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A quantum theory of spherically symmetric thin shells of null dust and theirgravitational field is studied. In Nucl. Phys. 603 (2001) 515 (hep-th/0007005),it has been shown how superpositions of quantum states with differentgeometries can lead to a solution of the singularity problem and black holeinformation paradox: the shells bounce and re-expand and the evolution isunitary. The corresponding scattering times will be defined in the presentpaper. To this aim, a spherical mirror of radius R_m is introduced. Theclassical formula for scattering times of the shell reflected from the mirroris extended to quantum theory. The scattering times and their spreads arecalculated. They have a regular limit for R_m\to 0 and they reveal a resonanceat E_m = c^4R_m/2G. Except for the resonance, they are roughly of the order ofthe time the light needs to cross the flat space distance between the observerand the mirror. Some ideas are discussed of how the construction of the quantumtheory could be changed so that the scattering times become considerablylonger.Comment: 30 pages and 5 figures; the post-referee version: shortened and some  formulations improved; to be published in Physical Revie

Quantum superposition principle and gravitational collapse: Scattering times for spherical shells