Quantum mechanical model for nuclear-resonant scattering of gamma radiation

Abstract

A one-dimensional quantum mechanical model for nuclear-resonant scattering of gamma radiation from matter is developed assuming the source radiation is gamma decay. A closed-form, finite-sum solution for the radiated intensity is obtained by restricting the calculation to coherent forward scattering. The solution provides a unified microscopic picture of nuclear-resonant scattering processes in which the radiation undergoes sequential scattering from one nucleus to another before reaching the detector. For recoil-free processes the various `paths' to the detector contribute coherently. The solution for this case gives results identical to the classical optical model. The one-dimensional model shows that the `speed-up' and `dynamical beating' effects are primarily a consequence of the fact that the single-nuclear scattering processes are out of phase with the incident radiation while the double-nuclear-scattering processes are in phase with the incident radiation. All multiple-scattering paths are, and must be, included. The model can treat the incoherent processes, i.e. processes involving gamma emission with recoil or conversion-electron emission. The results show that a correction may be needed when analysing time-differential Mössbauer spectroscopic data due to incoherent processes that occur in the absorber.