  In this paper, we study Schwinger pair production of charged massless
particles in constant electric fields of finite-extent. Exploiting a map from
the Dirac and Klein-Gordon equation to the harmonic oscillator, we find exact
pair production rates for massless fermions and scalars. Pair production rates
depend only on the ratio between the capacitor plate separation, $\ell$, and
the length-scale of the force-field, $\ell_F$. Chirality ensures that fermion
production smoothly vanishes with $\ell/\ell_F$. Scalar pair production though
diverges exponentially quickly in this limit. The same limit of the smooth
tanh-potential does not diverge; divergences seem tied to singularities in
current and charge densities.
