Nuclear resonance photon scattering

Figure 15. Out-of-plane tilt angle as a function of temperature for N2 on graphite. Circles nuclear resonance photon scattering of a compressed monolayer of coverage 1.05 0.02 [241]. Crosses molecular dynamics simulations of a complete monolayer [341]. (Adapted from Fig. 2 of Ref. 241.)...

The out-of-plane orientation of the molecular axes as a function of temperature was determined by nuclear resonance photon scattering [241] at a... 

APD = avalanche photodiode detector APS = advanced photon source DFT = density functional theory ESRF = European synchrotron radiation facility HOPE = high-density polyethylene IR = infrared INS = inelastic neutron scattering KED = kinetic energy distribution Mb = myoglobin NIS = nuclear inelastic scattering NRVS = nuclear resonance vibrational spectroscopy NRIXS = nuclear resonant inelastic X-ray scattering OEP = octaethylporphyrin sGC = soluble guanylate cyclase VDOS = vibrational density of states. 

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... 

Time spectra of nuclear resonant scattering from a FeAl single crystal aligned with the [110] direction along the wave vector of the photons for the indicated temperatures. (Reproduced from Ref. 90 with permission of Kluwer Academic Publishers.)... 

E.E. Alp, et al.. Nuclear resonant scattering beamline at the advanced photon source, Hyperfine Interact. 1994, 90(1-4), 323-334. 

A development of synchrotron radiation facility made possible to perform the nuclear resonant scattering with synchrotron radiation. Elastic scattering is identical, in principle, to the Mossbauer resonance by y photons from radioactive nuclei. From the inelastic scattering one can observe the scattering involved phonon annihilation and creation in solid. Nuclear resonant scattering with synchrotron radiation will briefly described in final part of this chapter. 

The photons emitted by the de-excitation of nuclear levels that are populated in the course of radioactive decays can be resonantly scattered. Nuclear resonance fluorescence experiments can give information on the velocity distribution of recoil atoms and the chemical modifications following transmutations and on the slowing-down process of hot atoms. This technique can be applied in gaseous, liquid, and solid systems, giving an advantage over Mossbauer spectroscopy. Nuclear resonance fluorescence has been reviewed, with particular reference to the following systems ... 

So far, we have discussed only the detection of y-rays transmitted through the Mossbauer absorber. However, the Mossbauer effect can also be established by recording scattered radiation that is emitted by the absorber nuclei upon de-excitation after resonant y-absorption. The decay of the excited nuclear state proceeds for Fe predominantly by internal conversion and emission of a conversion electron from the K-shell ( 90%). This event is followed by the emission of an additional (mostly Ka) X-ray or an Auger electron when the vacancy in the K shell is filled again. Alternatively, the direct transition of the resonantly excited nucleus causes re-emission of a y-photon (14.4 keV). 

Synchrotrons produce photons with energies in the range of nuclear Mossbauer transitions and can, in principle, be used to excite these transitions. However, synchrotron radiation can be monochromatized to only about 1 meV with new monochromators. Because the accessible nuclear levels are extremely narrow (between 10 and 10 eV), it is only about 10 of the incident photons that can excite the nuclear levels (excitation cross-section could be as much as 10 Fq). This is far weaker than radiation that is non-resonantly scattered by the electronic processes in the solid arising from the scattering of the entire 1 meV width of the incident radiation. 

Irradiation of adsorbate-covered surfaces with higher energy photons (typically up to 6.4 eV) with lower intensities opens the possibility of direct valence excitation. Since the lifetimes of electronic excitations at metal surfaces are much shorter than those for nuclear motion, photochemical reactions appear rather improbable. Surprisingly, however, the cross sections determined for photodesorption were found to be comparable to those found for reactions with free molecules, mainly because the short lifetime of the excited state is compensated by a much larger cross section for absorption of the light [32,62-64]. This process takes place in the near-surface region of the metal (within about 10 nm), where relaxation of the photoexcited electrons leads to rapid establishment of a transient energy distribution. As depicted in Fig. 4.11, these hot electrons may scatter at the surface or are resonantly attached to an empty level of the adsorbate. 

This derivation, which ignores all coherent interference between potentiah and resonance scattering, is the simplest for keeping spin factors in order. We consider a reaction where an incident particle a reacts with an initial nucleus A to form a compound nucleus C, which then decays by one of a number of possible decay modes symbolized hy h- B into an outgoing nuclear subunit, or photon, h, plus a final nucleus B. The final nucleus B and the fragment h may be in their ground states with respect to internal degrees of freedom, or in one of various possible excited states. The assumptions are ... 

Total cross section (in units of 1 barn = 10 m ) of photon interaction in carbon and lead as a function of photon energy and the contributions of the following processes photoelectric effect, Rayleigh and Compton scattering, pair production in the field of the nucleus (nuclear p.p.) and of the shell electrons (electron p.p.). Note the resonances ( edges" as they are called) in photoelectric effect. The total cross section curve is flat for another two orders of magnitude in energy beyond the plot... 

The possibility to finely tune the energy of the photons using high-resolution monochromators (HRMs) has resulted in a new technique for direct determination of the phonon density of states of the resonant element— the nuclear inelastic scattering (NIS) [23-25]. Thus, in the same experimental setup, one is able to probe simultaneously hyperfine interactions and lattice dynamics of the sample. 

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