= Mass-anisotropy enhancement of a weak-coupling BCS gap
{title2=$\Delta\simeq2\varepsilon_c e^{-1/(\lambda_0\gamma^{1/3})}$}
For a fixed-density balanced two-spin Fermi gas with masses $(m,m,\gamma m)$, the Fermi energy scales as $\gamma^{-1/3}$ while the single-spin Fermi-level <density of states> scales as $\gamma^{1/3}$. A constant attractive interaction $g$ within a narrow symmetric energy window $\varepsilon_c\ll\varepsilon_F$ therefore gives $1=\lambda_0\gamma^{1/3}\operatorname{arsinh}(\varepsilon_c/\Delta)$. Solving gives $\Delta=\varepsilon_c/\sinh[1/(\lambda_0\gamma^{1/3})]$, whose weak-coupling limit is displayed. Extrapolating to arbitrarily large anisotropy violates the assumptions that the Fermi energy dominates the window and that the pairing coupling is small.
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