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.

     

Polarization effects in resonant nuclear scattering

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^ο 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.

     

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.

     

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.     

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.     

Basic features of coherent nuclear resonant scattering of synchrotron radiation

The time dependences of spatially coherent nuclear resonant scattering of synchrotron radiation show a wealth of characteristic features which originate from the interference of several radiation components and from dynamical nuclear scattering. These effects will be of importance for the future fields of time domain Mössbauer spectroscopy and of nuclear resonant -ray optics. The basic features are discussed and experimental evidence is reviewed.     

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.     

Nuclear resonant scattering and molecular orbital calculations on an iron(II) spin‐crossover complex

Nuclear resonant scattering of synchrotron radiation was applied to investigate the spin‐crossover complex Fe(tpa)(NCS)₂ (tpa=tris(2‐pyridylmethyl)amine). The nuclear forward scattering experiments are compared with conventional Mössbauer experiments, and the nuclear inelastic scattering experiments are compared with the results from a theoretical normal mode analysis based on molecular orbital calculations.     

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.     

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.     

Hyperfine Spectroscopy with Nuclear Resonant Scattering of Synchrotron Radiation

Since its observation in 1985 nuclear resonant scattering of synchrotron radiation has become an excellent tool to study hyperfine interactions in solids. It combines the advantages of both local probe experiments and scattering techniques and gives valuable information on magnetic and electronic structures in case of NFS experiments. Experiments benefit from the outstanding beam quality of 3rd generation synchrotron radiation sources, as the small beam size and divergence. This revised version was published online in August 2006 with corrections to the Cover Date.     

Waves in resonant random media

Abstract

Electromagnetic properties of resonant inhomogeneous media are investigated. A new type of transverse electromagnetic wave arising due to the effective spatial dispersion is studied. It is shown that scattering on the fluctuations of the resonant frequency of the medium shifts the Cherenkov threshold and reduces the intensity of the Cherenkov radiation.     

Nuclear Resonant Inelastic and Forward Scattering of Synchrotron Radiation by 40K

We achieved excitation of the first excited state of ⁴⁰K and confirmed both energy and lifetime. Furthermore, we observed nuclear resonant inelastic scattering by ⁴⁰K in a powdered KCl sample at room temperature using a high-resolution monochromator. The time spectrum of the nuclear resonant forward scattering was measured at 50 K. Our observations of nuclear resonant inelastic and forward scattering by ⁴⁰K make electronic and dynamic studies for potassium practical. The measurements of nuclear resonant scattering for the radioactive ⁴⁰K nuclide will enable and lead to further studies of other radioactive nuclides. This revised version was published online in August 2006 with corrections to the Cover Date.     

High-Pressure Studies of Magnetism and Lattice Dynamics by Nuclear Resonant Scattering of Synchrotron Radiation

A review is given on recent high-pressure experiments using nuclear resonant scattering of synchrotron radiation. We shortly introduce the methodological aspects connected with high-pressure experiments applying nuclear forward scattering and nuclear inelastic scattering of synchrotron radiation. Selected examples for the study of magnetism are given for the Laves phases LuFe₂ and ScFe₂, where we studied the variation of the magnetic ordering temperature and of the Fe band moment as a function of pressure. An actual example for the study of lattice dynamics is a recent investigation of the phonon density-of-states in metallic iron with special emphasis on hcp ε-Fe, where the pressure-induced texture is used, in conjunction with theoretical calculations, to extract density of phonon states as seen parallel and perpendicular to the hexagonal c-axis. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

A New Way of Looking at Nuclear Resonant Scattering

A new model for nuclear-resonant scattering of gamma radiation from resonant matter has been developed and is summarized here. This “coherent-path” model has lead to closed-form, finite-sum solutions for radiation scattered in the forward direction. The solution provides a unified microscopic picture of nuclear-resonant scattering processes. The resonant absorber or scatterer is modeled as a one-dimensional chain of “effective” nuclei or “effective” planes. The solution is interpreted as showing that the resonant radiation undergoes sequential scattering from one absorber “nucleus” or “plane” to another before reaching the detector. For recoil-free processes the various “paths” to the detector contribute coherently. The solution for this case gives calculated results that are indistinguishable from those using the classical optical model approach, although the forms of the solutions are completely different. The coherent-path model shows that the “speed-up” and “dynamical beating” effects are primarily a consequence of the fact that the single “effective” nuclear scattering processes are 180° out of phase with the incident radiation while the double nuclear scattering processes are in phase with the incident radiation. All multiple scattering paths are, and must be, included. The model can also treat the incoherent processes, i.e., processes involving gamma emission with recoil or conversion-electron emission. The source of the resonant gamma radiation can be from a radioactive source or from synchrotron radiation: both cases are treated. The model is used to explain and understand the results when each of the following experimental procedures is applied: time-differential Mössbauer spectroscopy, time-differential synchrotron radiation spectroscopy, enhanced-resolution resonant-detector Mössbauer spectroscopy, and the “gamma echo”.     

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.     

Recent Developments in Synchrotron Mössbauer Reflectometry

Hyperfine Interactions - Synchrotron Mössbauer Reflectometry (SMR), the grazing incidence nuclear resonant scattering of synchrotron radiation, can be applied to perform depth-selective phase...     

Sound velocities of compressed Fe3C from simultaneous synchrotron X‐ray diffraction and nuclear resonant scattering measurements

The applications of nuclear resonant scattering in laser‐heated diamond anvil cells have provided an important probe for the magnetic and vibrational properties of ⁵⁷Fe‐bearing materials under high pressure and high temperature. Synchrotron X‐ray diffraction is one of the most powerful tools for studying phase stability and equation of state over a wide range of pressure and temperature conditions. Recently an experimental capability has been developed for simultaneous nuclear resonant scattering and X‐ray diffraction measurements using synchrotron radiation. Here the application of this method to determine the sound velocities of compressed Fe₃C is shown. The X‐ray diffraction measurements allow detection of microscale impurities, phase transitions and chemical reactions upon compression or heating. They also provide information on sample pressure, grain size distribution and unit cell volume. By combining the Debye velocity extracted from the nuclear resonant inelastic X‐ray scattering measurements and the structure, density and elasticity data from the X‐ray diffraction measurements simultaneously obtained, more accurate sound velocity data can be derived. Our results on few‐crystal and powder samples indicate strong anisotropy in the sound velocities of Fe₃C under ambient conditions.