Hyperfine Interactions 123/124 (1999)

Nuclear resonant scattering of synchrotron radiation Part I

Editors: E. Gerdau and H. de Waard

E. Gerdau and H. DeWaard
Nuclear resonant scattering of synchrotron radiation null-null

E. Gerdau, U. van Bürck and R. Rüffer
Historical overview and introduction 3-10

G. Mülhaupt and R. Rüffer
Properties of synchrotron radiation 13-30

G.V. Smirnov
General properties of nuclear resonant scattering 31-77

Yu. Kagan
Theory of coherent phenomena and fundamentals in nuclear resonant scattering 83-126

J.P. Hannon and G.T. Trammell
Coherent gamma-ray optics 127-274

Yuri V. Shvyd'ko
Coherent nuclear resonant scattering of X-rays: Time and space picture 275-299

R. Röhlsberger
Theory of X-ray grazing incidence reflection in the presence of nuclear resonance excitation 301-325

V.G. Kohn and G.V. Smirnov
Synchrotron radiation time spectra affected by diffusion: theory 327-345

Harry J. Lipkin
Mössbauer sum rules for use with synchrotron sources 349-366

W. Sturhahn and V.G. Kohn
Theoretical aspects of incoherent nuclear resonant scattering 367-399

R. Rüffer, H.D. Rüter and E. Gerdau
Hyperfine spectroscopy in diffraction geometry 405-426

A.I. Chumakov, L. Niesen, D.L. Nagy and E.E. Alp
Nuclear resonant scattering of synchrotron radiation by multilayer structures 427-454

R. Röhlsberger
Nuclear resonant scattering of synchrotron radiation from thin films 455-479

U. van Bürck
Coherent pulse propagation through resonant media 483-509

Yu.V. Shvyd'ko and U. van Bürck
Hybrid forms of beat phenomena in nuclear forward scattering of synchrotron radiation 511-527

Rainer Lübbers, Gerhard Wortmann and Hermann F. Grünsteudel
High-pressure studies with nuclear scattering of synchrotron radiation 529-559

A.X. Trautwein and H. Winkler
Biophysical applications 561-570

O. Leupold and H. Winkler
Relaxation experiments with synchrotron radiation 571-593

G. Vogl and B. Sepiol
Diffusion in crystalline materials 595-609

O. Leupold, A.I. Chumakov, E.E. Alp, W. Sturhahn and A.Q.R. Baron
Noniron isotopes 611-631

G.V. Smirnov and W. Potzel
Perturbation of nuclear excitons by ultrasound 633-663

Alfred Q.R. Baron
Transverse coherence in nuclear resonant scattering of synchrotron radiation 667-680

D.P. Siddons, U. Bergmann and J.B. Hastings
Polarization effects in resonant nuclear scattering 681-719

Yuji Hasegawa and Seishi Kikuta
Time-delayed interferometry with nuclear resonant scattering 721-739

Yu.V. Shvyd'ko and E. Gerdau
Backscattering mirrors for X-rays and Mössbauer radiation 741-776

A.I. Chumakov and W. Sturhahn
Experimental aspects of inelastic nuclear resonance scattering 781-808

W. Sturhahn and A. Chumakov
Lamb--Mössbauer factor and second-order Doppler shift from inelastic nuclear resonant absorption 809-824

Fritz Parak and Klaus Achterhold
Protein dynamics studied on myoglobin 825-840

H. Grünsteudel, H. Paulsen, H. Winkler, A.X. Trautwein and H. Toftlund
High-spin low-spin transition 841-846

W. Keune and W. Sturhahn
Inelastic nuclear resonant absorption of synchrotron radiation in thin films and multilayers 847-861

H. Franz, W. Petry and A.Q.R. Baron
Quasielastic scattering: slow dynamics of glasses 865-879

Hyperfine Interactions 125 (2000)

Nuclear resonant scattering of synchrotron radiation Part I

Editors: E. Gerdau and H. de Waard

T.S. Toellner
Monochromatization of synchrotron radiation for nuclear resonant scattering experiments 3-28

Alfred Q.R. Baron
Detectors for nuclear resonant scattering experiments 29-42

E.E. Alp, W. Sturhahn and T.S. Toellner
Polarizer--analyzer optics 45-68

R. Röhlsberger
Techniques for inelastic X-ray scattering with µeV-resolution 69-90

G.V. Smirnov
Synchrotron Mössbauer source of ⁵⁷Fe radiation 91-112

R. Coussement, J. Odeurs, C. L'abbé and G. Neyens
Heterodyne detection of synchrotron radiation 113-132

G. Faigel
Holography with resonant quanta 133-146

W. Sturhahn
CONUSS and PHOENIX: Evaluation of nuclear resonant scattering data 149-172

Yuri V. Shvyd'ko
MOTIF: Evaluation of time spectra for nuclear forward scattering 173-188

M. Haas, E. Realo, H. Winkler, W. Meyer-Klaucke and A.X. Trautwein
SYNFOS 189-195

H. Spiering, L. Deák and L. Bottyán
EFFINO 197-204

V.G. Kohn and A.I. Chumakov
DOS: Evaluation of phonon density of states from nuclear resonant inelastic absorption 205-221

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This article describes the basic mechanisms for the generation of synchrotron radiation. It gives the basic equations for the emission characteristics of a single transversally accelerated relativistic particle as well as the modifications to these equations due to the multi-particle behaviour of real accelerator beams. It also introduces the boundary conditions for emission of coherent radiation and at the end gives an overview of the parameters of synchrotron radiation sources presently used for nuclear resonance scattering.

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The process of nuclear resonant scattering resonant scattering is considered on the basis of an optical model. The coherent properties coherent properties of the radiation and scattering mechanism are described. The complementary pictures of gamma-ray resonant scattering in energy and time domains are presented. Special attention is paid to scattering of a gamma quantum by an ensemble of nuclei. The central concept of the theory of nuclear resonant scattering, the nuclear exciton, nuclear exciton as a delocalized nuclear excitation, is described in detail. It is shown that both temporal and spatial aspects of coherence play a crucial role in the evolution of the nuclear exciton. A large place is given to the analysis of resonant scattering of synchrotron radiation by nuclear ensembles.

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We discuss the general theory of coherent phenomena in nuclear resonant interaction of gamma-quanta with crystals. The coherence is realized in collective excitation of the ensemble of nuclei (nuclear exciton) with the conservation of phase memory and in the transformation of a gamma-quantum into a quasi-particle of Bloch type in a crystal. The collective character of excitations causes a change in the resonant nuclear parameters and in the lifetime of the excited state. This manifests itself in a speed-up of the decay in the forward direction in a thin crystal and, on the contrary, a strong reduction of elastic scattering in a thick crystal. The reconstruction of the wavefunction of an individual gamma-quantum in scattering under Laue or Bragg conditions leads to the suppression effect of inelastic incoherent channels. This effect is discussed in detail. The analysis is based on a derived general system of equations describing the resonant diffraction of gamma-quanta in a crystal with an arbitrary relation between the coherent and incoherent channels. This system is used to deduce the equations describing the time-dependent nuclear resonant scattering of synchrotron radiation. We discuss the most instructive experiments with revealing coherent phenomena.

Keywords: coherence, resonant diffraction, suppression effect, nuclear exciton, time-dependent NRS, synchrotron radiation

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With the advent of high brightness synchrotron radiation sources, an important new field has been opened up involving coherent nuclear excitations induced by synchrotron radiation pulses traversing a piece of matter. We review the theory of coherent resonant gamma-ray optics, including some of the interesting new phenomena which occur when systems of nuclei are excited by synchrotron radiation pulses, such as the creation of nuclear exciton states, superradiant and subradiant decay, spatially coherent quantum beats, and temporal Pendellösung. We also discuss the relation between the nuclear exciton states and multi-photon Dicke superradiance and gamma-ray lasers, and comment on neutron phasors and neutron superradiance in resonant neutron optics. The interesting features of coherent enhancement, superradiant decay, and dynamical beats are discussed from the fundamental perspective of the radiative normal modes of a system of nuclear resonators.

AMS subject classification: 73.20.Hb, 31.50.+w, 79.20.Rf, 79.20.-m

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The problem of coherent resonant scattering of X-rays by an ensemble of nuclei is solved directly in time and space. In a first step the problem with a single coherently scattered beam is considered -- nuclear forward scattering. The wave equation describing the propagation of the radiation through the nuclear ensemble is derived. It is a first order integro-differential equation. Its kernel is a double time function K(t,t) which represents the coherent single scattering response of the nuclear system at time t to excitation at t. The kernel is defined by the character of the interactions the nuclei experience with the environment and by the character of their motion. A general procedure of solution of the wave equation is introduced which is independent of the type of kernel. In a second step the wave equation is generalized to the case of many coherently scattered beams, which is, e.g., the case of nuclear Bragg diffraction. Kernels of the wave equations are derived for some particular cases: collective motion of nuclei in space, thermal lattice vibrations, time-independent hyperfine interactions, and time-dependent hyperfine interactions due to external magnetic-field switching.

Keywords: nuclear resonance, X-rays, coherent scattering, time dependence

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The dynamical theory of nuclear resonant diffraction is applied to the case of grazing incidence reflection. The solution of the dynamical equations is obtained by evaluation of a matrix exponential. This formalism is applied to grazing incidence reflection from arbitrary stratified media. However, the basic formalism is not restricted to this case, but can be used to describe a wide range of diffraction phenomena. This is demonstrated in the case of grazing incidence diffraction from gratings in the n-beam case. Moreover, the theory is extended to describe the influence of surface and boundary roughness.

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The general theory and a qualitative picture of time spectra in nuclear resonant scattering of synchrotron radiation in the presence of diffusive motion of atoms are presented. The coherent channel of the nuclear exciton decay with emission of a gamma quantum in a primary direction and the incoherent channel are considered. The theory is applied for three cases of diffusive motion: free diffusion in an unrestricted space, diffusion in a limited volume, and jump diffusion in a crystal.

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The availability of tunable synchrotron radiation sources with millivolt resolution has opened new prospects for exploring dynamics of complex systems with Mössbauer spectroscopy. Early Mössbauer treatments and moment sum rules are extended to treat inelastic excitations measured in synchrotron experiments, with emphasis on the unique new conditions absent in neutron scattering and arising in resonance scattering: prompt absorption, delayed emission, recoil-free transitions and coherent forward scattering. The first moment sum rule normalizes the inelastic spectrum. New sum rules obtained for higher moments include the third moment proportional to the second derivative of the potential acting on the Mössbauer nucleus and independent of temperature in the the harmonic approximation.

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The influence of nonrotational atomic motion on the scattering of X-rays by nuclei with sharp resonances is investigated. Two incoherent scattering channels, nuclear resonant fluorescence and nuclear resonant absorption followed by conversion electron emission and atomic fluorescence, are studied in detail. Time dependence and cross sections for these processes are given. In both cases, the cross section is proportional to the self-intermediate scattering function of the resonant isotope. The influence of other X-ray scattering processes on incoherent nuclear resonant scattering is discussed. We find that incoherent scattering channels dominate in off-resonance excitations. Self-intermediate scattering functions for the ideal gas and the harmonic lattice are calculated.

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With the advent of third generation synchrotron radiation sources nuclear Bragg diffraction became a powerful technique for the determination of hyperfine parameters and the electronic and magnetic structure of single crystals. Basic features are discussed theoretically and experimentally and are illustrated by examples such as YIG, FeBO₃, \alpha-Fe₂O₃, and Fe₃BO₆.

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Multilayer structures form a particular class of samples employed in nuclear resonant scattering of synchrotron radiation. Their specific properties lead to unusual energy and time characteristics of nuclear resonant scattering, which differ much from those of single crystals. The analysis of these distinctions is presented. Several approaches to achieve pure nuclear reflections with multilayers are discussed. Finally, we review the studies of multilayer structures with nuclear resonant scattering of synchrotron radiation.

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The optical properties of thin films containing Mössbauer isotopes undergo dramatic changes in the vicinity of a nuclear resonance. Remarkable phenomena are observed in the energetic and temporal response of X-rays resonantly scattered in grazing incidence geometry. These properties allow an effective discrimination of the resonantly scattered radiation from the nonresonant electronic charge scattering. In contrast to Bragg scattering from single crystals, the reflectivity of film systems can be tailored by their design and the way of preparation. As a result, several optical elements have been developed for ultra-narrow bandpass filtering of synchrotron radiation: Grazing-Incidence Antireflection (GIAR) films, nuclear resonant multilayers and reflection gratings. Moreover, resonant scattering in grazing incidence geometry is a very attractive tool to study properties of thin films themselves. This has led to applications, e.g., in the study of surface magnetism and the determination of vibrational properties of thin films. Such investigations benefit from the outstanding brilliance of third-generation synchrotron radiation sources, extending the sensitivity of the method into the monolayer regime.

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Resonant pulse propagation (RPP) is reviewed with special emphasis on the propagation of synchrotron radiation (SR) pulses through nuclear single-resonance media. The most remarkable feature in the time evolution of RPP is the dynamical beat (DB), a pronounced modulation with periods increasing with time and decreasing with increasing sample thickness. A comparison of RPP at gamma-wavelengths (SR and Mössbauer radiation) with RPP in the infrared and visible regimes in case of molecular, atomic and excitonic resonances reveals an astonishing universality of the observed phenomena. The DB is described within the double-hump picture and the group-velocity picture, and is finally attributed to the energy exchange between radiation field and oscillator system in multiple scattering.

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In nuclear forward scattering (NFS) of synchrotron radiation, inter-resonance interference leads to a quantum beat (QB), and intra-resonance interference to a dynamical beat (DB). In general both interference processes determine the time evolution of NFS. Only in the case of far distant resonances the resulting interference pattern can be interpreted as a well distinguishable combination of QB and DB. Multiple scattering by near neighbouring resonances, by contrast, leads to a hybridisation of QB and DB. In particular, asymmetrical continuous distributions of resonances make QB and DB blend into a fast hybrid beat with thickness dependent period and distribution sensitive modulation.

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The nuclear forward scattering (NFS) of synchrotron radiation is especially suited for probing magnetism at high pressure (h.p.), here in the Mbar range, by the nuclear resonances of ⁵⁷Fe and ¹⁵¹Eu. We report on high-pressure NFS studies with the 14.4 keV transition of ⁵⁷Fe, presenting at first the pressure induced \alpha--\varepsilon transformation in iron. Then a systematic study of magnetic RFe₂ Laves phases of cubic C15 structure (YFe₂, GdFe₂) and hexagonal C14 structure (ScFe₂, TiFe₂) at pressures up to 100 GPa (=1 Mbar) is given. First, high-pressure NFS studies performed with the 21.5 keV resonance of ¹⁵¹Eu are also presented, probing valence transitions in EuNi₂Ge₂ and the magnetism in the CsCl-type h.p. phase of EuTe. Finally, we discuss future applications, such as high-pressure studies of phonon densities of states, using the inelastic channel of nuclear scattering of synchrotron radiation.

Keywords: high pressure, magnetism, valence transition, phase transition

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Nuclear forward scattering (NFS) of synchrotron radiation was applied to investigate the electronic and magnetic properties of (i) the diamagnetic ``picket-fence'' porphyrin FeO<sub>2</sub>(SC<sub>6</sub>HF<sub>4</sub>)(TP<sub>piv</sub>P), which is a model for oxygenated hemoglobin and myoglobin and (ii) the paramagnetic ``picket-fence'' porphyrin [Fe(CH₃COOH)(TP_pivP)]^-, which is a model for the ferrous state of the prosthetic group, termed P460, of the multi-heme enzyme hydroxylamine oxidoreductase from the bacterium Nitrosomonas europeae.

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Relaxation phenomena show up in standard energy-domain Mössbauer spectra via line broadening. The evaluation of such spectra is in most cases done by applying the stochastic theory of lineshape mainly developed in the 60's and 70's. Due to the time structure and the polarization of the synchrotron radiation nuclear resonance forward scattering in the time domain gives valuable additional information on relaxation mechanisms. We report here mainly on Nuclear Forward Scattering (NFS) experiments, investigating the paramagnetic relaxation of high-spin Fe²⁺ and Fe³⁺ ions, superparamagnetic relaxation and briefly on recent investigations of charge fluctuations in Eu₃S₄.

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Recently nuclear scattering of synchrotron radiation proved to be a powerful new method to study the elementary diffusion jump in crystalline solids. The scattered radiation decays faster when atoms move on the time scale of the excited-state lifetime of a Mössbauer isotope because of a loss of coherence. The acceleration of the decay rate differs for different crystal orientations relative to the beam providing information not only about the rates but also about the directions of the elementary jumps. We discuss first applications of the method.

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This article reports on experimental developments and first results for Mössbauer isotopes other than ⁵⁷Fe. We will restrict ourselves to basic features of the resonances of ¹⁶⁹Tm, ¹¹⁹Sn, ⁸³Kr, ¹⁸¹Ta, and ¹⁵¹Eu and want to point out remarkable differences in instrumentation -- like monochromator design -- compared with ⁵⁷Fe. Some applications can be found in other sections of this issue.

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The coherent decay of a nuclear exciton created by synchrotron radiation in spatially separated targets is studied in the presence of ultrasound (US) vibrations in one of the targets. The time evolution of the nuclear exciton perturbed in such a way is described by interference between the wave packets re-emitted by both targets and radiative coupling between the targets. Since the condition for initial phasing of the wave packets and coupling can be restored periodically by US, strong intensity enlargements in the time response, called nuclear exciton echoes, are observed. If the targets have different resonant energies quantum beats arise which are frequency modulated by the US perturbation. A complete dynamical theory is presented which provides a quantitative description of all experimental results discussed.

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We discuss the effects of transverse coherence in time domain nuclear resonant scattering experiments using synchrotron radiation. The importance of source and detector sizes, as well as the Fresnel zone size of the sample are described. These effects are demonstrated in experiments using a rotating stainless-steel foil [1]. The emphasis of the text is to provide simple physical explanations while mathematical details are discussed in the appendix.

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Polarization phenomena are present in every radiative transition, whether it is of atomic or nuclear origin. Nuclear resonant scattering of synchrotron radiation is an ideal technique for their study because (a) the probing radiation is in a well characterized polarization state, in most cases linear, (b) the scattered radiation can be efficiently analyzed with polarization filters, and (c) synchrotron pulses are very short compared to the lifetime of a nuclear resonance, resulting in a clean signal. In the following article we describe experimental and theoretical studies of the 14.4 keV Mössbauer resonance of ⁵⁷Fe and its transitions with linear and circular polarization. After introducing the required instrumentation a formalism to calculate time dependent polarization phenomena is derived. With the help of different scattering geometries we illustrate various aspects, such as polarization mixing and selective excitation of subsets of the resonance. Perhaps the most fascinating example is the Faraday geometry where the E-vector rotates several 360^&deg; turns during the lifetime of the resonant scattering. A comparison of this phenomenon with the optical Faraday effect is given. New powerful synchrotron radiation sources will enable researchers to exploit polarization phenomena in nuclear resonant scattering to detect subtle changes in physically and chemically relevant systems.

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Experimental results of ``time-delayed interferometry'' with nuclear resonances at KEK are reported. Mössbauer nuclei were used as a cavity for X-rays in these experiments. Various interference effects were observed on a macroscopic scale with the ``perfect crystal'' interferometer. The property of coherence and the combined system showed some characteristics of collective nuclear excitations, e.g., absorption of photons without the reduction of the detection probability, the phase information transfer, and spontaneous emission with phase relation. Interferometry with a large optical path length, i.e., 4.2 mm, was accomplished with a wave-front division type X-ray interferometer. An interference experiment with a vibrating resonant scatterer exhibited quantum beat oscillations in the time domain. Interferograms with samples of different thicknesses revealed a remarkable phase shift of pi in the time evolution, which is induced by the dispersion effect at the nuclear resonance. A future perspective of time-delayed interferometry is also presented, e.g., for temporal phenomena in nuclear resonant scattering. Time-delayed interferometry has established a new field of X-ray optics, which can be of help for fundamental, nuclear, and solid state physics.

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Observation of exact backscattering of X-rays and studies of its energy and angular dependences; test of the validity of the dynamical theory of diffraction in the extreme case of exact backscattering; backscattering high-energy-resolution monochromators; backscattering interferometers, in particular of the Fabry--Pérot interferometer type; and precise, up to 5· 10^-9 Å, measurements of crystal lattice parameters: these are central topics of the paper. Special attention is paid to the selection of crystals to be used as backscattering mirrors. Noncubic crystals like Al₂O₃, SiC, etc., allow backscattering for X-rays with practically any energy above 10 keV. Feasibility of backscattering mirrors for Mössbauer radiation of ⁵⁷Fe (14.4 keV), ¹⁵¹Eu (21.5 keV), ¹¹⁹Sn (23.9 keV), and ¹⁶¹Dy (25.6 keV) nuclei is demonstrated by Al₂O₃ crystals. A concrete design of a sapphire Fabry--Pérot--Bragg étalon is presented.

Keywords: Bragg backscattering, X-rays, monochromators, interferometers, Al₂O₃, SiC

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We present an introduction to the technique of inelastic nuclear scattering. The details of experimental setup, instrumentation, and measuring procedure are discussed. The typical appearance of experimental results and a brief description of data treatment methods are illustrated by examples of recent studies. Finally, the scope of information on lattice dynamics that is accessible with inelastic nuclear scattering is outlined.

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The derivation of Lamb--Mössbauer factors and second-order Doppler shifts from data that are measured by inelastic nuclear resonant absorption of synchroton radiation is demonstrated. This approach offers a viable alternative to procedures that are based on elastic absorption and scattering techniques. The sources of error are evaluated, and a selection of examples is provided.

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Two methods of inelastic scattering of synchrotron radiation were used to measure the dynamics of myoglobin in the temperature range from T=60 K to 300 K. The inelastic Rayleigh scattering of metmyoglobin was analyzed by delayed elastic nuclear forward scattering of an iron foil. This yields averaged information on all phonons within the sample. The mean square displacement of the atoms due to this dynamics is [ x²]/T =2.1· 10^-4 Ų K^-1 on average. Complementary information was obtained by phonon assisted nuclear scattering on deoxymyoglobin. This method selects the phonons coupling to the iron atom in the active center of the protein. The mean square displacement of the iron was measured to be [ x²]/T=0.6· 10^-4 Ų K^-1. The results are in agreement with Mössbauer absorption experiments in the low temperature range. Above 200 K the results allow one to distinguish between harmonic and quasidiffusive dynamics within the protein. A comparison with Raman spectroscopy is made.

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Temperature dependent nuclear inelastic-scattering (NIS) of synchrotron radiation was applied to investigate both spin states of the spin-crossover complex [Fe(tpa)(NCS)₂] (tpa=tris(2-pyridylmethyl)amine). A remarkable increase of the iron--ligand bond stretching upon spin crossover has unambiguously been identified by comparing the measured NIS spectra with theoretical simulations based on density-functional calculations.

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Inelastic nuclear resonant absorption of synchrotron radiation is an efficient and unique method for the direct measurement of vibrational density of states (VDOS) of thin films and interfaces that contain Mössbauer isotopes. This is demonstrated for the ⁵⁷Fe nuclear resonance in the case of amorphous and crystalline Tb--Fe alloy thin films and buried Fe/Cr interfaces in epitaxial \alpha-Fe(0 0 1)/Cr(0 0 1) superlattices.

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The dynamics of glasses shows some distinct differences with respect to the crystalline state. Both in the short time regime (boson peak) and the microscopically slow regime (alpha- and beta-relaxation) there are glass-typical features. The outstanding sharpness of nuclear transitions offers a new tool to investigate the properties of glasses at long times, i.e., some nanoseconds to microseconds. The article will give a short introduction to glass-dynamic and convenient parameters for the theoretical description and will summarize recent results on model systems.

Keywords: quasielastic scattering, structural relaxation, non-resonant scattering, disordered systems

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An introduction to monochromatization of synchrotron radiation in the energy range of 5--30 keV is presented for applications involving nuclear resonant scattering. The relevant relationships of the dynamical theory of X-ray diffraction are used to explain basic concepts of monochromatization. These relations are combined with ray-tracing techniques to design high-energy-resolution monochromators. Transmission-optimized and energy-resolution-optimized designs that achieve high energy resolutions (10⁶ < E/\Delta E < 10⁸) are discussed separately. Practical silicon monochromators of both types are presented for a variety of nuclear resonances in this energy range.

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Detectors detectors and electronics electronics for nuclear resonant scattering (NRS) experiments using synchrotron radiation are discussed. An introduction to X-ray timing measurements timing measurements is given, followed by a historical look at the detectors that have been employed. The bulk of the article discusses silicon avalanche photodiodes avalanche photodiodes (APDs), APD as these are presently the most commonly used devices. APDs from several manufacturers are discussed, with emphasis on their relative merits.

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The principles behind the design and operation of polarization-based optics for nuclear resonant scattering of synchrotron radiation are discussed. With perfect single crystals and collimated X-rays emitted from undulator-based third-generation synchrotron radiation sources, polarization-selective optics with a sensitivity of parts per billion can be obtained. A general approach to optical activity is introduced, and the polarization dependence of the index of refraction is calculated for nuclear forward scattering for a medium with unidirectional symmetry. Some recent experimental results are reviewed and future applications are discussed.

Keywords: nuclear resonant scattering, synchrotron radiation, polarization, crystal optics

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A new spectroscopic technique is introduced that allows tuning of a µeV-wide beam of synchrotron radiation over a range of a few meV. It relies on nuclear resonant scattering that is subject to the Doppler effect in high speed rotary motion. Two mechanisms are discussed how to extract the resonantly scattered radiation out of the broad band of synchrotron radiation: (a) grazing incidence reflection from a rotating disk in combination with a polarization filtering technique and (b) deflection of resonantly scattered radition via the recently discovered Nuclear Lighthouse Effect. Implications for inelastic X-ray scattering and elastic nuclear resonant scattering are discussed.

Keywords: X-ray spectroscopy, nuclear resonant scattering, Doppler effect

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A non-radioactive source of Mössbauer radiation is described for use in Mössbauer absorption and scattering spectroscopy. The radiation is generated by synchrotron X-rays in an iron borate single crystal set in diffraction conditions at the Néel temperature (75.3^&deg;C). Like a conventional Mössbauer source the new Synchrotron Mössbauer (SM) source emits single-line radiation of about natural linewidth, but in addition the emitted radiation is fully recoilless, highly directed and of pure linear polarization. An extremely high suppression of the electronic scattering is achieved. The latter circumstance allows one to perform Mössbauer experiments using pulsed synchrotron radiation in a steady state mode as in a normal Mössbauer measurement.

The theory of the SM source is developed. First Mössbauer spectra obtained with the SM source are shown. Applications of the SM source are discussed.

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A time integral method for the study of resonant nuclear scattering of synchrotron radiation in the forward direction is presented. The method relies on the interference of radiation scattered by nuclei in two samples, one moving with respect to the other. The method, termed heterodyne detection of synchrotron radiation, gives the same information on hyperfine parameters as the well known differential method. The general formalism is developed for the case where the reference is a single line sample and the investigated sample has magnetic or quadrupole splitting. The first experiments are discussed. A comparison of time differential synchrotron radiation spectroscopy, heterodyne detection and Mössbauer spectroscopy is given.

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Atomic resolution holography is a new, emerging field of research. In this paper we give the basic ideas of the inside source/detector holography using short wavelength electromagnetic radiation. The characteristics of \gamma-ray holography are discussed and the first experimental results of this type are given.

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Evaluation methods for data obtained by nuclear resonant scattering techniques are discussed. The CONUSS software package for the interpretation of time or energy spectra from coherent elastic nuclear resonant scattering, i.e., forward scattering and Bragg/Laue scattering, is presented. The analysis of phonon spectra obtained by incoherent nuclear resonant scattering is demonstrated using the PHOENIX software.

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The computer program MOTIF calculates time dependences for nuclear forward scattering (NFS) of synchrotron radiation and allows fully automatic fits of experimental data. A multiple scattering technique of calculations directly in space and time is used. The source code of MOTIF is written in Fortran 77. It has been worked out since 1993 and tested on several Unix platforms by fitting the NFS time spectra of ⁵⁷Fe, ¹¹⁹Sn, ¹⁵¹Eu, ¹⁶¹Dy, and ¹⁸¹Ta nuclei in various compounds with different time-independent and time-dependent hyperfine interactions.

Keywords: nuclear resonance, X-rays, coherent scattering, time dependence

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An expression for the amplitude of a pulse of synchrotron radiation coherently scattered in the forward direction by a Mössbauer absorber consisting of randomly oriented paramagnetic iron-containing molecules (for example, a frozen solution of a ⁵⁷Fe protein) in an applied magnetic field is derived from the theory of \gamma optics. It is assumed that the hyperfine splittings present in the Mössbauer nuclei can be described in the framework of the spin-Hamiltonian formalism. In the general case of a thick Mössbauer sample of this kind the response on an incident monochromatic and fully polarized beam cannot be given analytically because of the integrations involved. How nuclear forward-scattering for this general case is evaluated in the program package called SYNFOS is outlined.

Keywords: randomly oriented scatterer, nuclear resonant forward scattering, synchrotron radiation

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The program EFFINO (Environment For FItting Nuclear Optics) evaluates Mössbauer absorption and time spectra both in nuclear forward scattering and in grazing incidence reflection geometry. Time-integral prompt and delayed angular scan spectra are also treated. The time spectra are calculated by Fourier transformation from frequency to time domain. The electric quadrupole and magnetic dipole fields at the nuclear sites are considered static at present. The specimen in both forward scattering and grazing incidence is assumed to be a multilayer, with individual thickness and interface roughness (the latter only for the grazing incidence case at present) and electronic index of refraction. Up to eight different layers plus eight repetition periods of those layers are treated. Each layer may contain zero to eight nuclear sites (zero in all layers being prompt X-ray reflectivity), with their own effective thickness or (for grazing incidence) their own complex nuclear index of refraction. From the forward scattering amplitude, a differential 4x4 propagation matrix is constructed for each layer. Several experimental spectra of the same or different type(s) can be fitted simultaneously. Correlations between parameters of the same or of different spectra can be introduced.

Keywords: nuclear optics, correlations, energy domain, time domain, forward scattering, grazing incidence, inequivalent nuclear site, cover layer, substrate layer, periodic multilayer, simultaneous fit

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Theoretical background and specific features of the calculation of the phonon density of states from energy spectra of nuclear resonant inelastic absorption of synchrotron radiation are presented. Double Fourier transformation is used to deconvolute data and an instrumental function and to eliminate the multiphonon contributions. A computer program is developed and an example of its work is shown.

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