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Nuclear Physics A

The coupling of valence shell and particle-hole degrees of freedom in a partial random phase approximation

DAVID J. ROWE, P. Rochford, Richard Le Blanc

Published Mar 1, 1987• 13 citations
Publisher
DOI
10.1016/0375-9474(87)90421-0

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Extension of the second random-phase approximation

D. Gambacurta, M. Grasso, F. Catara +1 more

The second random-phase approximation (SRPA) is the simplest and most natural extension of the RPA. It enlarges the space of the elementary modes introduced to describe the collective states by adding 2 particle -2 hole excitations to the 1 particle -1 hole ones of the RPA. In deriving the SRPA equations, use is made, as in the RPA, of the so-called quasi-boson approximation (QBA) where expectation values in the ground state of the system are approximated by their values in the uncorrelated reference state. This, however, has been shown to imply a degree of approximation worse than that in the RPA. It is, therefore, necessary to improve the QBA by considering a reference state which contains some correlations. Having in mind to perform such calculations for realistic systems, we consider a simple extension of the SRPA in which the reference state contains 2 particle - 2 hole correlations. The quality of such an extension is tested by applying it to a solvable three-level model and found to be good.

Physical Review C•Feb 28, 2006•21 citations
The spectral function of the closed-shell neon atom is computed by expanding the electron self-energy through a set of Faddeev equations. This method describes the coupling of single-particle degrees of freedom with correlated two-electron, two-hole, and electron-hole pairs. The excitation spectra are obtained using the random-phase approximation (RPA), rather than the Tamm-Dancoff framework employed in the third-order algebraic diagrammatic construction method. The difference between these two approaches is studied, as well as the interplay between ladder and ring diagrams in the self-energy. Satisfactory results are obtained for the ionization energies as well as the energy of the ground state with the Faddeev RPA scheme, which is also appropriate for the high-density electron gas.
The second random-phase approximation (SRPA) is the simplest and most natural extension of the RPA. It enlarges the space of the elementary modes introduced to describe the collective states by adding 2 particle -2 hole excitations to the 1 particle -1 hole ones of the RPA. In deriving the SRPA equations, use is made, as in the RPA, of the so-called quasi-boson approximation (QBA) where expectation values in the ground state of the system are approximated by their values in the uncorrelated reference state. This, however, has been shown to imply a degree of approximation worse than that in the RPA. It is, therefore, necessary to improve the QBA by considering a reference state which contains some correlations. Having in mind to perform such calculations for realistic systems, we consider a simple extension of the SRPA in which the reference state contains 2 particle - 2 hole correlations. The quality of such an extension is tested by applying it to a solvable three-level model and found to be good.