Time-dependent--S-matrix Hartree-Fock theory of complex reactions

Journal Article · Tue Apr 01 04:00:00 EST 1980 · Phys. Rev., C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.21.1351· OSTI ID:5408151

Griffin, J J; Lichtner, P C; Dworzecka, M

Some limitations of the conventional time-dependent Hartree-Fock method for describing complex reactions are noted, and one particular ubiquitous defect is discussed in detail: the post-breakup spurious cross channel correlations which arise whenever several asymptotic reaction channels must be simultaneously described by a single determinant. A reformulated time-dependent--S-matrix Hartree-Fock theory is proposed, which obviates this difficulty. Axiomatic requirements minimal to assure that the time-dependent--S-matrix Hartree-Fock theory represents an unambiguous and physically interpretable asymptotic reaction theory are utilized to prescribe conditions upon the definition of acceptable asymptotic channels. That definition, in turn, defines the physical range of the time-dependent--S-matrix Hartree-Fock theory to encompass the collisions of mathematically well-defined ''time-dependent Hartree-Fock droplets.'' The physical properties of these objects then circumscribe the content of the Hartree-Fock single determinantal description. If their periodic vibrations occur for continuous ranges of energy then the resulting ''classical'' time-dependent Hartree-Fock droplets are seen to be intrinsically dissipative, and the single determinantal description of their collisions reduces to a ''trajectory'' theory which can describe the masses and relative motions of the fragments but can provide no information about specific asymptotic excited states beyond their constants of motion, or the average properties of the limit, if it exists, of their equilibrization process. If, on the other hand, the periodic vibrations of the time-dependent Hartree-Fock droplets are discrete in energy, then the time-dependent--S-matrix Hartree-Fock theory can describe asymptotically the time-average properties of the whole spectrum of such periodic vibrations.

• Research Organization: Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742
• OSTI ID: 5408151
• Journal Information: Phys. Rev., C; (United States), Journal Name: Phys. Rev., C; (United States) Vol. 21:4; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653003* -- Nuclear Theory-- Nuclear Reactions & Scattering
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
CLASSICAL MECHANICS
DIFFERENTIAL EQUATIONS
EIGENSTATES
EIGENVALUES
EQUATIONS
FUNCTIONS
HARTREE-FOCK METHOD
MATRICES
MECHANICS
S MATRIX
SCATTERING
SCHROEDINGER EQUATION
TIME DEPENDENCE
WAVE EQUATIONS
WAVE FUNCTIONS