= Interaction-dominated ground state with nearly ideal condensation temperature
{title2=$N^{-1}\ll a/L\ll N^{-1/3}$}
In a box of size $L$, confinement <energy> scales as $\hbar^2/(mL^2)$, transition <temperature> as that scale times $N^{2/3}$, and mean interaction <energy> as $\hbar^2Na/(mL^3)$. The displayed window therefore makes interaction <energy> large compared with confinement but small compared with $k_BT_c$. It simultaneously implies dilute-gas parameter $na^3\ll1$. Ground-state interaction dominance does not require a large relative shift of the condensation <temperature>.
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