= Energy selectivity for evaporation to increase phase-space density
{title2=$\epsilon_{\rm ev}>4k_BT$}
For a classical three-dimensional harmonic trap of fixed <frequencies>, $E=3Nk_BT$ and $\mathcal D\propto NT^{-3}$. Combining $dE=\epsilon_{\rm ev}dN$ with these equations gives $d\ln\mathcal D/d\ln N=4-\epsilon_{\rm ev}/(k_BT)$. Since evaporation decreases $N$, <phase-space density of an atomic gas> increases only when the removed mean <energy> exceeds $4k_BT$. Merely lowering <temperature> requires only $\epsilon_{\rm ev}>3k_BT$. Changing confinement adds trap work and changes these formulas.
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