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 `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`

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 `69-90`

** G.V. Smirnov**

Synchrotron Mössbauer source of ^{57}`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`

H. DeWaard

*
*

U. van Bürck

R. Rüffer

*
^{a}II. Institut für Experimentalphysik, Universität Hamburg, D-22761 Hamburg, Germany
*

^{b}Physik-Department E15, Technische Universität München, D-85748 Garching, Germany

^{c}European Synchrotron Radiation Facility, BP 220, F-38043, Grenoble, France

R. Rüffer

*
European Synchrotron Radiation Facility, F-38049 Grenoble, France
*

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.

*
Russian Research Center `Kurchatov Institute', Kurchatov Square 1, 123182 Moscow, Russia E-mail: smirnov@polyn.kiae.su
*

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

*
Russian Research Center ``Kurchatov Institute'', 123182 Moscow, Russia
*

We discuss the general theory of coherent phenomena in nuclear resonant interaction of

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

G.T. Trammell

*
Physics Department, Rice University, Houston, TX 77005-1892, USA
*

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

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

*
II. Institut für Experimentalphysik, Universität Hamburg, D-22761 Hamburg, Germany E-mail: yuri.shvydko@desy.de
*

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

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

*
Fachbereich Physik, Universität Rostock, August-Bebel-Str. 55, D-18055 Rostock, Germany
*

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

G.V. Smirnov

*
Russian Research Centre ``Kurchatov Institute'', Moscow 123182, Russia
*

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

*
Department of Particle Physics, Weizmann Institute of Science, Rehovot 76100, Israel and School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel and Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA
*

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.

V.G. Kohn

*
^{a}Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA
*

^{b}Russian Research Centre ``Kurchatov Institute'', Moscow 123182, Russia

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.

H.D. Rüter

E. Gerdau

*
^{a}European Synchrotron Radiation Facility, F-38043 Grenoble, France
*

^{b}II. Institut für Experimentalphysik, Universität Hamburg, D-22761 Hamburg, Germany

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, FeBO_{3}_{2}_{3}_{3}_{6}

L. Niesen

D.L. Nagy

E.E. Alp

*
^{a}European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble, France E-mail: chumakov@esrf.fr
*

^{b}Nuclear Solid State Physics, Materials Science Center, Groningen University, Nijenborgh 4, 9747 AG Groningen, The Netherlands

^{c}KFKI Research Institute for Particle and Nuclear Physics, P.O.B. 49, H-1525 Budapest, Hungary

^{d}Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA

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.

*
Fachbereich Physik, Universität Rostock, August-Bebel-Str. 55, D-18055 Rostock, Germany E-mail: roehle@physik1.uni-rostock.de
*

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.

*
Physik-Department E15, Technische Universität München, D-85748 Garching, Germany
*

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

U. van Bürck

*
^{a}II. Institut für Experimentalphysik, Universität Hamburg, D-22761 Hamburg, Germany E-mail: yuri.shvydko@desy.de
*

^{b}Physik-Department E15, Technische Universität München, D-85748 Garching, Germany E-mail: uwe.vbuerck@ph.tum.de

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.

Gerhard Wortmann

Hermann F. Grünsteudel

*
^{a}FB Physik, University of Paderborn, D-33095 Paderborn, Germany
*

^{b}European Synchrotron Radiation Facility, F-38043 Grenoble, France

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 ^{57}^{151}^{57}_{2}_{2}_{2}_{2}_{2}^{151}_{2}_{2}

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

H. Winkler

*
Institut für Physik, Medizinische Universität zu Lübeck, D-23538 Lübeck, Germany
*

Nuclear forward scattering (NFS) of synchrotron radiation was applied to investigate the electronic and magnetic properties of (i) the diamagnetic ``picket-fence'' porphyrin FeO_{2}_{6}_{4}_{piv}_{3}_{piv}^{-}

H. Winkler

*
^{a}II. Institut für Experimentalphysik, Universität Hamburg, D-22761 Hamburg, Germany
*

^{b}Institut für Physik, Medizinische Universität zu Lübeck, D-23538 Lübeck, Germany

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 Fe^{2+}^{3+}_{3}_{4}

B. Sepiol

*
Institut für Materialphysik der Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
*

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.

A.I. Chumakov

E.E. Alp

W. Sturhahn

A.Q.R. Baron

*
^{a}II. Institut für Experimentalphysik, Universität Hamburg, D-22761 Hamburg, Germany
*

^{b}European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble, France

^{c}Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA

^{d}SPring-8, 323-3 Mihara, Mikazuki-cho, Sayo-gun, Hyogo 679-5198, Japan

This article reports on experimental developments and first results for Mössbauer isotopes other than ^{57}^{169}^{119}^{83}^{181}^{151}^{57}

W. Potzel

*
^{a}Russian Research Center ``Kurchatov Institute'', Moscow 123182, Russia
*

^{b}Physik-Department E15, Technische Universität München, D-85747 Garching, Germany

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.

*
SPring-8, 323-3 Mihara, Mikazuki-cho, Sayo-gun, Hyogo 679-5198, Japan E-mail: baron@spring8.or.jp
*

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.

U. Bergmann

J.B. Hastings

*
^{a}National Synchrotron Light Source, Brookhaven National Laboratory, Upton, NY 11973, USA
*

^{b}Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

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 ^{57}^{&}deg;

Seishi Kikuta

*
Department of Applied Physics, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113, Japan
*

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

E. Gerdau

*
II. Institut für Experimentalphysik, Universität Hamburg, D-22761 Hamburg, Germany
*

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 ^{-9}_{2}_{3}^{57}^{151}^{119}^{161}_{2}_{3}

**Keywords:** Bragg backscattering, X-rays, monochromators, interferometers, Al_{2}O_{3}, SiC

W. Sturhahn

*
^{a}European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble, France
*

^{b}Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA

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.

A. Chumakov

*
^{a}Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA
*

^{b}European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble, France

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.

Klaus Achterhold

*
Physik-Department E17, Technische Universität München, D-85747 Garching, Germany
*

Two methods of inelastic scattering of synchrotron radiation were used to measure the dynamics of myoglobin in the temperature range from ^{2}]/T =2.1· 10^{-4}^{2}^{-1}^{2}]/T=0.6· 10^{-4}^{2}^{-1}

H. Paulsen

H. Winkler

A.X. Trautwein

H. Toftlund

*
^{a}Department of Chemistry, University of Odense, DK-5230 Odense, Denmark
*

^{b}Institut für Physik, Medizinische Universität Lübeck, D-23538 Lübeck, Germany E-mail: trautwein@physik.mu-luebeck.de

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}

W. Sturhahn

*
^{a}Laboratorium für Angewandte Physik, Gerhard-Mercator-Universität Duisburg, D-47048, Duisburg, Germany
*

^{b}Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA

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 ^{57}

W. Petry

A.Q.R. Baron

*
^{a}Physik Department E13, Technische Universität München, D-85748 Garching, Germany
*

^{b}Spring-8 / JASRI, Hyogo 678-12, Japan

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

*
Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA
*

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 (^{6} < E/\Delta E < 10^{8}

*
SPring-8, 1-1-1 Kouto, Mikazuki-cho, Sayo-gun, Hyogo-ken, 679-5198 Japan E-mail: baron@spring8.or.jp
*

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.

W. Sturhahn

T.S. Toellner

*
Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA E-mail: eea@aps.anl.gov
*

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

*
Universität Rostock, Fachbereich Physik, August-Bebel-Str. 55, D-18055 Rostock, Germany
*

A new spectroscopic technique is introduced that allows tuning of a

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

*
Russian Research Center ``Kurchatov Institute'', 123182 Moscow, Russia
*

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;

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.

J. Odeurs

C. L'abbé

G. Neyens

*
Instituut voor Kern- en Stralingsfysica, University of Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium
*

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.

*
Research Institute for Solid State Physics, POB 49, Budapest 114, Hungary
*

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

*
Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA
*

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.

*
II. Institut für Experimentalphysik, Universität Hamburg, D-22761 Hamburg, Germany E-mail: yuri.shvydko@desy.de
*

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 ^{57}^{119}^{151}^{161}^{181}

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

E. Realo

H. Winkler

W. Meyer-Klaucke

A.X. Trautwein

*
^{a}Institute of Physics, University of Tartu, 51014 Tartu, Estonia
*

^{b}Institut für Physik, Medizinische Universität zu Lübeck, D-23538 Lübeck, Germany

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 ^{57}

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

L. Deák

L. Bottyán

*
^{a}Institut für Anorganische und Analytische Chemie, Johannes Gutenberg Universität Mainz, Staudinger Weg 9, D-55099 Mainz, Germany E-mail: spiering@iacgu7.chemie.uni-mainz.de
*

^{b}KFKI Research Institute for Particle and Nuclear Physics, P.O. Box 49, H-1525 Budapest, Hungary

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

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

A.I. Chumakov

*
^{a}Russian Research Centre ``Kurchatov Institute'', 123182 Moscow, Russia
*

^{b}European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble, France

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.