Frequency distribution of a gamma photon emitted without recoil by a nucleus considering multiple scattering processes

Abstract

The time-dependent frequency distribution of a gamma photon emitted without recoil by an excited source nucleus is calculated; the emitted photon is submitted to nuclear quasi-resonant scattering in an absorber and recorded by a detector. The problem is formulated for an arbitrary number of quasi-resonant nuclei in the absorber, including both radiative decay (decay by means of gamma radiation) and decay by electron conversion (decay where the nuclear de-excitation energy is transmitted directly to an atomic electron). The problem of multiple scattering is treated by means of the so-called coherent path model developed years ago. The properties of the radiation leaving the absorber under these conditions are complex. The calculated probabilities of finding a gamma photon thus emitted as a function of frequency show a rich structure, with among others, maxima and minima that vary with time. The frequency distribution changes continuously as a function of time. For times long compared to the nuclear mean life of the excited state, the envelop of the frequency distribution resembles a Lorentz distribution, the details show some oscillatory behaviour as well as an asymmetry with respect to the nuclear frequency in the case of quasi-resonance between the source and the absorber nuclei. If the source and absorber nuclei are in exact resonance, the frequency distribution is symmetric but the oscillatory behaviour is still present. The frequency distribution is determined by the source nucleus as well as by the quasi-resonant absorber nuclei, hence by the multiple scattering processes. The model presented can be used to calculate analytically the properties of the transmitted gamma radiation for any number of absorber nuclei, although the simulation of the results will obviously necessitate some tedious computer work.