Ground State and Low Excited States of a Boson Liquid with Applications to the Charged Boson System

Abstract

The maximum deviation of the radial distribution function $g\left(r\right)\mathrm{}$ from its asymptotic value, $g\left(\infty \right)=1\mathrm{}$, is used as an expansion parameter in calculating the properties of a degenerate boson system. The uniform limit, defined by the condition $1-g\left(0\right)\mathrm{}\ll 1$, holds at low densities under appropriate constraints on the Fourier transforms of the interaction potential and also at high densities for the charged-boson system. In the uniform limit a procedure based on (1) a Jastrow-type trial function, (2) the Wu-Feenberg functional for the kinetic energy, (3) the Kirkwood superposition approximation, or the more accurate Abe form for the three-particle distribution function, yields the Bogoliubov formulas for the ground-state energy and the excitation energies of a degenerate or nearly degenerate boson system. Results for the ground state of the high-density charged-boson system include $\frac{〈\mathrm{KE}〉}{N}=-\frac{1}{5}\frac{〈\mathrm{PE}〉}{N}+O\left({r_s}^0\right),$ $\frac{E}{N}\leqq -\frac{0.8031}{{r_s}^{\frac{3}{4}}}+\mathrm{0.028.}\mathrm{}$ Numerical results are also computed at intermediate and moderately low densities ($0.01\leqq r_s\leqq 100$).