ON THE TWO-BODY FORMULATION OF HIGH-ENERGY NUCLEAR SCATTERING PROBLEMS
Attention is given to several formal and practical problems directly or indirectiy related to the theoretical description of the scattering of high- energy particles, and in particular, nucleons, from complex nuclei. The underlying physical viewpoint of the theoretical description is to picture such scatterings as occurring through the successive interaction of the incident particle with each of the target nucleons, Then, via the so-called impulse approximation (I.A.), the scattering may be approximated by a series of two-body processes. An entirely new and complete theory of the integral equations satisfied by the partial-wave amplitudes of the scattering operators appropriate to, say, a two-nucleon system is presented. The essential feature of the theory is the recognition of the fact that the integral equations are singular or quasisingular in nature. A reduction of the (quasi-) singular equations to Fredholm forms is carried out. The Fredholm forms admit approximation procedures and a physical interpretation that seems to be distinctly superior to all customary techniques. Integral equations satisfied by the scattering operators in the case when the irteraction contains a hard core are derived. The integral equations are cast into a form identical to the case when no hard core is present. Thus, the Fredholm formalism applies equally well whether or not a hard core is contnined in the interaction. An extensive discussion is given of the I.A. This approximation is considered in the context of the formulation of multiple- scattering theories, and a prescription is found for its application. Three new multiple -scattering theories were developed in order to study various aspects of the l.A. It was found that one of the customary methods of applying the I.A. seems to lead to inconsistencies and, in addition, is definitely cumbersome in the description of multiple scatterings; numerical calculations are performed that support the contention that this particular form of the I.A. is inconsistent. A derivation of the optical-model formalism, rigorously valid for arbitrary nuclei, was found. This formalism is used to evaluate the contributions due to the excited target states during intermediate multiple scatterings of a particle that is elastically scattered by a nucleus in its ground state. The principal usefulness of this formalism is in the case of very light nuclei where the customary optical-model formalisms are either invalid or inconvenient. With suitable approximations, the customary formalisms can be derived from the present formalism. A method is presented for solving the multiple-scattering equations in the case when the nucleus remains in its ground state during all intermediate multiple scatterings. The method is similar in spirit to the methods used for the partial-wave amplitudes of the scattering operators Finally, an evaluation was made of the nuclear matrix elements of the two-nucleon scattering operators for the case of a deuteron target. This calculation differs from those previously executed in that the dominint effects of the internal motion of the nuclear particles is taken into account. The results oE this calculation are used, in the single-scattering approximation, to compute the cross section and polarization for the elastic scattering of a nucleon by a deuteron, An improved agreement with experiment was obtained. (Dissertation Abstr., 24: No. 9, March 1964)
- Research Organization:
- Originating Research Org. not identified
- NSA Number:
- NSA-18-021337
- OSTI ID:
- 4005597
- Resource Relation:
- Other Information: Thesis. Orig. Receipt Date: 31-DEC-64
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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