Heterodyne detection of synchrotron radiation

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.     

How to do resonant nuclear experiments with synchrotron radiation

Summary The use of synchrotron radiation to excite low-lying nuclear resonances is a rapidly developing field showing great promise for hyperfine spectroscopy, phonon spectroscopy and kinetic studies, crystallography, and fundamental physics experiments. Recent technical advances in synchrotron sources, optics, and fast detectors have drastically increased signal rates and expanded the range of samples that can be studied. A typical experiment today uses a high-brightness synchrotron source having X-ray pulses well-separated in time, a meV-bandpass monochromator using perfect crystals of silicon or germanium, a sample containing resonant nuclei, and an avalanche photodiode timing detector. Both coherent and incoherent scattering can be observed; the coherent scattering is used for hyperfine spectroscopy and studies of diffraction interference phenomena, and the incoherent-scattering signal promises to be very useful for phonon spectroscopy and other studies of excitations in condensed systems. At this point seven nuclear isotopes have been used to resonantly scatter synchrotron radiation, but the number is rapidly increasing. Paper presented at the ICAME-95, Rimini 10–16 September 1995.     

Resonant scattering of an X-ray photon by a heavy atom

The influence of many-body and relativistic effects on the absolute values and shape of the double differential cross section for the resonant scattering of a linearly polarized X-ray photon by a free xenon atom near the K-shell ionization threshold has been theoretically analyzed. The evolution of the spatially extended structure of the scattering cross section to the K _{α, β} structure of the X-ray spectrum of the xenon atom emission has been demonstrated. The calculations have been performed in the dipole approximation for the anomalous dispersion component of the total inelastic scattering amplitude and in the impulse approximation for the contact component of this amplitude. The contribution of the Rayleigh (elastic) scattering component is taken into account using the methods developed in Hopersky et al., J. Phys. B 30, 5131 (1997). The effects of the radial relaxation of the electron shells, spin-orbit splitting, double excitation/ionization of the atomic ground state, as well as the Auger and radiative decays of the produced main vacancies, are considered. Using the results obtained by Tulkki, Phys. Rev. A 32, 3153 (1985) and Biggs et al., At. Data Nucl. Data Tables 16, 201 (1975), the nonrelativistic Hartree-Fock wavefunctions are changed to the relativistic Dirac-Hartree-Fock wavefunctions of the single-particle scattering states when constructing the process probability amplitude. The calculations are predicting and are in good agreement with the synchrotron experiment on the measurement of the absolute values and shape of the double differential cross section for the resonant scattering of an X-ray photon by a free xenon atom reported by Czerwinski et al., Z. Phys. A 322, 183 (1985).     

Optimization of the conditions of synchrotron Mössbauer experiment for studying electronic transitions at high pressures by the example of (Mg, Fe)O magnesiowustite

The effect of the experimental conditions on the shape of the nuclear resonant forward scattering (NFS) from (Mg_0.75Fe_0.25)O magnesiowustite has been studied at high pressures up to 100 GPa in diamond anvil cells by the method of the NFS of synchrotron radiation from the Fe-57 nuclei at room temperature. The behavior of the system in the electronic transition of the Fe²⁺ ion from the high-spin to low-spin state (spin crossover) near 62 GPa is analyzed as a function of the sample thickness, degree of nonhydrostaticity, and focusing and collimation conditions of a synchrotron beam. It is found that the inclusion of dynamical beats associated with the sample thickness is very important in the approximation of the experimental NFS spectra. It is shown that the electronic transition occurs in a much narrower pressure range (±6 GPa) rather than in a broad range as erroneously follows from experiments with thick samples under strongly nonhydrostatic conditions.     

Modulation effects of rotating radiofrequency field in forward nuclear scattering of synchrotron radiation

The quantization of a nuclear angular momentum in the rotating hyperfine (HF) field of any frequency is theoretically studied in resonant forward scattering of synchrotron radiation (SR). The adiabatically slow rotation of the quantization axis does not perturb the multilevel structure of nuclear states created by the static hyperfine interaction. It follows directly from the pattern of quantum beats of a resonant response (RR) to an SR pulse. When the rotation frequency is of the order of the Larmor frequencies, determining the stationary HF sublevels, the pattern of quantum beats of an RR is formed by the nuclear resonant transitions between quasienergy levels. At the rotation frequency much larger than the Larmor frequencies the multilevel structure of nuclear states results from the quadrupole interaction only. This revised version was published online in August 2006 with corrections to the Cover Date.     

Quantum proximity resonances

The zero-range potential approximation is used to show that quantum proximity resonances discussed recently by Heller [Phys. Rev. Lett. 77 (1996) 4122] may also occur in the absence of single-scatterer resonances. It is argued that for two identical scatterers a resonant structure appears in the Σ_u-wave rather than in the P-wave partial cross section.     

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.     

High resolution feshbach spectroscopy of cesium

We measure high-resolution Feshbach resonance spectra for ultracold cesium atoms colliding in different hyperfine and magnetic sublevels. More than 25 resonances are observed for magnetic fields up to 230 G and their positions are measured with an accuracy down to 0.03 G. From these spectra several ground-state molecular interaction parameters can be extracted with sufficient accuracy to permit for the first time an unambiguous and accurate determination of cesium's ultracold collision properties [P. J. Leo, C. J. Williams, and P. S. Julienne, following Letter, Phys. Rev. Lett. 85, 2721 (2000)].     

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)     

Space-time characteristics of nuclear resonant excitation during Bragg reflection from multilayers

Mössbauer experiments using synchrotron radiation have opened up a new method for investigating nuclear-resonance scattering — in the time domain. It is shown that the field distribution in a multilayer structure, including periodic interlayers of a resonant isotope, under Bragg reflection conditions is substantially different in the energy and time differential regimes of investigation. For separate delay times the field does not decay into the medium, but rather it undergoes complicated dynamic beats. The positions of the antinodes of the “ energy” and “temporal” standing waves are also different. In consequence the energy (Mö ssbauer) and temporal spectra of nuclear resonant reflection contain substantially different information about the structure of the films.     

Nuclear forward scattering for high energy mössbauer transitions

We have studied nuclear forward scattering of synchrotron radiation for the 67.41 keV resonance of 61Ni using a silicon crystal monochromator with low-index reflections and a multielement detector. This approach can be extended to other high-energy M?ssbauer transitions and does not pose any restrictions on the sample environment. Under conditions of large sample thickness and short nuclear lifetime, typical for work with high-energy nuclear resonances, the nuclear decay follows a universal dependence where both thickness effects and hyperfine interactions are taken into account by time scaling.     

Nuclear resonant time spectra for Sn in Co2TiSn Heusler alloy films

Co₂TiSn Heusler alloy films were grown on MgO substrates at the substrate temperature between 200 and 600 °C using atomically controlled alternate deposition and magnetic hyperfine field at the Sn nuclei was measured by the Mössbauer spectroscopy and the nuclear resonant scattering method. The relation between the hyperfine field and the structural disorder estimated by X-ray diffraction measurements was also examined. The results showed that the sample prepared at higher substrate temperature has higher degree of L2₁ order and larger hyperfine field. For the Co₂TiSn film grown at 600 °C, the hyperfine field estimated from the oscillatory pattern of the nuclear resonant time spectra was 6.1 T at room temperature and increased with a decrease of temperature to 7.5, 8.1, and 8.3 T at 200, 100, and 5 K, respectively, which shows that the film prepared by this method and condition has almost the same magnetization value and Curie temperature as bulk samples.     

Simple algorithm for quantitative analysis of reflection electron energy loss spectra (REELS)

A detailed comparison of two different physical approaches for quantitative analysis of reflection electron energy loss spectra (REELS) is presented. The Tougaard–Chorkendorff (TC) algorithm [S. Tougaard, I. Chorkendorff, Phys. Rev. B35 (1987) 6570] is analyzed theoretically and applied to experimental spectra of four elemental solids (Si, Cu, Ag, and Au). A closed expression is derived for the quantity retrieved by the TC-algorithm, the so-called “effective” cross section, which was originally only given as a recursive procedure. Single scattering loss distributions are derived from the experimental spectra using the bivariate reversal method [W.S.M. Werner, Phys. Rev. B74 (2006) 075421]. The latter agree satisfactorily with density functional theory (DFT) calculations and other data found in the literature. Using these single scattering loss distributions, the TC “effective” cross section can be perfectly reproduced if the fact is taken into account that the effective cross section is not a single scattering loss distribution and is governed to a significant extent by elastic scattering. On the basis of the above results, a dramatically simplified deconvolution scheme for quantitative analysis of REELS is developed.     

Nuclear Resonant Reflectivity Investigations of a Thin Magnetic 57Fe Layer Adjacent to a Superconducting V Layer

Hyperfine Interactions - With nuclear resonant scattering of synchrotron radiation we have investigated the magnetic hyperfine fields of a thin (～2 nm) 57Fe layer below and above the...     

The effect of radiofrequency modulation of 57Fe hyperfine interaction by rotating magnetic field

The effect of ⁵⁷Fe hyperfine interaction radiofrequency (rf) modulation by external rotating magnetic field was studied in thin Permalloy foil by means of Mössbauer spectroscopy. The rf effect was investigated as a function of intensity for several rf field frequencies. The experiments show that the external rotating rf field causes considerable changes in the hyperfine pattern. The obtained spectra are in disagreement with those obtained by Perlow [Phys. Rev. 172 (1968) 319]. They also are inconsistent with magnetostriction hypothesis. Proceeding from the Mössbauer spectrum analysis one may conclude that the magnetization of investigated foil changes its direction in a complex manner. However, the undertaken experiments show that the essential number of Mössbauer nuclei experience the rotating magnetic field influence.     

Resonances in electron scattering and photon absorption

A short survey is given of the development of ideas about resonances in atomic scattering processes and their connection with the theory of resonant states in nuclei, impurity resonances in solids, ion-atom scattering and recombination in plasmas. A detailed discussion of the experimental situation for atomic resonances is then given, followed by a review of the theory of resonance reactions as applied to them. Special attention is given to effective range and quantum defect methods, and to Fano's configuration interaction theory. Theoretical results for line positions, shapes and widths are compared with experimental data and the need for more angular distribution data is emphasized.     

Absolute intensity and phase of the resonant X-ray scattering from a germanium crystal

The 222 and 600 reflections near the germanium absorption K edge were studied on the Kurchatov synchrotron radiation source. The energy spectrum of the 222 reflection is caused by the interference of the weak nonresonant and purely resonant contributions to the tensor atomic factor, whereas the 600 reflection is purely resonant. The energy dependence of the magnitude and phase of the resonant contribution to the scattering amplitude was determined from a change in the interference pattern. The numerical simulation of the energy spectra of reflections with the inclusion of the dipole-quadrupole and thermally induced contributions shows that the latter is dominant at room temperature.     

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 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.     

Diffusion Studies with Synchrotron Radiation and with Neutron Scattering

With scattering methods we are able to detect the elementary diffusion jump. This is a report on investigations with methods working in the time domain, i.e., nuclear resonant scattering of synchrotron radiation and neutron spin echo. The accent of this paper is on diffusion in ordered alloys. We finish with an outlook on what will be possible with the upcoming potential of future synchrotron sources. This revised version was published online in August 2006 with corrections to the Cover Date.