  We investigate the behavior of the critical charge for spontaneous pair
production, $Z_C$, defined as the charge at which the total energy of a
$K$-shell electron is $E=-m_e$, as a function of the radius $R$ of the charge
distribution. Our approach is to solve the Dirac equation for a potential
$V(r)$ consisting of a spherically symmetrical charge distribution of radius
$R$ and a Coulomb tail. For a spherical shell distribution of the type usually
associated with color-flavor locked strange quark nuggets, we confirm the
relation $Z_C=0.71 R({\rm fm})$ for sufficiently large $R$ obtained by Madsen,
who used an approach based on the Thomas-Fermi model. We also present results
for a uniformly charged sphere and again find that $Z_C\sim R$ for large enough
$R$. Also discussed is the behavior of $Z_C$ when simple {\it ad hoc}
modifications are made to the potential for $0\leq r < R$.
