Elastic Nucleon-Deuteron Scattering

Some formal and practical problems concerning the effects of the internal target nucleon motion and of the multiple scattering on the elastic scattering of high-energy nucleons by deuterons are considered. In order to provide a foundation for the examination of these effects, two well-known forms of the impulse approximation are studied within the context of a multiple-scattering formalism, and it is found that the form due to Watson appears to be the most convenient and consistent in its application. Some methods for solving the multiple-scattering equations are investigated. The direct use of the optical-model approach is shown to be impractical for very light nuclei and, in particular, for the deuteron. An alternative means of obtaining solutions of the multiple-scattering equations (when the number of target nucleons is small) which permits the exact treatment of the ground-state scattering while allowing a systematic treatment of the contributions due to the excited intermediate nuclear states is discussed. A practical technique is developed for generating approximate solutions of the two-body integral equations which occur in the various multiple-scattering formalisms.In the study of the consequences of the internal target nucleon motion, the impulse approximation is used to express the complete nucleon-deuteron transition matrix element in terms of two-nucleon transition (t) matrices in the form of integrals over the internal-momentum distribution of the target nucleons; these integrals are then evaluated under the assumption that the principal contribution to the scattering occurs for those values of the relative target nucleon momentum, q, such that q=zκ, where κ is one-half the momentum transfer and $0<~z<~1$. The variation of the off-the-energy-shell t matrix elements over this range of q is taken into account for the Hamada potential. The integrals are then employed to calculate (in the single-scattering approximation) the cross sections and polarizations for elastic nucleon-deuteron scattering for incident nucleon (lab) energies of 40, 95, and 150 MeV and c.m. scattering angles of 30^∘{} to 150^∘{}. A comparison is made between the present calculation and results obtained with the customary procedures of either neglecting entirely the q dependence of the t matrices (Chew approximation) or assuming that these matrices depend only linearly on q. At 150 MeV, where the off-the-energy-shell effects are largest, the results are shown to depend significantly on the type of t operator used, especially at large angles. The best fit to the polarization at 150 MeV is obtained with a t operator which corresponds approximately to Watson's form of the impulse approximation.