THE TWO-BODY t-MATRIX FOR A FREE-BOUND SYSTEM. PART I. APPLICATION TO NUCLEAR CHARGE EXCHANGE
The nuclear charge exchange X(/sub 2/A/sub n/ /sub 1/ /sub b-1/ A/sub n+1/)Y can be reduced in a fully antisymmetrized description to one of elementary nature, n + p and up to st r n' + p'. The t-matrix for the latter has to be averaged over the momenta distribution of the bound constituents. For sufficiently large bombarding energies and small Q values, the nucleon carried by the incident system may be considered as quasi-free. That carried by the outgoing system is then described in a similar fashion. This sort of approximation is consistent with the determination of t from an equation of the Bethe-Goldstone type. Solutions of this equation are sought which apply to the finite nucleus. One of the nuclear constituents is viewed as being in continuum states, the other in bound states. The application of the development to Be/sup 9/(He/sup 3/,T)B/sup 9/ is solely for the purpose of concreteness. A major aspect of the analysis is that the virtual excited states of the intermediate system are taken into account. This is done by making specific assumptions concerning the single particle transitions brought about by the addition of a nucleon to the target nucleus. The possibility of a collective intermediate state excitation is considered. This is described through the introduction of a continuum two-particle bound state. Such a state gives rise to the principal renormalization of the two-particle transition operator. The final form of the elementary transition operator is one having a singleparticle spectrum of excitations, renormalized by the coupling to the collective state. The transition operator is additive and can be classified both as to diagonality of its matrix elements and according to the resonance structure of these. In its form as a sum of diagonal and nondiagonal operators, the former is responsible for nuclear distortions, the latter for the physical change of state. It is the non-diagonal operator which determines the direct interaction processes. It, in particular, induces changes of state for just a few target constituents. The diagonal part of the interaction operator is moreover expressible as a sum of resonant and non-resonant terms. These are, respectively, contributions arising from the continuum bound state and those described as potential scattering. The latter again include virtual transitions of the interacting constituents. Emphasis is put upon viewing the reaction problem in terms of the self- consistency requirements of the H-F method. This, together with procedures arising out of Brueckner theory, leads to the characterization of the interaction dynamics. (auth)
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- DOE Contract Number:
- W-7405-ENG-36
- NSA Number:
- NSA-17-020987
- OSTI ID:
- 4715578
- Report Number(s):
- LA-2805
- Resource Relation:
- Other Information: Orig. Receipt Date: 31-DEC-63
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
BERYLLIUM 9
BETHE-GOLDSTONE EQUATION
BINDING ENERGY
BRUECKNER MODEL
CHARGE EXCHANGE
COLLECTIVE MODEL
DIFFERENTIAL EQUATIONS
DIRECT REACTIONS
DISTRIBUTION
ELECTRIC CHARGES
ENERGY
ENERGY LEVELS
EXCITATION
HELIUM 3
INTERACTIONS
IRRADIATION
MANY BODY PROBLEM
MATRICES
MOMENTUM
NEUTRONS
NUCLEAR MODELS
NUCLEAR REACTIONS
NUCLEAR STRUCTURE
NUCLEONS
PROTONS
Q-VALUE
QUANTUM MECHANICS
REACTION KINETICS
RESONANCE
SCATTERING
T-MATRIX
TARGETS
TRITONS
VIRTUAL STATES