Enhancement and speedup in nuclear resonant diffraction

The interaction of Mössbauer radiation with the nuclei in a single crystal provides the unique possibility to enhance the coherent channel in nuclear resonance scattering by means of a properly phased excitation of the scattering centers. When a primary beam is incident in the exact Bragg direction, all nuclei are excited in phase. The resonance parameters of such a collective nuclear excitation of a perfect single crystal (γ-exciton) are entirely different from those of an individual nuclear excitation. In Bragg geometry diffraction, the resonance lines are shifted and broadened (enhancement effect), the lifetime of the collective excited state is shortened (speedup effect) and the reflectivity becomes total (suppression effect). Recent experiments arc reviewed, where these effects were studied in the resonant diffraction of Mössbauer and of synchrotron radiation.

     

Resonant X-ray scattering from a rotating medium: The Nuclear Lighthouse Effect

A coherently excited nuclear state is carried with a rotating sample so that its radiative decay is redirected by the rotation angle that has developed during its lifetime. As a result, the time spectrum of the nuclear decay is mapped to an angular scale. This effect has been observed in nuclear resonant scattering of synchrotron radiation from a rotating ⁵⁷Fe metal foil. Applications with respect to elastic and inelastic nuclear resonant scattering are discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Nuclear resonant scattering of synchrotron radiation by multilayer structures

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.

     

General properties of nuclear resonant scattering

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 γ-ray resonant scattering in energy and time domains are presented. Special attention is paid to scattering of a γ 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.

     

Introduction to nuclear resonant scattering with synchrotron radiation

The concepts leading to the application of synchrotron radiation to elastic and inelastic nuclear resonant scattering are discussed. The resulting new experimental techniques are compared to conventional Mössbauer spectroscopy. A survey of situations that favor experiments with synchrotron radiation is offered.

     

Time-dependent polarization in Mössbauer experiments with synchrotron radiation (II)

The resonant forward scattering of X-rays from⁵⁷Fe nuclei is strongly polarization dependent. The broad band excitation provided by synchrotron radiation (SR) results in an interesting time-dependent polarization mixing. This mixing can be used to substantially reduce the nonresonant (nonrotated) scattering from electrons. The presented technique will allow the full utilization of next-generation synchrotron facilities as a source for Mössbauer experiments.     

Multiple nuclear Bragg scattering

Multiple nuclear resonant scattering from an ⁵⁷FeBO₃ single crystal has been observed in the three-beam case. A change of the lifetime and a modulation of the quantum beat were observed in our study. The high brilliance of synchrotron radiation and the high perfection of the synthetic ⁵⁷FeBO₃ single crystal enabled us to observe such an effect. This revised version was published online in August 2006 with corrections to the Cover Date.     

Nuclear resonant scattering using synchrotron radiation

A one-dimensional quantum model for nuclear resonant scattering using synchrotron radiation has been developed. This model gives a clear physical interpretation of the most prominent features of the coherent forward scattering process namely, the “speed-up” and “dynamical beat” effects. The form of the solution, for the time-dependent forward scattered intensity of the resonant radiation from the resonant medium after synchrotron radiation excitation, is a finite series. This unique solution can be interpreted in terms of a summation over all multiple forward scattering paths the radiation takes in reaching the detector. The resonant medium is represented by a linear chain of N effective resonant nuclei. The analysis starts from a coupled set of quantum mechanical equations for the relevant amplitudes in frequency space. Transformation to the time domain gives an analytical expression for the forward scattered intensity. The contribution of every order of the multiple scattering processes from the N effective nuclei appears naturally. The expression gives a clear physical understanding of all relevant aspects of resonant forward nuclear scattering. Furthermore, the present formalism allows the consideration of incoherent processes. This permits the study of processes in which there is gamma emission with recoil or emission of internal-conversion electrons. This revised version was published online in August 2006 with corrections to the Cover Date.     

Inelastic nuclear resonant absorption of synchrotron radiation in thin films and multilayers

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 α-Fe(0 0 1)/Cr(0 0 1) superlattices.

     

Nuclear resonant scattering of synchrotron radiation

The principal ideas of the theory and the main results of the experimental studies of the coherent resonant scattering of-radiation by nuclear ensembles in matter are briefly over-viewed. An analysis of transmission of the Mössbauer-radiation and of synchrotron radiation through a nuclear resonant medium is suggested using an approach based on the optical theory. The feasibilities of the nuclear resonant scattering of synchrotron radiation as a new technique for studying the hyperfine interactions and some other phenomena of the physics of condensed matter are considered.     

High-pressure Mössbauer spectroscopy with nuclear forward scattering of synchrotron radiation

Abstract

Using a diamond anvil cell, high-pressure ⁵⁷Fe Mössbauer spectroscopy has been performed with the nuclear forward scattering of synchrotron radiation. A pressure-induced magnetic hyperfine interaction at ⁵⁷Fe in SrFeO_{2, 97} has been detected at 44 GPa and 300 K for a first time by a quantum-beat modulation of the decay rate after collective nuclear excitation by the synchrotron pulse. The basic concept and method used to detect nuclear forward scattering with synchrotron radiation are discussed.     

Nuclear resonant scattering of synchrotron radiation for the study of dynamics around the glass transition

Motion of ⁵⁷Fe can be observed on a scale of nsec to μsec through nuclear resonant forward scattering of synchrotron radiation. Additional information is obtained by measuring simultaneously incoherent nuclear resonant scattering at nonzero angles. In a glass, one measures the Lamb-Mößbauer factor; in the viscous phase, structural relaxation is observed directly. We apply the method to ferrocene / dibutylphthalate between 140 and 205 K. The mean relaxation times do not follow the observed temperature dependence of other, macroscopic relaxation measurements. We attribute this to a strong wavenumber dependence of the relaxation time. The prospects of nuclear resonant scattering for studying the dynamics of viscous liquids are discussed.     

Studies of nuclear resonant scattering at TRISTAN-AR

Studies of nuclear resonant scattering of synchrotron radiation undertaken with the X-ray undulator installed in the TRISTAN Accumulation Ring at the National Laboratory for High Energy Physics, KEK, are reported. These studies have evaluated the effect of fast magnetic switching on the nuclear collective decay in an FeBO₃ crystal, the change in the polarization state of nuclear Bragg scattering by fast magnetic switching, and the influence of this switching on the time evolution of the nuclear forward scattering. The phenomenon of interferometric nuclear forward scattering has also been studied.     

Time-domain, nuclear-resonant, forward scattering: theclassical approach

This paper deals with the interaction of electromagnetic radiation with matter assuming the matter to have nuclear transitions in resonance with incident electromagnetic radiation. The source of the radiation is taken to be of two types; natural radioactive gamma decay and synchrotron radiation. Numerical examples using ⁵⁷Fe are given for the two types of source radiation. Calculated results are contrasted for the two cases. Electromagnetic radiation produced by recoil-free gamma-ray emission has essentially the natural linewidth. Electromagnetic radiation from a synchrotron, even with the best monochromators available, has a relatively broad-band spectrum, essentially constant for these considerations. Polarization effects are considered. In general, the nuclear-resonant medium changes the polarization of the input radiation on traversing the medium. Calculations are presented to illustrate that synchrotron radiation studies using nuclear-resonant forward scattering have the potential for making high-precision measurements of hyperfine fields and recoilless fractions. An interesting aspect of nuclear-resonant forward scattering, relative to possible gamma-ray laser development, is the so-called “speed-up” effect. This revised version was published online in August 2006 with corrections to the Cover Date.     

Relaxation experiments with synchrotron radiation

Relaxation phenomena show up in standard energy domain Mössbauer spectra via line broadening. The evaluation of such spectra is in most cases done by adopting the stochastic theory mainly developed in the 60s and 70s. Due to the time structure and the polarization of the synchrotron radiation nuclear resonance forward scattering in the time domain gives valuable information on relaxation mechanisms. We report here mainly on Nuclear Forward Scattering (NFS) experiments investigating the paramagnetic relaxation of the Fe³⁺ ion in (NH)₄Al_0.95 ⁵⁷Fe_0.05(SO₄)₂·12H₂O and briefly on recent investigations on charge fluctuations in Eu₃S₄.     

Developments in time domain Mössbauer spectroscopy

Time differential measurements of nuclear resonance scattering using synchrotron radiation have been performed with the low energy Mössbauer transitions of⁵⁷Fe,¹¹⁹Sn, and¹⁶⁹Tm since 1984. Various methods of filtering the nuclear energy band from the incident synchrotron radiation are now available. The possibilities of applying these methods to transition energies above 30 keV are discussed. A new technique is proposed, which is especially effective for the high energy Mössbauer transitions. It takes advantage of the different dependence of the electronic Debye-Waller factor and the Mössbauer-Lamb factor on the scattering angle.     

Techniques for inelastic X‐ray scattering with μeV‐resolution

A new spectroscopic technique is introduced that allows tuning of a eVwide 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 Xray scattering and elastic nuclear resonant scattering are discussed.     

Synchrotron Mössbauer reflectometry using stroboscopic detection

The concept of the heterodyne/stroboscopic detection of nuclear resonance scattering of synchrotron radiation is extended to the grazing incidence geometry. Model calculations for an antiferromagnetic [⁵⁷Fe/Cr]₂₀ multilayer are shown and discussed. Principles and methodological aspects of stroboscopic synchrotron Mössbauer reflectometry are briefly reviewed.     

Diffusion in crystalline materials

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.

     

Pure nuclear resonant scattering of synchrotron radiation by a multilayer structure: Theoretical analysis for 169Tm

The possibility of observing pure nuclear resonant scattering of synchrotron radiation by a multilayer structure containing the ¹⁶⁹Tm isotope is analyzed theoretically. The main problem is the need to suppress the enormous background of radiation scattered by electrons. Two methods for the destructive interference of a synchrotron radiation beam in reflection at grazing incidence by a layered system containing Tm nuclei in one of the layers are considered, and their efficiency as applied to the conditions of third-generation synchrotron radiation sources, such as in the European Synchrotron Radiation Facility (ESRF), is calculated. An electron scattering suppression efficiency parameter is formulated as the ratio of the integrated nuclear scattering intensity (with a time delay) to the total prompt electron scattering intensity in assigned ranges of angles and energies. In the first method thin films of a special type on a substrate, viz., GIAR films, are used. In the second method a new effect, which is termed the Bragg antipeak effect and involves the destructive interference of a wave that is Bragg-diffracted in a multilayer superlattice and a wave reflected on the upper boundary of the sample, is employed. The physical properties of the Bragg antipeak effect are considered, and it is found that its efficiency is sufficient for practical use. Zh. éksp. Teor. Fiz. 114, 3–22 (July 1998)