Charged Bose Gas

Green-function techniques are applied to the charged Bose gas at the absolute zero of temperature. The procedure permits some general remarks to be made concerning the expansions of the ground-state energy and depletion parameter in terms of ${\mathcal{r}}_S$, the ratio of the interparticle spacing to the Bohr radius. It is found that these series contain not only all integer powers of ${{\mathcal{r}}_S}^{\frac{3}{4}}$ as had been conjectured, but additional functions of ${\mathcal{r}}_S$ as well. The first-two terms in the expansion of the ground-state energy are calculated exactly as are the first-four terms in the expansion of the depletion parameter. The former expansion agrees with the results of Lee and Feenberg. The latter, containing a noninteger power of ${{\mathcal{r}}_S}^{\frac{3}{4}}$, is new. It is shown that the ground-state energy diagrams which must be summed in the Bose gas are characterized by equal numbers of variables of integration. It is emphasized that these are not the most divergent diagrams as in the electron-gas calculation of Gell-Mann and Brueckner. This difference leads us to reformulate the diagrammatic procedure so as to emphasize its self-consistency. The underlying similarity of the charged Fermi and Bose-gas calculations is then made apparent.