Elliott H. Lieb and Jakob Yngvason
Ground State Energy of the Low Density Bose Gas
(25K, Revtex)
ABSTRACT. Now that the properties of low temperature Bose gases at low density,
$\rho$, can be examined experimentally it is appropriate to revisit
some of the formulas deduced by many authors 4-5 decades ago. One of
these is that the leading term in the energy/particle is $2\pi \hbar^2
\rho a/m$, where $a$ is the scattering length. Owing to the delicate
and peculiar nature of bosonic correlations, four decades of research
have failed to establish this plausible formula rigorously. The only
known lower bound for the energy was found by Dyson in 1957, but it was
14 times too small. The correct bound is proved here.