Single determinantal reaction theory as a Schroedinger analog: the time-dependent S-matrix Hartree-Fock method
It is suggested that the TDHF method be viewed, not as an approximation to but as a model of the exact Schroedinger system; that is, as a gedanken many-body experiment whose analysis with digital computers provides data worthy in itself of theoretical study. From such a viewpoint attention is focused on the structural analogies of the TDHF system with the exact theory rather than upon its quantitative equivalence, and the TDHF many-body system is studied as a challenge of its own which, although much simpler than the realistic problem, may still offer complexity enough to educate theorists in the present state of knowledge. In this spirit, the TDHF description of continuum reactions can be restructured from an initial-value problem into a form analogous to the S-matrix version of the Schroedinger theory. The resulting TD-S-HF theory involves only self-consistent single determinantal solutions of the TDHF equations and invokes time averaging to obtain a consistent interpretation of the TDHF analogs of quantities which are constant in the exact theory, such as the S-matrix and the asymptotic reaction channel characteristics. Periodic solutions then play the role of stationary eigenstates in the construction of suitable asymptotic reaction channels. If these periodic channel states occur only at discrete energies, then the resulting channels are mutually orthogonal (on the time average) and the theory exhibits a structure fully analogous to the exact theory. In certain special cases where the periodic solutions are known to occur as an energy continuum, the requirement that the periodicity of the channel solutions be gauge invariant provides a natural requantization condition which (suggestively) turns out to be identical with the Bohr-Sommerfeld quantization rule. 11 references.
- Research Organization:
- University of Maryland, College Park, MD
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- EY-76-S-05-5126
- OSTI ID:
- 5865713
- Report Number(s):
- ORO-5126-68; CONF-790660-6; TRN: 79-021897
- Resource Relation:
- Conference: Conference on large amplitude collective nuclear motion, Lake Balaton, Hungary, 10 Jun 1979
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
HARTREE-FOCK METHOD
S MATRIX
SCHROEDINGER EQUATION
NUCLEAR REACTIONS
BOHR THEORY
BOUNDARY CONDITIONS
EIGENSTATES
GAUGE INVARIANCE
MANY-BODY PROBLEM
SELF-CONSISTENT FIELD
TIME DEPENDENCE
VARIATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
INVARIANCE PRINCIPLES
MATRICES
WAVE EQUATIONS
653003* - Nuclear Theory- Nuclear Reactions & Scattering