Diagrammatic Analysis of the Method of Correlated Basis Functions. II. Perturbation Theory for a Weakly Interacting Bose Gas

Continuing the diagrammatic analysis of the method of correlated basis functions (CBF) for the weakly interacting Bose gas, as reported in the preceding paper, we take off from the unperturbed problem, which is solved essentially by a variational method using a Jastrow correlating factor as the trial wave function. We compute low-order corrections to the unperturbed energy, using a set of correlated basis functions. It is found that the simplest second-order correction in the CBF accounts for all discrepancies (between the Hugenholtz-Pines theory and the unperturbed CBF calculation) which arise in the fourth order of the interaction strength $O\left({\lambda }^4\right)$. It is also demonstrated indirectly that the Jastrow function sums rings and ladders at least up to $O\left({\lambda }^5\right)$.