Electric Quadrupole Absorption Research Articles

Magnetic dipole and electric quadrupole absorption in carbon dioxide

Magnetic dipole and electric quadrupole absorption in carbon dioxide are addressed in details. The selection rules for both processes are presented. The equations for the line intensities are given. In the case of the quadrupole absorption the Herman-Wallis functions are derived. The results of the present paper were used in the analysis of the carbon dioxide absorption band at 3.3 µm in the atmosphere of Mars (Trokhimovskiy A, Perevalov V, Korablev O, Fedorova A, Olsen KS, Bertaux JL, Patrakeev A, Shakun A, Montmessin F, Lefèvre F, Lukashevskaya A. First observation of the magnetic dipole CO2 absorption band at 3.3 µm in the atmosphere of Mars by ExoMars Trace Gas Orbiter ACS instrument. A&A 639, A142 (2020)). The retrieved from the Martian atmosphere spectra vibrational transition magnetic dipole moment for the 01111–00001 (ν2+ν3) band of 12C16O2M01111←000001|Δℓ2|=1=0.96μN (where μN is nuclear magneton) is one order of magnitude larger than the gyromagnetic ratio in the case of the rotation-induced magnetic dipole moment.

First observation of the magnetic dipole CO2absorption band at 3.3μm in the atmosphere of Mars by the ExoMars Trace Gas Orbiter ACS instrument

The atmosphere of Mars is dominated by CO2, making it a natural laboratory for studying CO2spectroscopy. The Atmospheric Chemistry Suite (ACS) on board the ExoMars Trace Gas Orbiter uses solar occultation geometry to search for minor atmospheric species. During the first year of ACS observations, the attention was focused on the spectral range covering the methaneν3absorption band, 2900–3300 cm−1, which has previously been observed on Mars. No methane was detected by ACS; instead, an improvement of the data processing has led to the identification of 30 weak absorption lines that were missing from spectroscopic databases. Periodic series of absorptions up to ~1.6% deep are observed systematically around the position of the methaneQ-branch when the line of sight penetrates below 20 km (creating an optical path length of 300–400 km, with an effective pressure of a few millibar). The observed frequencies of the discovered lines match theoretically computed positions of theP-,Q-, andR-branches of the magnetic dipole and electric quadrupole 01111-00001 (ν2+ν3) absorption bands of the main CO2isotopologue; neither band has been measured or computed before. The relative depths of the observed spectral features support the magnetic dipole origin of the band. The contribution of the electric quadrupole absorption is several times smaller. Here we report the first observational evidence of a magnetic dipole CO2absorption.

Resonant X-ray emission with a standing wave excitation

The Borrmann effect is the anomalous transmission of x-rays in perfect crystals under diffraction conditions. It arises from the interference of the incident and diffracted waves, which creates a standing wave with nodes at strongly absorbing atoms. Dipolar absorption of x-rays is thus diminished, which makes the crystal nearly transparent for certain x-ray wave vectors. Indeed, a relative enhancement of electric quadrupole absorption via the Borrmann effect has been demonstrated recently. Here we show that the Borrmann effect has a significantly larger impact on resonant x-ray emission than is observable in x-ray absorption. Emission from a dipole forbidden intermediate state may even dominate the corresponding x-ray spectra. Our work extends the domain of x-ray standing wave methods to resonant x-ray emission spectroscopy and provides means for novel spectroscopic experiments in d- and f-electron systems.

Borrmann spectroscopy

Under conditions of Anomalous X-ray Transmission (known as the Borrmann Effect), an X-ray standing wave is set up inside a crystal, leading to a strong reduction in electric dipole absorption. We show that electric quadrupole absorption is not similarly diminished and is thus relatively enhanced by a large factor. Absorption measurements, made under thick-crystal Laue (transmission) diffraction conditions in Gd3Ga5O12 (GGG) and Y3Fe5O12 (YIG), show a range of spectral features that can be assigned unambiguously to electric quadrupole events. This phenomenon, which seems to have been overlooked for decades, opens up new possibilities for studying important electronic states with hard x-ray beams. In this paper, we outline the origin of the effect and a phenomenological description of its temperature dependence, and consider the possibility of measuring the angle dependence of enhanced quadrupole absorption.

Optical rectification and frequency doubling in metal vapors

It is theoretically shown that, under conditions of two-photon absorption of radiation by metal vapors, the medium becomes considerably polarized and efficiently doubles the radiation frequency. Two physical mechanisms by which these effects can occur are detected. The first of them results from the ring frequency mixing, while the second one is caused by a polarization nonlinearity that is quadratic in the field amplitude and that is formed as a result of the electric quadrupole absorption due to the forbidden transition. The effects predicted can form the basis for new optical methods for measuring the electric quadrupole and magnetic dipole moments for forbidden atomic transitions.

Quadrupole transitions revealed by Borrmann spectroscopy

The Borrmann effect-a dramatic increase in transparency to X-ray beams-is observed when X-rays satisfying Bragg's law diffract through a perfect crystal. The minimization of absorption seen in the Borrmann effect has been explained by noting that the electric field of the X-ray beam approaches zero amplitude at the crystal planes, thus avoiding the atoms. Here we show experimentally that under conditions of absorption suppression, the weaker electric quadrupole absorption transitions are effectively enhanced to such a degree that they can dominate the absorption spectrum. This effect can be exploited as an atomic spectroscopy technique; we show that quadrupole transitions give rise to additional structure at the L(1), L(2) and L(3) absorption edges of gadolinium in gadolinium gallium garnet, which mark the onset of excitations from 2s, 2p(1/2) and 2p(3/2) atomic core levels, respectively. Although the Borrmann effect served to underpin the development of the theory of X-ray diffraction, this is potentially the most important experimental application of the phenomenon since its first observation seven decades ago. Identifying quadrupole features in X-ray absorption spectroscopy is central to the interpretation of 'pre-edge' spectra, which are often taken to be indicators of local symmetry, valence and atomic environment. Quadrupolar absorption isolates states of different symmetries to that of the dominant dipole spectrum, and typically reveals orbitals that dominate the electronic ground-state properties of lanthanides and 3d transition metals, including magnetism. Results from our Borrmann spectroscopy technique feed into contemporary discussions regarding resonant X-ray diffraction and the nature of pre-edge lines identified by inelastic X-ray scattering. Furthermore, because the Borrmann effect has been observed in photonic materials, it seems likely that the quadrupole enhancement reported here will play an important role in modern optics.

Multipolar interband absorption in a semiconductor quantum dot I Electric quadrupole enhancement

We present a theoretical investigation of a semiconductor quantum dot interacting with a strongly localized optical field as encountered in high-resolution near-field optical microscopy. The strong gradients of these localized fields suggest that higher-order multipolar interactions will affect the standard electric dipole transition rates and selection rules. For a semiconductor quantum dot in the strong confinement limit we calculated the interband electric quadrupole absorption rate and the associated selection rules. We found that the electric quadrupole absorption rate is comparable with the absorption rate calculated in the electric dipole approximation. This implies that near-field optical techniques can extend the range of spectroscopic measurements beyond the standard dipole approximation. However, we also show that spatial resolution cannot be improved by the selective excitation of electric quadrupole transitions.

Resonant1s→3dx-ray Bragg diffraction and structure factors for transition-metal compounds

Structure factors for Bragg diffraction of x rays enhanced by electric quadrupole absorption $(1\stackrel{\ensuremath{\rightarrow}}{s}3d)$ are calculated for several configurations of the resonant ions found to exist in transition-metal compounds. The configurations include the spontaneous order (fully compensating and noncollinear antiferromagnetism) and field-induced states of ferrous niobate, and paramagnetic iron pyrite. The calculation is couched in terms of spherical tensors, which describe the orbital magnetism of $3d$ electrons, and highlights the essential components contributing to the results, namely, use of an atomic model for the resonant contribution to the x-ray scattering length, the influence of the elements of symmetry pertinent to a resonant ion and the crystal structure, and linear and circular polarization effects. Spatial anisotropy in the $3d$ orbital moments leads to charge-forbidden reflections. Associated structure factors are calculated as functions of the canting angle of the principal axis, and the (azimuthal) angle of rotation of the crystal about the Bragg wavevector. In the model for ferrous niobate the orbital moment arises from a conventional mechanism based on the spin-orbit coupling.

Electric quadrupole photoneutron reactions inO16

Photoneutron energy spectra from the $^{16}\mathrm{O}(\ensuremath{\gamma},{\mathrm{n}}_{0})^{15}\mathrm{O}$ reaction were measured as functions of laboratory angle over a range of excitation energies from 30 to 35 MeV. Angular distribution Legendre-polynomial coefficients were extracted up to third order as functions of excitation energy. Nonzero values of the coefficients ${a}_{1} (+0.25\ifmmode\pm\else\textpm\fi{}0.02)$ and ${a}_{3} (\ensuremath{-}0.2\ifmmode\pm\else\textpm\fi{}0.02)$ were observed over the energy region explored, indicating interference between states of opposite parity. These values can be accounted for in a simple model incorporating electric quadrupole absorption strength decaying via the ground-state photoneutron channel. When combined with the previously-determined amplitude ratio for the $E1$ $p\ensuremath{\rightarrow}s$ and $p\ensuremath{\rightarrow}d$ single-particle transitions, the present results suggest that about 4% of the isovector energy-weighted sum rule is found in the ($\ensuremath{\gamma}$,${\mathrm{n}}_{0}$) channel in the energy range studied. The value of the ($\ensuremath{\gamma}$,${\mathrm{n}}_{0}$) cross section was found to vary from 1.5\ifmmode\pm\else\textpm\fi{}0.1 mb at ${E}_{x}=30$ MeV to 0.8\ifmmode\pm\else\textpm\fi{}0.1 mb at 35 MeV. The average magnitude of the $E2$ contribution to this cross section was estimated to be 0.05\ifmmode\pm\else\textpm\fi{}0.02 mb. This is in reasonable agreement with a recent continuum randomphase approximation shell model calculation, but is in disagreement with a previous measurement.

E2Strength inC12Determined by Elastic Photon Scattering

The elastic-photon-scattering cross section for /sup 12/C has been measured at 90/sup 0/ and 135/sup 0/ in the energy range from 23.5 to 39 MeV. These data disagree with the predicted scattering, derived from the measured photonuclear absorption cross section, if only E1 transitions are assumed. To explain the difference in these cross sections, a large component of electric quadrupole absorption between 24 and 40 MeV is inferred.

A study of the giant dipole resonance of vibrational nuclei in the 103 ≦ A ≦ 133 mass region

This paper presents a set of experimental data concerning the giant dipole resonance of nuclei (GDR) in the 103 ≦ A ≦ 133 mass region. The cross sections σ(γ,n) and σ(γ, 2n) were obtained in the energy region 8–30 MeV by means of a monochromatic photon beam produced by annihilation in flight of positons. This paper attempts also to give an interpretation of the experimental behaviour of the GDR for vibrational nuclei in the 103 ≦ A ≦ 133 mass region in terms of the simple dynamic collective model. In particular it is shown that the width of the GDR increases as β increases and as E 2+ decreases and that the theoretically predicted spreading of the dipole strength is confirmed by our experimental results. As to the characteristic behaviour of the GDR above its peak value at E 0, we come to the conclusion that the actual state of the art in ( γ, xn) research does not allow one to make an unambiguous choice between isospin splitting or electric quadrupole absorption. Finally the numerical evaluations of the different sum rules are given and some empirical results concerning the average energy of the GDR as a function of A are also presented.

Effects of Molecular Interactions on Coherent Electric Quadrupole Radiation Processes

The theory of the line shape in coherent electric quadrupole absorption and emission processes involving $N$ interacting molecules is developed, both quantum mechanically and with the use of a classical model. The theory is applied to small clusters and to linear chains of molecules. As in the dipole case, the effects of the interaction include in general a splitting of each molecular transition line into a number of components, a shift of each component from the molecular transition frequency, and a broadening or narrowing of each component relative to the width of the molecular line.

On the interpretation of photonuclear angular distributions

Photonucleon angular distributions are calculated in the j− j coupling scheme for single-particle excitations. The electromagnetic interaction of the nucleus with the photon beam is treated in electric dipole and quadrupole absorption approximations. The general results allow the extraction of information about the one-particle-one-hole transition strengths from the experimentally-measured angular distributions. The importance of the coherent interference terms in the electric dipole cross section is discussed. It is shown that, except in special cases, the amount of electric quadrupole absorption involved in photoproton production can be estimated only to the nearest order of magnitude from the asymmetry about 90° in the angular distribution. The effects of inclusion of the spin-orbit force on the interpretation by Shoda of systematics in 1d-2s shell nuclei are described briefly.

Note on the electric quadrupole absorption in the nuclear photoreaction

Note on the electric quadrupole absorption in the nuclear photoreaction

Note on the electric quadrupole absorption in the nuclear photo-reaction

The behavior of the EQ absorption cross section in the « Giant resonance » region is discussed through the analysis of the angular distributions of emitted particles by using the direct interaction model. The difference between proton’s and neutron’s angular distributions is attributed to the difference between the effective charges of the proton and the neutron for EQ radiation. The excitation functions for the EQ absorption are computed for40A(γp)39Cl and59Co(γ p)58Fe. It is pointed out that the integrated cross sections for the EQ absorption are favorable to explain the feature of the angular distributions and the excitation curves have a peak near the maximum energy of the « Giant resonance ». The agreement between our results and the experiments for the angular distributions of the above reactions is good in part. On the whole, however, the ratio of the ED to the EQ absorption cross section is too small in comparison to that required from the experiments. The results of this model are closely discussed and the direction of the modification is also indicated.

Photoproduction of Neutral Pions in Hydrogen: Magnetic Analysis of Recoil Protons

The photoproduction of neutral pions from hydrogen has been studied by counting the recoil protons with a magnetic spectrometer and scintillation counters. The process has been studied between photon energies of 260 and 450 Mev and between center-of-momentum pion angles of 70\ifmmode^\circ\else\textdegree\fi{} and 153\ifmmode^\circ\else\textdegree\fi{}. The excitation functions show a resonance type shape with maxima at about 320 Mev. Angular distributions are analyzed in the form $A+Bcos\ensuremath{\theta}+C{cos}^{2}\ensuremath{\theta}$ in the center-of-momentum system. The coefficient $B$, which gives the front-back asymmetry, is small at all energies; and the ratio $\ensuremath{-}\frac{A}{C}$ is 1.22\ifmmode\pm\else\textpm\fi{}0.10 at all energies between 295 and 450 Mev. The maximum cross section at 90\ifmmode^\circ\else\textdegree\fi{} in the c.m. system is 26\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}30}$ ${\mathrm{cm}}^{2}$/steradian for 320-Mev photons. The total cross section divided by the square of the c.m. photon wavelength has a maximum near 340 Mev, and drops by nearly a factor of two at 450 Mev. These results are consistent with magnetic dipole and electric quadrupole absorption leading to a resonant state of the pion-nucleon system of angular momentum $\frac{3}{2}$ and isotopic spin $\frac{3}{2}$.

Electrodisintegration ofCu63,Zn64,Ag109, andTa181

The ratio of the ($\ensuremath{\gamma}, n$) photodisintegration cross section to the ($e, {e}^{\ensuremath{'}}n$) electrodisintegration cross section for the isotopes ${\mathrm{Cu}}^{63}$, ${\mathrm{Zn}}^{64}$, ${\mathrm{Ag}}^{109}$, and ${\mathrm{Ta}}^{181}$ was measured for electron energies of 24 to 35 Mev. This ratio was found to decrease with energy in contrast with the Weizs\"acker-Williams approximation which predicts a constant ratio. However, the Weizs\"acker-Williams method does yield a result which is of the right order of magnitude for Cu, Zn, and Ag and which is within a factor of two of the observed value of Ta.Assuming approximately one-half of the total photon absorption of nuclei to be attributed to the ($\ensuremath{\gamma}, n$) reaction, then comparison of the experimental results for Cu, Zn, and Ag with calculations of Blair is consistent with the suggestion of Bethe and Levinger that the main absorption mechanism of nuclei for photons is electric dipole with a contribution of \ensuremath{\sim}6 percent electric quadrupole absorption. However, for Ta no simple correlation between experiment and theory was found. This is attributed to a failure of the Born approximation used in the Blair calculations.