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.     

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.     

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.

     

Polarizer–analyzer optics

The principles behind the design and operation of polarizationbased optics for nuclear resonant scattering of synchrotron radiation are discussed. With perfect single crystals and collimated Xrays emitted from undulatorbased thirdgeneration synchrotron radiation sources, polarizationselective 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.     

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.     

Nuclear Resonance Beamline at ESRF

The Nuclear Resonance Beamline at ESRF is dedicated to the excitation of nuclear levels by synchrotron radiation. The sources of radiation and optical elements are optimized to provide an intense, highly monochromatic, collimated and stable X-ray beam of small cross-section at the Mössbauer transition energies between 6 and 30 keV. The set-up of the beamline allows to perform studies in diffraction, small angle scattering, forward scattering and incoherent scattering. Equipment is available to maintain the sample at variable temperature and magnetic field. Fast detectors and timing electronics serve to separate the delayed nuclear scattering from the prompt electronic scattering and to measure the time spectra of nuclear radiation with sub-nanosecond resolution. The general lay-out and the parameters of the beamline are reported. Typical domains of applications are discussed and illustrated by first experimental results.     

Development of Mössbauer diffractometer by using nuclear resonant scattering at SPring-8 BL11XU

A Mössbauer diffractometer has been developed by using ⁵⁷Fe nuclear resonant scattering apparatus at SPring-8 BL11XU in order to obtain a crystal-site-selective Mössbauer spectrum. A ??-2?? goniometer was newly installed between the nuclear monochromator and a detector. From a single crystal Fe₃ O ₄ mounted on the goniometer, the 111, 222, and 220 reflected γ-rays were used to collect the diffraction spectra at room temperature. The intensity ratio of the two subspectra, corresponding to A- and B-site Fe ions, changes notably according to the reflection index. The diffraction spectrum is composed of a major absorption spectrum and a minor emission spectrum. The former is given by the γ-ray due to the electron scattering and nuclear absorption, whereas the latter is given by the γ-ray due to the nuclear resonant scattering. Interference effects between these two γ-rays are also seen as line broadenings, asymmetric line shapes, and slope of the base lines. These features can be successfully expressed by a Fano function. We consider that the emission spectrum due to the nuclear resonant scattering represents crystal-site-selective Mössbauer spectrum.     

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.     

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.     

CONUSS and PHOENIX: Evaluation of nuclear resonant scattering data

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.     

Intensity of γ radiation back-scattered as a result of the Mössbauer effect

In the geometry of total backscattering, the intensity of scattered Mössbauer radiation is calculated. The contribution of various scattering channels to the spectrum is discussed: resonant and nonresonant, elastic and inelastic. Scattering at samples of different thickness is considered. Only one-time scattering of quanta in the material is taken into account.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii. Fizika, No. 8, pp. 23–29, August, 1989.     

Temperature dependence of phonon energy spectra with nuclear resonant scattering of synchrotron radiation

Summary The phonon energy spectra of a polycrystalline α-Fe foil were observed at 150 K and 300 K by using the nuclear resonant scattering of synchrotron radiation. In each spectrum, inelastic scattering was observed at both sides of the elastic peak. It was found that the ratio of the elastic-scattering component and the asymmetry of the intensity of the side bands observed at 150 K are larger than those observed at 300 K, respectively. The observed temperature-dependent spectra are in good agreement with the spectra calculated from the phonon energy distribution function. One of the advantageous features of this method is that the excitation of only a specific element is possible. Our results show that this method is applicable to the study of lattice dynamics and opens a new field of the nuclear resonant scattering spectroscopy. Paper presented at ICAME-95, Rimini, 10–16 September 1995.     

Mean lifetime of the 720 keV level of45Sc

The lifetime of the fourth excited state of⁴⁵Sc, at an energy of 720 keV, was determined in a nuclear resonant scattering experiment. Gamma rays of the desired energy for the excitation of this level were obtained by Compton scattering of the 1173 and 1332 keV photons from a 4300 Ci radioactive⁶⁰Co source. A value of (5.6±1.2) meV was found for the radiation width of the level, assuming a value of 5/2 for its spin. The corresponding mean lifetime is (0.12 _?0.02 ^+0.04 ) ps. An attempt was made to determine the spin of the level by means of angular distribution measurements.     

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.     

Transverse coherence in nuclear resonant scattering of synchrotron radiation

Hyperfine Interactions - We discuss the effects of transverse coherence in time domain nuclear resonant scattering experiments using synchrotron radiation. The importance of source and detector...     

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.

     

Modeling of electron tunneling times in asymmetric double quantum wells

A scattering process modeled by an imaginary potential V _I in the wide well of an asymmetric double quantum well structure (DQWS) is used to model the electron tunneling from the narrow well. Taking V _I –5 meV, the ground resonant level lifetimes of the narrow well in the DQWS are in quantitative agreement with the experimental resonance and non-resonance tunneling times. The corresponding scattering time 66 fs is much faster than the intersubband scattering time of LO-photon emission.     

MOTIF: Evaluation of time spectra for nuclear forward scattering

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 timeindependent and timedependent hyperfine interactions.     

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”.