Goldstone-type diagrams

The diagrams just discussed—with antisymmetrized vertices at spin-orbital level — are of Hugenholtz type [32]. One can alternatively define [30] diagrams of Goldstone type [33] with spin-free vertices. 

Figure 8 Second order correlation energy diagrams for a closed-shell system described in zero order by a single determinantal Hartree-Fock wave function constructed from canonical orbitals. The one Brandow diagram of this type is shown in (a). The exchange diagrams are shown in Goldstone form in (b)...

However, this problem is overcome by introducing the reaction matrix G, displayed by the summation of ladder type of diagrams in Fig. 1, which accounts for the effects of two-nucleon correlations. The G-matrix is given by the solution of the Bethe-Goldstone equation... 

Let us examine first the third-order perturbation energy for a general closed-diell system. There are three types of associated diagrams, of which the Goldstone (leading term only) and Hugenholz representations are... 

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