deformed optical model and the folding model increases with multipolarity. Following the theoretical work of R. Satchler, we recommend the use of a folding model to extract deformation lengths and multipole moments from inelastic scattering measurements. We present the state of the field concerning Electric Giant Resonances and multiphonon excitations. We introduce the different sum rules which can be found usually in the literature and we show the link between them. The excitation of Giant Resonances with intermediate energy or high energy heavy ions, measured at GANIL or GSI and the technical problems met in the analysis of these experiments are discussed. Recent results concerning the two-phonon excitation of the Giant Quadrupole and Dipole mode are presented. Concerning the breathing mode, macroscopic and microscopic prescriptions introduced to access the compressibility of the nuclear matter are discussed. We show, in the light of theoretical arguments developed recently by J.P. Blaizot and collaborators, that microscopic calculations remain the most reliable tool for the determination of the nuclear matter compression modulus from the energy of the monopole vibration of nuclei.