 Cooper pair binding energy

For shell width $D$, attraction $g>0$ and constant single-spin density of states $\rho$, $1=(g\rho /2)\log [(2D+B)/B]$ gives $B=2D/[\exp (2/(g\rho ))-1]$. The pair energy relative to the free threshold is $-B$. At weak coupling this scale is nonanalytic in $g$.