Jastrow Theory versus Correlated Basis Functions: Excitation Spectrum of the Charged Bose Gas

By computing the excitation spectrum of the charged Bose gas, we demonstrate explicitly the distinction between Jastrow's theory and Feenberg's method of correlated basis functions. Using a Jastrow correlating factor in the correlated basis functions, we obtain the spectrum exactly to two orders in ${r_s}^{\frac{3}{4}}$. A rearranged expression results when the true ${\psi }_0$ is employed as a correlating factor. We take advantage of the difference between these two procedures to obtain $S\left(k\right)\mathrm{}$ exactly to two orders.