Coherent resonant x-ray scattering from a rotating medium

A coherently excited nuclear state in a rotating sample acquires a phase shift during its time evolution that is proportional to its angular momentum and the rotation angle. As a consequence, the radiative decay of the excited state proceeds into the rotated direction, and the time spectrum of the nuclear decay is mapped onto an angular scale. This effect has been observed in nuclear resonant scattering of synchrotron radiation from a 57Fe metal foil rotating at 18 kHz.     

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.     

Fast scintillation detectors for high-energy X-ray region

We have developed fast scintillation detectors for nuclear resonant scattering experiments using synchrotron radiation and a nuclear excited level existing in >30?keV. A fast x-ray detector using an organic-inorganic perovskite scintillator of phenethylamine lead bromide (PhE-PbBr₄) had a dominant light emission with a fast decay time of 9.9?ns. An x-ray detector equipped with a 0.9-mm-thick PhE-PbBr₄ crystal (size: ～8 × 7?mm²) was used to detect nuclear resonant scattering in ⁶¹Ni (the first excited level: 67.41?keV; half-life: 5.3?ns). We could successfully record the decaying gamma rays emitted from ⁶¹Ni with a relatively high detection efficiency of 24%. A lead-doped plastic scintillator (NE142, Pb ～5?wt% doped) had been known to have a faster decay time of 1.7?ns. Following a test of a single NE142 detector, a four-channel NE142 detector was fabricated and successfully applied to the synchrotron-radiation based M?ssbauer spectroscopy experiment on ⁶¹Ni.     

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.     

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.

     

Elastic properties of filled-Skutterudite compounds probed by Mössbauer nuclei

We have carried out Mössbauer spectroscopy and nuclear resonant inelastic scattering to elucidate the lattice dynamics in filled-Skutterudite compounds, especially phosphides. The second-order Doppler shift obeys the Debye model in RFe₄P₁₂. Nuclear quadrupole interaction reveals an unusual temperature dependence in these compounds. An anomaly is observed in ⁵⁷Fe nuclear resonant inelastic scattering of these compounds. The energy where the anomaly observed in SmFe₄P₁₂ agrees with the phonon excitation energy observed by ¹⁴⁹Sm nuclear resonant inelastic scattering. We have also performed the ⁹⁹Ru Mössbauer measurements of SmRu₄P₁₂.     

Nuclear matrix elements for the resonant neutrinoless double electron capture

The rate of the neutrinoless double electron capture ( 0n\ensuremath 0\nu ECEC) decay with a resonance condition depends sensitively on the mass difference between the initial and final nuclei of decay. This is where the JYFLTRAP Penning-trap measurements at the JYFL become invaluable in estimation of the half-lives of these decays. In this work the resonant 0n\ensuremath 0\nu ECEC decay is discussed from the point of view of its theoretical aspects, in particular regarding the resonance condition and the involved nuclear matrix elements (NME). The associated decay amplitudes are derived and the calculations of the NMEs by the microscopic many-body approach of the multiple-commutator model are outlined. The resonant 0n\ensuremath 0\nu ECEC decays of ⁷⁴Ge\ensuremath {\rm ^{74}Ge} and ¹³⁶Ce\ensuremath {\rm ^{136}Ce} are discussed as applications of the theory framework.     

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.     

Influence of the laser-induced continuum structure on cross sections of the over threshold scattering of photons on atom

Process of photon scattering on atoms is considered at energy above the ionization threshold. Influence of the resonant structure in the continuum, induced by a laser field due to coupling with the level 4¹ S in helium, on the cross sections of elastic and inelastic scattering of a probe radiation on atom in the meta-stable state 2¹ S is theoretically investigated. In the rotating wave approximation approach dependences of resonant scattering cross sections on the probe and laser radiation characteristics are obtained. The frequency and polarization dependences of the scattering cross sections to the final states of atom 1¹ S, 2¹ S and 4¹ S are calculated.     

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.

     

Nuclear matrix elements for rare decays

Neutrinoless double electron capture (0νECEC) is being vigorously investigated because of the possibility of it telling us something about the absolute mass scale of the neutrino. The resonant 0νECEC is particularly interesting due to the potentially huge enhancement of its decay rate by a resonance condition. Recently the mass differences of two atom pairs were measured in order to study the enhancement of the 0νECEC rates of ⁷⁴Se and ¹¹²Sn. The associated nuclear matrix elements were also evaluated. The neutrino mass can also be detected by using beta decays with low Q values. Related to this we have investigated the second-forbidden decay branch of ¹¹⁵In with its ultra-low Q value. Open questions about nuclear and atomic contributions to the associated decay rate emerge.     

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.     

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 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 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.

     

Low-energy theorems for nuclear compton and raman scattering and 0+ → 0+ two-photon decays in nuclei

Low-energy theorems for elastic photon scattering (nuclear Compton scattering) from a nucleus of arbitrary spin are derived in the nonrelativistic approximation through terms quadratic in the photon frequency. The same derivation is made for the special case of 0⁺ → 0⁺ nuclear excitation by inelastic photon scattering (nuclear Raman scattering). Use is made of the general principle of gauge invariance, which bypasses the need to specify the form of the current operator explicitly. A general discussion of the contribution of mesonic exchanges is made and their effect is isolated. The center-of-mass correction to the nuclear diamagnetic susceptibility is calculated. The 0⁺ → 0⁺ two-photon decay amplitude is obtained from the nuclear Raman amplitude and the transition rate is calculated.     

Calculation of the imaginary part of the nucleon-nucleus optical-model potential

The imaginary part of the optical-model potential for the scattering of nucleons by nuclei is studied in the frame of the shell-model approach to nuclear reactions. Special attention is paid to the one-hole target nuclei. The imaginary part of the optical-model potential in the second order in the nucleon-nucleus interaction is divided into two parts. The first corresponds to the average resonant scattering. The second corresponds to the inelastic scattering leading to the non-collective states of the target nuclei. A local potential equivalent to the non-local theoretical one is constructed in order to facilitate comparison with experiment. Numerical calculations concern the scattering of 14.5 MeV protons by ³⁹K. It is found that the imaginary part depends upon the angular momentum and that its radial variation is governed by strong shell effects. The predicted absorption is approximately 60% of the experimental one. The average resonant scattering contributes to the imaginary part of the optical-model potential as much as the inelastic non-collective excitations of the target.     

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.     

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.     

High pressure experiments with synchrotron radiation

Using a diamond anvil cell (DAC), high pressure ⁵⁷Fe Mössbauer spectroscopy has been performed with the nuclear forward scattering of synchrotron radiation. We used monochromatized synchrotron radiation from an in‐vacuum type undulator as a high‐density strong Mössbauer source with a quite small beam size. Pressure‐induced magnetic hyperfine interactions at ⁵⁷Fe in SrFeO_2.97 has been detected at 74 GPa by a quantum‐beat modulation of the decay rate after collective nuclear excitation with the synchrotron radiation pulse. Evidence for a transition from antiferromagnetism to ferromagnetism of Fe in SrFeO_2.97 at 74 GPa and 300 K has been obtained from the nuclear forward scattering under a transverse magnetic field.