BCS population above the normal-state Fermi surface ($\Delta N/N\simeq 3\Delta /(4\mu )$)

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.