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Journal of the Physical Society of Japan, June 15, 2013, Vol. 82, No. 6

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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 \(c_{\text{ip}}\sim O(1)\) to the expressions reported by Lee et al. [Phys. Rev. 106 (1957) 1135] as \(E/N=(2\pi\hbar^{2}an/m)[1+(128/15\sqrt{\pi}+16c_{\text{ip}}/5)\sqrt{a^{3}n}]\) and \(n_{0}/n=1-(8/3\sqrt{\pi}+c_{\text{ip}})\sqrt{a^{3}n}\), 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 \(c_{\text{ip}}\); the third-order perturbation expansion yields \(c_{\text{ip}}=0.412\).

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