TD-S-HF single determinantal reaction theory and the description of many-body processes, including fission. [Schroedinger equation, constructive analysis S matrix, review]

Conference · Mon Jan 01 04:00:00 EST 1979

OSTI ID:5824703

Griffin, J. J.; Lichtner, P. C.; Dworzecka, M.; Kan, K. K.

The restrictions implied for the time dependent many-body reaction theory by the (TDHF) single determinantal assumption are explored by constructive analysis. A restructured TD-S-HF reaction theory is modelled, not after the initial-value form of the Schroedinger reaction theory, but after the (fully equivalent) S-matrix form, under the conditions that only self-consistent TDHF solutions occur in the theory, every wave function obeys the fundamental statistical interpretation of quantum mechanics, and the theory reduces to the exact Schroedinger theory for exact solutions which are single determinantal. All of these conditions can be accomodated provided that the theory is interpreted on a time-averaged basis, i.e., physical constants of the Schroedinger theory which are time-dependent in the TDHF theory, are interpreted in TD-S-HF in terms of their time averaged values. The resulting reaction theory, although formulated heuristically, prescribes a well defined and unambiguous calculational program which, although somewhat more demanding technically than the conventional initial-value TDHF method, is nevertheless more consonant with first principles, structurally and mechanistically. For its physical predictions do not depend upon the precise location of the distant measuring apparatus, and are in no way influenced by the spurious cross channel correlations which arise whenever the description of many reaction channels is imposed upon one single-determinantal solution. For nuclear structure physics, the TDHF-eigenfunctions provide the first plausible description of exact eigenstates in the time-dependent framework; moreover, they are unencumbered by any restriction to small amplitudes. 14 references.

• Research Organization: University of Maryland, College Park,MD
• Sponsoring Organization: USDOE
• DOE Contract Number: EY-76-S-05-5126
• OSTI ID: 5824703
• Report Number(s): ORO-5126-69; CONF-790507-8
• Country of Publication: United States
• Language: English

Related Subjects

653003* -- Nuclear Theory-- Nuclear Reactions & Scattering
653006 -- Nuclear Theory-- Spontaneous & Induced Fission
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
DOCUMENT TYPES
EIGENFUNCTIONS
EIGENSTATES
EQUATIONS
FISSION
FUNCTIONS
GAUGE INVARIANCE
HARTREE-FOCK METHOD
INVARIANCE PRINCIPLES
MANY-BODY PROBLEM
MATHEMATICS
MATRICES
MECHANICS
NUCLEAR REACTIONS
QUANTUM MECHANICS
REVIEWS
S MATRIX
SCHROEDINGER EQUATION
STATISTICS
TIME DEPENDENCE
VARIATIONAL METHODS
WAVE EQUATIONS
WAVE FUNCTIONS