Mean field methods in large amplitude nuclear collective motion

Abstract

The time dependent Hartree-Fock method (TDHF) is reviewed and its success and failure are discussed. It is demonstrated that TDHF is a semiclassical theory which 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 genuine quantum mechanical processes as e.g. spontaneous fission, subbarrier fusion, phase shifts 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. Applications to various nuclear observables as e.g. astrophysical S-factors in subbarrier fusion, ground state rotational bands, elastic HI-scattering, etc., are shown. The decoupling properties of ATDHF-paths are discussed in detail. Recent theories based on path integral approaches (PIA) are reviewed, which aim at quantizing TDHF in order to describe stationary vibrational states and subbarrier fusion. The relationship of quantized ATDHF to PIA is explored in the case of bound vibrations. A derivation of the quantization prescription by means of the generator coordinate method is presented. 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 as able to enlarge the fluctuations of one-body observables, obtained in TDHF, by an order of magnitude.