Resonance energy shifts during nuclear Bragg diffraction of x rays

Abstract

We have observed dramatic changes in the time distribution of synchrotron x rays resonantly scattered from 57 Fe nuclei in a crystal of yttrium iron garnet, which depend on the deviation angle of the incident radiation from the Bragg angle. These changes are caused by small shifts in the effective energies of the hyperfine-split nuclear resonances, an effect of dynamical diffraction for the coherently excited nuclei in the crystal. The very high brightness of the synchrotron x-ray source allows this effect to be observed in a 15-min measurement. PACS numbers: 76.80.+y, 07.85.+n, 42.10.Qj, 61.10.DpWhen the 14.4-keV Mossbauer resonance in 57 Fe in a Bragg-diffracting crystal is excited by a short, broadband pulse of radiation from a synchrotron light source, the time distribution of the diffracted radiation exhibits a beat pattern due to interference between the coherently excited nuclear hyperfine levels. 1 " 4 Analysis of this time distribution gives a very accurate determination of the hyperfine fields in the crystal.We have used an undulator beam line at the PEP storage ring at Stanford Synchrotron Radiation Laboratory (SSRL) to resonantly scatter x rays from 57 Fe in a nearly perfect crystal of yttrium iron garnet (YIG). The high brightness of this x-ray source allowed us to obtain a time distribution with excellent statistics in less than 15 min, with a data collection rate nearly 2 orders of magnitude higher than in previous experiments of this type 2,3,5-7 Along with the beat pattern due to the hyperfine splitting of the nuclear resonance, we observed dramatic changes in the time distribution that depend sensitively on the deviation of the incidence angle of the radiation from the Bragg angle. These changes are due to small shifts in the effective resonance energies of the collection of Fe nuclei in the crystal lattice, an effect of dynamical diffraction, and are the subject of this Letter.Analysis of the dynamical diffraction theory for a perfect lattice of simple resonant nuclei shows that the resonance energy plays a role complementary to that of the diffracting wave vector, since the crystal reflectivity depends strongly on both the angular deviation from the Bragg angle and the energy deviation from the resonance energy. For both resonant and nonresonant scattering, the reflectivity of a thick crystal in Bragg geometry is maximized when the quantity [(a -2go) 2 -4g£] 1/2 is minimized, 8 " 10 where a is proportional to the deviation of the incident radiation from the Bragg angle, go is the scattering amplitude in the forward direction, and gK is the scattering amplitude in the reflected direction (this assumes that the crystal is centrosymmetric). The scattering amplitude for nonresonant electronic scattering is KV where Kis the unit-cell volume and F e (K) is the complex electronic scattering length of the unit cell, including the geometrical structure factor, electronic form factors, imaginary electronic absorption factors, and DebyeWaller temperature factors. In contrast, the energydependent scatteri...

Scientific legacy of Stanley Ruby

“…If there are magnetic and/or quadrupole hyperfine fields Fig. 3 Nuclear level scheme of 40m K and the observed 29.8 keV Mossbauer resonance spectrum reported in [12] present at these nuclei, the time development of the re-emitted wave packet from nuclei will produce a complex beat pattern due to interference between coherently excited hyperfine levels [21,22]. Indeed the analysis of hyperfine interactions measured in this fashion using the time domain spectroscopy became far more convoluted than that obtained from the energy spectroscopy performed using conventional Mossbauer spectroscopy.…”

“…Nearly 10 years after this suggestion, numerous groups made progress in the field. It became clear from the experiments performed at PEP storage ring at Stanford that an undulator source is best suited to carry out nuclear resonant scattering studies [21,22]. The third generation synchrotron radiation sources designed and built soon after (such as APS at Argonne, ESRF at Grenoble, and SPring-8 at Harima City) incorporated beamlines based on undulator sources to perform such experiments.…”

Time-sliced Mössbauer absorption spectroscopy using synchrotron radiation and a resonant Bragg monochromator

“…[1][2][3][4][5][6][7][8][9][10][11][12] This manifests itself as an increased energy bandwidth in the resonantly scattered beam. Time-integrated measurements of the Doppler energy width for resonant nuclear scattering have been performed using both radioactive [1][2][3][4]13 and synchrotron sources, 5,8,9 and Kagan et al 14 have made detailed theoretical calculations of the spectral energy width of angle-integrated ͑i.e., mosaic crystal͒ resonant Bragg scattering for the case of pulsed x rays.…”

Atomic and molecular science with synchrotron radiation

“…One singular example of the fruitful application of synchrotron radiation to scattering experiments is the recent work on nuclear Bragg diffraction of hard x rays from the PEP storage ring at Stanford (Arthur et al, 1989). Dramatic changes were observed in the time distribution of synchrotron x rays resonantly scattered 14 from 3/ Fe nuclei in a crystal.…”