= Density crossover of a fixed-coupling BCS cutoff model
{title2=$n_\theta=(2m\theta/\hbar^2)^{3/2}/(3\pi^2)$}
Set the <chemical potential> equal to the degenerate three-dimensional spin-degenerate <Fermi energy>, proportional to $n^{2/3}$, and keep the effective coupling and upper cutoff fixed. The <asymmetric-cutoff BCS transition temperature> scales as $n^{1/3}$ below $n_\theta$ and saturates above it. At low density the predicted $k_BT_c/\mu$ instead grows as $n^{-1/3}$, eventually invalidating the degenerate and logarithmic approximations. This is a prescribed cutoff model, not a self-consistent treatment of the <BCS-BEC crossover>.
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