Ground-State Energy and Condensate Density of a Dilute Bose Gas Revisited

Abstract

The ground-state energy per particle $E/N$ and condensate density $n_0$ of a dilute Bose gas are studied with a self-consistent perturbation expansion satisfying the Hugenholtz-Pines theorem and conservation laws simultaneously. A class of Feynman diagrams for the self-energy, which has escaped consideration so far, is shown to add an extra constant $c_{ip}\sim O(1)$ to the expressions reported by Lee, Huang, and Yang [Phys. Rev. 106, 1135 (1957) ] as $E/N=(2\pi\hbar^2 an/m)[1+(128/15\sqrt{{\pi}}+16c_{ip}/5)\sqrt{{a^3n}}]$ and $n_0/n=1-(8/3\sqrt{{\pi}}+c_{ip})\sqrt{{a^3n}}$, where $a$, $n$, and $m$ are are the s-wave scattering length, particle density, and particle mass, respectively. We present a couple of estimates for $c_{ip}$; the third-order perturbation expansion yields $c_{ip}=0.412$.