  We study the spectrum of the semiclassical Witten Laplacian $\Delta_{f}$
associated to a smooth function $f$ on ${\mathbb R}^d$. We assume that $f$ is a
confining Morse--Bott function. Under this assumption we show that $\Delta_{f}$
admits exponentially small eigenvalues separated from the rest of the spectrum.
Moreover, we establish Eyring-Kramers formula for these eigenvalues. Our
approach is based on microlocal constructions of quasimodes near the critical
submanifolds.
