Extended quasiparticle approximation and Brueckner theory

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Abstract
The time-dependent Green’s function method provides a basic theory for nuclear dynamics and heavy-ion collisions. The spectral function plays an important role in this theory containing information on correlations in the medium. These are usually neglected by using a quasiparticle approximation. In order to evaluate this particular approach it is important to establish in the static limit a link between this method and other traditional nuclear many-body theories such as the Brueckner approach. Using a self-consistent T-matrix approximation for the self-energy in the Green’s-function approach, treating particles and holes on equal footing, the self-energy can be obtained and compared with the Brueckner expression. In the quasiparticle limit it contains terms up to and analogous to the Brueckner second order rearrangement energy. In an extended quasiparticle approximation (EQP) which does not violate the sum rule for the spectral function the Brueckner third-order rearrangement energy can also be reproduced. The latter approximation constitutes a bridge between the Brueckner and Green’s-function methods. It assumes small absorption (and energy dependence) of the mean field. Some numerical estimates of the different approximation schemes that we discuss are shown. An iteration scheme for applying the EQP approximation is suggested.