Coherent Elastic Nuclear Resonant Scattering

1 Brief Theoretical Background In the case of coherent elastic scattering, a macroscopic ensemble of scattering atoms can be replaced by a continuous medium characterized by an index of refraction n [39]  

For anisotropic media, the index of refraction depends on the polarization state of light and is represented by a 2 x 2 matrix [40]. In that case, the propagation of light in forward direction is described by the propagation matrix F = ko + f, with f = lit/kd) being the forward scattering matrix. Then (1.2) can be written in more general form  

From (1.2) and (1.3) directly follows the relation between the index of refraction n and the forward scattering matrix f. n = I +f/ko- 

The propagation matrix F describes the modification of the wave field A upon propagation from coordinate z to coordinate z + dz. It is a multidimensional matrix with dimension given by the number of the open scattering channels. This formalism is successfully applied not only to describe the propagation of light in forward direction but also in case of X-ray diffraction from single crystals, and reflection from surfaces, thin films, and multilayers. 

For the case of 2 -pole resonance, the resonant scattering length is given by [41] 

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R. Rohlsberger, Coherent elastic nuclear resonant scattering, in Nuclear Condensed Matter Physics with Synchrotron Radiation—Basic Principles, Methodology and Applications, Springer, Berlin, 2004, pp. 67-180. 

Since the nuclear resonant scattering is a coherent elastic process it is impossible to identify the scattering atom in the sample. Instead, for each individual resonant nucleus there is a small probability that this nucleus is excited. The summation of all these small amplitudes gives the total probability amplitude for a photon to interact resonantly with the nuclei. If the incident radiation pulse is short compared to the nuclear lifetime Tq. these probability amplitudes exhibit the same temporal phase. As a result, a collectively excited state is created, where a single excitation is coherently distributed over the resonant atoms of the sample [44]. The wave function of this collectively excited state is given by a coherent... 

Ro-vibronic spectroscopies in the UV-Visible-Infrared and Micro-wave energy range, X ray and electron diffraction, incoherent and coherent elastic and inelastic neutron scattering, Raman scattering. Nuclear Magnetic resonances etc. all contain a vibrational contribution. Other non spectroscopic properties such as the various thermodynamical quantities contain the vibrational contributions. 

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