Formation time of the nuclear exciton due to a synchrotron radiation pulse

Abstract

The Schr\"odinger equation for the system, formed by resonant nuclei incorporated in a lattice interacting with synchrotron radiation pulses, has been solved for times directly after the delivery of the pulse. The general problem of synchrotron radiation interacting with nuclear resonant material has been treated previously for all times using a number of different approaches including the nuclear-exciton model. This model assumes the nuclear exciton is formed immediately after the synchrotron radiation pulse. Here it is found that the synchrotron photons, having energies close to the nuclear resonance energy, disappear from the pulse according to an exponential law. The decay constant of the exponential is equal to a natural radiative decay constant multiplied by a number related to the nuclear resonant thickness of the sample. The formation of the exciton can be characterized by a time constant that is the inverse of this decay constant. Thus, the time constant for forming the nuclear exciton is inversely proportional to the sample thickness. This justifies the hypothesis, in the nuclear-exciton model, that the nuclear exciton is formed promptly after the synchrotron radiation flash.