Toward Sub-meV, Momentum-Resolved, Inelastic X-Ray Scattering using a Nuclear Analyzer

We consider the use of nuclear resonant scattering to analyze momentum-resolved inelastic x-ray scattering with sub-meV resolution. Here the main issue is that the analyzer bandwidth is too small, and mismatched to conventional (Bragg-reflection based) x-ray optics. Under rather optimistic conditions, we find the nuclear analyzer has an effective bandwidth, for the purpose of estimating count-rates, of up to 10 mu eV for the 23.9 keV resonance of Sn-119, while more conservative estimates suggest the best option may be the 14.4 keV resonance of Fe-57 with similar to 0.5 mu eV effective bandwidth. To a first approximation, count rates with a nuclear analyzer will therefore be reduced 2 to 3 orders of magnitude from that of more conventional high-resolution crystal analyzers with meV resolution. The feasibility of experiments is then considered in more detail.