  The semi-classical collapse, including lowest order back-reaction, of a thin
shell of self-gravitating quantized matter is illustrated. The conditions for
which self-gravitating matter forms a thin shell are first discussed and an
effective Lagrangian for such matter is obtained. The matter-gravity system is
then quantized, the semi-classical limit for gravitation is taken and the
method of adiabatic invariants is applied to the resulting time dependent
matter Hamiltonian. The governing equations are integrated numerically, for
suitable initial conditions, in order to illustrate the effect of
back-reaction, due to the creation of matter, in slowing down the collapse near
the horizon.
