A New Way of Looking at Nuclear Resonant Scattering

A new model for nuclear-resonant scattering of gamma radiation from resonant matter has been developed and is summarized here. This “coherent-path” model has lead to closed-form, finite-sum solutions for radiation scattered in the forward direction. The solution provides a unified microscopic picture of nuclear-resonant scattering processes. The resonant absorber or scatterer is modeled as a one-dimensional chain of “effective” nuclei or “effective” planes. The solution is interpreted as showing that the resonant radiation undergoes sequential scattering from one absorber “nucleus” or “plane” to another before reaching the detector. For recoil-free processes the various “paths” to the detector contribute coherently. The solution for this case gives calculated results that are indistinguishable from those using the classical optical model approach, although the forms of the solutions are completely different. The coherent-path model shows that the “speed-up” and “dynamical beating” effects are primarily a consequence of the fact that the single “effective” nuclear scattering processes are 180° 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 also treat the incoherent processes, i.e., processes involving gamma emission with recoil or conversion-electron emission. The source of the resonant gamma radiation can be from a radioactive source or from synchrotron radiation: both cases are treated. The model is used to explain and understand the results when each of the following experimental procedures is applied: time-differential Mössbauer spectroscopy, time-differential synchrotron radiation spectroscopy, enhanced-resolution resonant-detector Mössbauer spectroscopy, and the “gamma echo”.