Halo Nucleus Scattering Glauber Theory

The investigation on the halo structure of drip-line nuclei is one of the most important subjects and has attracted much attention both experimentally and theoretically. The halo nucleus is a weakly bound system, which has very peculiar properties. Usually it is considered to have a few-body structure, which is composed of a core and valence nucleons with a large diffused density distribution. It is well know that the Glauber theory is one of the most popular approaches for analyzing the experimental data of halo nucleus scatterings, which directly connects the matter radius and density distribution of the halo nucleus to the reaction cross section. The optical-limit Glauber theory has been of great success in describing the stable nucleus scattering at high energies. As it is extended to the nucleus scattering at low and intermediate energies, the modification of the Coulomb field to the effective impact parameter and the diffuseness of the nucleon-nucleon (N-N) scattering in the forward direction has to be taken into account. Through a systematic study on reaction cross sections and the angular distribution of the stable nucleus scatterings, we find that the inclusion of the N-N finite range interaction and Coulomb modification in the Glauber theory plays very important role in reproducing the experiment data at these energy regions. Due to the repulsive Coulomb field, the effective impact parameter increases, and therefore the calculated reaction cross section decreases. Considering the diffuseness of the N-N scattering in the forward direction results in an increased reaction cross section. And also the angular distributions calculated in the Glauber theory including these two corrections are in good agreement with the experiment data.In the investigation of the halo nucleus reaction with a loosely bound structure, one has to consider the strong spatial correlations among its constituents. Recently a few-body Glauber theory has been proposed, where the core and halo nucleons are treated separately. We apply the few-body Glauber theory to halo nucleus reactions and extend it to the halo nucleus with more than one or two halo nucleons. Both the reaction and nucleon removal cross section are derived with or without considering the meson production, and the relevant expressions are given. We further formulate the momentum distribution of a fragment in the halo nucleus scattering. Itsdetailed expressions in the elastic dissociation process with considering the final-state interaction and the inelastic dissociation process without considering the final-state interaction are obtained, respectively. Particularly an analytical expression for the longitudinal momentum distribution is derived if the density distribution of halo nucleons is assumed as a Gaussian type function. A direct connection of the width of the momentum distribution to the bound state wave function of halo nucleons is established.Since in the few-body Glauber theory the core and valence nucleons of a halo nucleus are treated separately, the obtained expressions of the reaction cross section, the nucleon removal cross section and the momentum distribution are all involved in multidimensional integrations. In order to make the theoretical calculation feasible, we first obtain an analytical formalism of partial integrals with respect to the coordinates of the core and target in the phase-shift functions and their cross terms of scattering matrix elements, if the density distributions of the core and target are fitted to a few Gaussian forms. Then the rest multidimensional integrals with respect to the impact parameter and coordinates of halo nucleons are performed by a Monte Carlo method. Therefore we could carry out numerical calculations and obtain the reaction cross section, the nucleon removal cross section and the momentum distribution in the scattering of a halo nucleus with any types of density distributions.We compare the reaction cross sections calculated in the few-body Glauber theory and the optical-limit Glauber theory...