Time Dependent Hartree-Fock and Beyond

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Abstract
The time dependent Hartree-Fock method (TDHF) is reviewed and its success and failure are discussed following realistic numerical results. It is demonstrated that TDHF is basically able to describe the time evolution of one-body operators, the energy loss in inclusive deep inelastic collisions, and fusion reactions above the Coulomb barrier. For spontaneous fission, subbarrier fusion and the description of bound vibrations the quantized adiabatic time dependent Hartree-Fock theory (quantized ATDHF) is suggested and reviewed. Realistic three-dimensional calculations for heavy ion systems of A1 + A2 ≤ 32 are presented. Recent theories based on integral approaches (PIA) are discussed, which aim at quantizing TDHF in order to describe stationary vibrational states and subbarrier fission. The relationship of quantized ATDHF to PIA is explored in the case of vibrations including the fluctuations on top of the periodic TDHF orbits. The above methods to go beyond TDHF concern the quantum mechanical content of TDHF. For the description of width of one-body observables in inclusive reactions the time dependent generator coordinate method (TDGCM) is reviewed. It appears in one-dimensional calculations to be able to enlarge the width obtained in TDHF by an order of magnitude. It is argued that this is because a superposition of mean fields is considered in contrast to other approaches which consider collision terms in a single modified TDHF mean field.

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