  A quantum theory of spherically symmetric thin shells of null dust and their
gravitational field is studied. In Nucl. Phys. 603 (2001) 515 (hep-th/0007005),
it has been shown how superpositions of quantum states with different
geometries can lead to a solution of the singularity problem and black hole
information paradox: the shells bounce and re-expand and the evolution is
unitary. The corresponding scattering times will be defined in the present
paper. To this aim, a spherical mirror of radius R_m is introduced. The
classical formula for scattering times of the shell reflected from the mirror
is extended to quantum theory. The scattering times and their spreads are
calculated. They have a regular limit for R_m\to 0 and they reveal a resonance
at E_m = c^4R_m/2G. Except for the resonance, they are roughly of the order of
the time the light needs to cross the flat space distance between the observer
and the mirror. Some ideas are discussed of how the construction of the quantum
theory could be changed so that the scattering times become considerably
longer.

General Relativity and Quantum Cosmology;High Energy Physics - Theory