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The European Physical Journal A

Dynamical basis generation and structure of the Hartree-Fock approximation

Guillermo H. Bozzolo, James P. Vary, N. Canosa, J. N��ez, A. Piastino

Published Sep 1, 1985• 2 citations
Publisher
DOI
10.1007/bf01411975

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A variational method inspired by the Hartree-Fock approximation but not restricted to a single Slater determinant trial space is investigated. The physical motivation is that a method should attempt to find a subspace of collective states which are most strongly coupled to the ground state. This method attempts to do this by providing a systematic technique to generate basis states from the collective Hartree-Fock type of state. In the resulting basis space a residual diagonalization is easily performed. Results of a test with the four-nucleon problem with realistic effective nuclear Hamiltonians are shown.
In order to try to open a new scope to explore the mutual dependence between the single-particle and collective modes of motion near to the level crossing region, a general method is developed to investigate the nonlinear resonant structure of the time-dependent Hartree-Fock (TDHF) manifold, without depending on the adiabatic assumption. By using the Lie canonical transformation method with the Deprit perturbation treatment, in this method, the maximal integrable-form representation of the TDHF manifold is introduced. This representation plays an essential role in exploring the nonlinear resonant structure of the TDHF manifold, which characterizes complex topology of the manifold. Aiming at relating the nonlinear resonance in the TDHF manifold with the dynamics between the single-particle and collective modes of motion near to the level crossing region, structure of the TDHF wave function in the nonlinear resonant region is investigated. It is clarified that an isolated nonlinear resonant region of the TDHF manifold is characterized by a local constant of motion (dynamical symmetry) and generates a new type of dynamical stable single-Slater-determinant states, which is topologically different from the TDHF states near the HF ground state, and cannot be reached by the conventional static Hartree-Fock method, constrained Hartree-Fock method, nor the adiabatic TDHF theories. One may expect that the appearance mechanism of the new dynamical stable single-Slater-determinant states gives us a new scope for understanding occurrence mechanism of a variety of collective sideband structure near to the level crossing region.