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Nuclear Physics A

Time-dependent Hartree approximation and time-dependent harmonic oscillator model

Jean-Paul Blaizot, H. Schulz

Published Mar 1, 1982• 3 citations
Publisher
DOI
10.1016/0375-9474(82)90331-1

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In this paper, we present benchmark results for dissipative dynamics of a harmonic oscillator coupled to an anharmonic bath of Morse oscillators. The microscopic Hamiltonian has been chosen so that the anharmonicity can be adjusted as a free parameter, and its effect can be isolated. This leads to a temperature dependent spectral density of the bath, which is studied for ohmic and lorentzian cases. Also, we compare numerically exact multiconfiguration time-dependent Hartree results with approximate solutions using continuous configuration time-dependent self-consistent field and local coherent state approximation.
A new numerical method of calculating the Hartree-Fock-Bogoliubov (HFB) and time-dependent HFB (TDHFB) with the Gogny interaction is proposed. The three-dimensional harmonic-oscillator (3DHO) basis functions are replaced by one-dimensional spatial grid points of Lagrange mesh plus two-dimensional harmonic-oscillator basis functions in the perpendicular plane to the direction of the spatial grid points [Lagrange mesh and harmonic oscillator (LMHO)]. By using the LMHO, the calculations of the HFB and TDHFB are carried out in the typical nuclei of 20O{}^{20}\mathrm{O}20O and 34Mg{}^{34}\mathrm{Mg}34Mg as an illustration of the feasibility of the TDHFB formulation with the LMHO. The strength functions of the quadrupole vibrations (K=0K=0K=0) are obtained and are compared with the ones calculated with the 3DHO.