Single Determinantal Reaction Theory: Asymptoticity, Periodicity, Time Averaging, Channel Orthogonality, Requantization and Gauge Invariance

摘要

The TDHF description of continuum reactions can be restuctured 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 labels. Periodic TDHF solutions then play the role of stationary eigenstates, in the construction of suitable asymptotic reaction channel states. 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 a gauge invariant property provides a natural requantization condition, which (suggestively) turns out to be identical with the Bohr-Sommerfield quantization rule. 11 references. (ERA citation 05:002173)