Perturbation Theory, Bethe-Goldstone Equation, and the Binding Energy of Solid Helium

Perturbation diagrams of the Brueckner-Goldstone expansion are partially summed to derive a Bethe-Goldstone equation for the short-range correlations in solid helium. The three corresponding two-body wave equations used in binding-energy calculations by Guyer, by Horner, and by Ebner and Sung are critically compared with the present one by means of the theory of $t$-matrix propagator perturbations. This provides qualitative explanations for the discrepancies between these published calculations and experiment.