Corrections to Local Density Approximation for superfluid trapped fermionic atoms from the Wigner-Kirkwood $\hslash$ expansion

Peter Schuck, Michael Urban, Xavier Viñas

A semiclassical second-order differential equation for the inhomogeneous local gap $\Delta (r)$ is derived from a strict second-order $\hslash$ expansion of the anomalous pairing tensor an…