Cold Bose Gases with Large Scattering Lengths

We calculate the energy and condensate fraction for a dense system of bosons interacting through an attractive short range interaction with positive $s$-wave scattering length $a$. At high densities $n\gg a^{-3\mathrm{}}$, the energy per particle, chemical potential, and square of the sound speed are independent of the scattering length and proportional to $n^{2/3}$, as in Fermi systems. The condensate is quenched at densities ${\mathrm{na}}^3\simeq 1$.