Coherent-path model for nuclear resonant scattering of gamma radiation from nuclei excited by synchrotron radiation

Previous theoretical descriptions of nuclear resonant scattering of synchrotron radiation have been based on the semiclassical optical model or on several quantum mechanical models. These models are fine but do not give a clear physical picture of all the processes. The theory presented here gives a clear physical picture of all the relevant aspects of nuclear resonant scattering. The model treats the nuclear resonant sample as a one-dimensional chain of ``effective'' nuclei. However, the model is deceptive. It only appears to be one dimensional. It actually treats the sample as a series of ``effective'' planes. The analysis uses the time-dependent quantum mechanical techniques due to Heitler. A closed form solution, for the time-dependent forward-scattered intensity, is found. The only parameter in the theory is N the number of ``effective'' nuclei (planes) in the model. It is shown that the prominent experimental features, the ``speed-up'' and ``dynamical beat'' effects, are primarily due to a π phase change of reemitted radiation, compared to the incident radiation, that occurs when radiation is absorbed and reemitted without recoil by a single ``effective'' nucleus (plane). The model also predicts results for the incoherent processes.