= BCS population above the normal-state Fermi surface
{c}
{title2=$\Delta N/N\simeq3\Delta/(4\mu)$}
For a uniform isotropic weak-gap BCS state, the zero-temperature <electron> occupation is $n(\xi)=(1-\xi/\sqrt{\xi^2+\Delta^2})/2$. The number above the normal-state <Fermi surface> is approximately $D(\mu)\int_0^\infty n(\xi)d\xi$. The integral equals $\Delta/2$, while a three-dimensional parabolic band including both spins has $D(\mu)=3N/(2\mu)$. This gives the displayed leading fraction.
The result measures redistribution relative to a normal <Fermi sea>, not bosonic single-mode condensate depletion or <quasiparticle> occupation. A different band dimension or anisotropic gap requires its actual density-of-states or <momentum> integral. Material estimates need specified gap and chemical-potential scales.
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