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Europhysics Letters (EPL)

Self-Consistent RPA Based on the Thermo Field Dynamics

Р.Б. Бегжанов, E. M. Galinsky

Published Mar 1, 1992• 0 citations
Publisher

Abstract

The conventional RPA is extended to take into account the effect of the Pauli principle and the ground-state correlations based on the thermo field dynamics formalism. The calculations have been performed for the dipole state in the scheme of 58 nucleons within the degenerate schematic model. A comparison of these results with the calculations carried out within the framework of the standard thermo field dynamics of the RPA is made.

DOI
10.1209/0295-5075/18/5/002

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The conventional RPA is extended to take into account the effect of the Pauli principle and the ground-state correlations based on the thermo field dynamics formalism. The calculations have been performed for the dipole state in the scheme of 58 nucleons within the degenerate schematic model. A comparison of these results with the calculations carried out within the framework of the standard thermo field dynamics of the RPA is made.
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Self-Consistent RPA is extended in a way so that it is compatible with a variational ansatz for the ground-state wave function as a fermionic many-body vacuum. Employing the usual equation-of-motion technique, we arrive at extended RPA equations of the Self-Consistent RPA structure. In principle the Pauli principle is, therefore, fully respected. However, the correlation functions entering the RPA matrix can only be obtained from a systematic expansion in powers of some combinations of RPA amplitudes. We demonstrate for a model case that this expansion may converge rapidly.
Working within a schematic model and in a boson formalism, we provide a descrip tion of the ground and first-excited states of a nuclear system in terms of two independent phonon operators. The description reveals itself quite effective in reproducing the energies of the states. A comparison between these two phonon operators allows us to localize a region where a correct description of these states is compatible with the Random Phase Approximation (RPA) requirement of a single phonon. This region is found to coincide approximately with that spanned by the standard RPA. Outside this region, the two phonons start differing rapidly therefore making the application of the RPA scheme impossible. This allows a better understanding of recently performed higher-order RPA calculations.
The self-consistent RPA (SCRPA) developed by Schuck and coauthors is extended to finite temperatures. The corresponding equations are derived by using the formalism of thermofield dynamics. The intrinsic energy of a system is calculated as the expectation value of the Hamiltonian with respect to a T -dependent thermal vacuum state for a thermal-phonon operator. A nonvanishing number of thermal quasiparticles in the vacuum state are assumed. By virtue of the assumption, the thermal Hartree-Fock (HF) equations appear to be coupled to the equations of motion for phonon variables. The thermal occupation numbers are also calculated in a consistent way with the energies of the HF quasiparticles. The approximation is applied to the two-level Lipkin model. Advantages of the thermal SCRPA (TSCRPA) are most obvious at temperatures near the phase-transition point. In the TSCRPA, the phase transition occurs at lower T than in other approximations. Moreover, within the TSCRPA, a statistical behavior of the Lipkin model is described with an appropriate accuracy at any T even if the HF transformation parameter is kept fixed at a value corresponding to the “spherical” phase of the HF field.