  We study numerically the collapse of massless scalar fields in
two-dimensional dilaton gravity, both classically and semiclassically. At the
classical level, we find that the black hole mass scales at threshold like
$M_{\rm bh} \propto |p-p^*|^{\gamma}$, where $\gamma \simeq 0.53$. At the
semiclassical level, we find that in general $M_{\rm bh}$ approaches a non-zero
constant as $p \rightarrow p^*$. Thus, quantum effects produce a mass gap not
present classically at the onset of black hole formation.
