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Elastic Nucleon-Deuteron Scattering

1963; American Institute of Physics; Volume: 130; Issue: 1 Linguagem: Inglês

10.1103/physrev.130.276

1536-6065

K. L. Kowalski, David Feldman,

Superconducting Materials and Applications

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 $\mathbf{q}=z\ensuremath{\kappa}$, where $\ensuremath{\kappa}$ 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\ifmmode^\circ\else\textdegree\fi{} to 150\ifmmode^\circ\else\textdegree\fi{}. 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.