  We derive upper and lower bounds on the critical temperature $T_c$ and the
energy gap $\Xi$ (at zero temperature) for the BCS gap equation, describing
spin 1/2 fermions interacting via a local two-body interaction potential
$\lambda V(x)$. At weak coupling $\lambda \ll 1$ and under appropriate
assumptions on $V(x)$, our bounds show that $T_c \sim A \exp(-B/\lambda)$ and
$\Xi \sim C \exp(-B/\lambda)$ for some explicit coefficients $A$, $B$ and $C$
depending on the interaction $V(x)$ and the chemical potential $\mu$. The ratio
$A/C$ turns out to be a universal constant, independent of both $V(x)$ and
$\mu$. Our analysis is valid for any $\mu$; for small $\mu$, or low density,
our formulas reduce to well-known expressions involving the scattering length
of $V(x)$.
