. Agency Use Onlyleave Blank 2. Report Date 3. Report Type and Dates Covered Quasi-elastic Nuclear Scattering at High Energies 6. Authors

The quasi-elastic scattering of two nuclei is considered in the highenergy optical model. Energy loss and momentum transfer spectra for projectile ions are evaluated in terms of an inelastic multiplescattering series corresponding to multiple knockout of target nucleons. The leading-order correction to the coherent projectile approximation is evaluated. Calculations with uncorrelated wave functions are compared with experimental results. Introduction The assessment of radiation risk to astronauts from cosmic radiation is currently an area of active investigation. Predictions of biological damage will ultimately require a knowledge of the particle uence spectra at the endpoint of interest. In turn, these particle uence spectra are determined from charged-particle transport codes that must contain a description of all important physical processes that occur as the incident ions and subsequent generation fragment nuclei pass through natural and protective radiation shielding. A theoretical model for the prediction of fragmentation cross sections is extremely useful, as it cannot be expected that enough experiments will be performed for all the collision pairs and energies of interest in cosmic ray studies. Experimental data are most often in the form of inclusive measurements where a single reaction product is typically detected in a many-particle nal state. Although several mechanisms may lead to the single product, models must be compared with the inclusive measurements for validation. The inelastic collision of two nuclei at intermediate or high energies is often described as a two-step process. The rst step includes multiple scatterings between projectile and target nucleons leading to the knockout of nucleons and clusters, the production of particles, and the deposition of energy. The second step involves the cascade of initially struck particles within their host nuclei and the de-excitation of the nuclear systems, which may proceed through particle emission. Recently, we have considered inclusive heavy-ion scattering using the high-energy optical model (refs. 1 and 2). The multiple scatterings between projectile and target nucleons can be divided into elastic and inelastic collision terms corresponding to a distortion e ect and the knockout of nucleons, respectively. Calculations (ref. 2) with the independent particle model (IPM) show that even for large collision pairs, the number of inelastic collisions that occur is quite small, usually two to four. Although correlation e ects may be important corrections to the IPM, especially for cluster knockout, the rapid convergence in the number of inelastic collisions favors a \doorway" picture of heavy-ion fragmentation. In the doorway picture the rst step involves only a small number of knocked-out nucleons, with the subsequent motion of these particles and nuclear de-excitation leading to the large number of nal fragmentation channels observed in experiments. In our previous work (refs. 1 and 2) the cross-section distribution in total momentum transfer was considered. Herein, we extend this work in order to evaluate the energy loss cross section of the projectile in inclusive scattering. The relationship of the projectile energy loss to the target response function and excitation energy is considered and the e ects of multiple inelastic scatterings are treated. The correction to the coherent projectile assumption (ref. 1) is evaluated to leading order. Previous calculations in high-energy formulations (refs. 3 to 5) have considered only elementary projectiles and usually assume a zero-range two-body interaction (ref. 4) or a factorization approximation (ref. 3). In this work only forward-peaked wave functions are assumed in the evaluation of higher order terms. The model presented herein is immediately applicable to the development of nuclear transport codes for bulk shielding materials, as is