The few-body problem for trapped bosons with large scattering length

Abstract

We calculate energy levels of two and three bosons trapped in a harmonic oscillator potential with oscillator length $a_{\mathrm{o}sc}$. The atoms are assumed to interact through a short-range potential with a scattering length $a$, and the short-distance behavior of the three-body wave function is characterized by a parameter $\hat{I}¸$. For large positive $a/a_{\mathrm{o}sc}$, the energies of states which, in the absence of the trap, correspond to three free atoms approach values independent of $a$ and $\hat{I}¸$. For other states the $\hat{I}¸$ dependence of the energy is strong, but the energy is independent of $a$ for $|a/a_{\mathrm{o}sc}|\gg 1$.

4 pages, 3 figures