Glory Effect Research Articles

Glory interference spectroscopy in Sr atom

Slow (meV) photoelectron imaging spectroscopy is employed in the experimental study of near-threshold photoionization of strontium atoms in the presence of an external static electric field. Specifically, the study is devoted to the glory effect, that is, the appearance of an intense peak at the center of the recorded photoelectron images, when dealing with m= 0 final ionized Stark states (m denoting the magnetic quantum number). This critical effect is formally identical to that encountered in classical scattering theory, where, for a nonzero value of the impact parameter, the zero-crossing of the deflection function leads to a divergent classical differential cross section. By recording the magnitude variation of this glory peak as a function of electron excitation energy, we observe that, besides the traces of classical origin, it also exhibits intense quantum interference and beating phenomena, above and below the zero-static-field ionization threshold. We study both, single- and two-photon ionization of Sr, thus enabling a comparison not only between the different excitation schemes, but also with an earlier work devoted to two-photon ionization of Mg atom by Kalaitzis et al (2020 Phys. Rev. A 102 033101). Our recordings are analyzed within the framework of the Harmin–Fano frame transformation Stark effect theory that is applied to both the hydrogen atom and a non-hydrogenic one simulating Sr. We discuss the various aspects of the recorded and calculated glory interference and beating structures and their ‘short time Fourier transforms’ and classify them as either atom-specific or atom independent. In particular, we verify the ‘universal’ connection between the glory oscillations above the zero-field threshold and the differences between the origin-to-detector times of flight corresponding to pairs of classical electron trajectories that end up to the image center.

Asymmetry in the atmosphere of the ultra-hot Jupiter WASP-76 b

Context. WASP-76 b has been a recurrent subject of study since the detection of a signature in high-resolution transit spectroscopy data indicating an asymmetry between the two limbs of the planet. The existence of this asymmetric signature has been confirmed by multiple studies, but its physical origin is still under debate. In addition, it contrasts with the absence of asymmetry reported in the infrared (IR) phase curve. Aims. We provide a more comprehensive dataset of WASP-76 b with the goal of drawing a complete view of the physical processes at work in this atmosphere. In particular, we attempt to reconcile visible high-resolution transit spectroscopy data and IR broadband phase curves. Methods. We gathered 3 phase curves, 20 occultations, and 6 transits for WASP-76 b in the visible with the CHEOPS space telescope. We also report the analysis of three unpublished sectors observed by the TESS space telescope (also in the visible), which represents 34 phase curves. Results. WASP-76 b displays an occultation of 260 ± 11 and 152 ± 10 ppm in TESS and CHEOPS bandpasses respectively. Depending on the composition assumed for the atmosphere and the data reduction used for the IR data, we derived geometric albedo estimates that range from 0.05 ± 0.023 to 0.146 ± 0.013 and from <0.13 to 0.189 ± 0.017 in the CHEOPS and TESS bandpasses, respectively. As expected from the IR phase curves, a low-order model of the phase curves does not yield any detectable asymmetry in the visible either. However, an empirical model allowing for sharper phase curve variations offers a hint of a flux excess before the occultation, with an amplitude of ~40 ppm, an orbital offset of ~ −30°, and a width of ~20º. We also constrained the orbital eccentricity of WASP-76 b to a value lower than 0.0067, with a 99.7% confidence level. This result contradicts earlier proposed scenarios aimed at explaining the asymmetry observed in high-resolution transit spectroscopy. Conclusions. In light of these findings, we hypothesise that WASP-76 b could have night-side clouds that extend predominantly towards its eastern limb. At this limb, the clouds would be associated with spherical droplets or spherically shaped aerosols of an unknown species, which would be responsible for a glory effect in the visible phase curves.

Scattering of electrons and positrons from aluminum isonuclear series

The current study investigates the scattering of electrons and positrons from aluminum isonuclear series within the framework of the Dirac relativistic partial wave analysis. For the neutral aluminum atoms, the scattering phenomena are described by employing a short-range complex optical potential. For the ionic series, on the other hand, this potential is supplemented by the Coulomb potential. The calculations are reported for the differential cross-section, total cross-section, integrated elastic cross-section, inelastic cross-section, momentum transfer cross-section, viscosity cross-section, and total ionization cross-section over the energy range 1 eV ≤ E i ≤ 1 MeV. The Sherman function S and spin asymmetry parameters T and U are also predicted for the same scattering systems over the same energy range. In addition, for the first time, we report a systematic study of the critical minima in the differential cross sections as well as the associated maximum spin polarization points in the Sherman function. We also compute the inelastic, elastic, momentum transfer, viscosity and total mean free paths for the aforesaid scattering systems. The Coulomb glory effect, the amplification of elastic backscattering of electrons from positive ions, is examined throughout the ionic series of aluminum. A comparison of our results to the reported theoretical and experimental studies reveals a good consistency over the compared energy range. The present theoretical method is thus expected to be useful for the fast generation of accurate cross-sections needed in many areas of science, technologies, and industries.

Forward Glory Effect Observed in Differential Cross Sections for the One-Electron Capture Process in Ne4+–He System at Ecm = 6.3 eV

Forward Glory Effect Observed in Differential Cross Sections for the One-Electron Capture Process in Ne⁴⁺–He System at <i>E</i>_cm = 6.3 eV

The coulomb glory effect in collisions of antiprotons with heavy ions

The Coulomb glory effect in the back scattering of antiprotons with energies of from 100 eV to 3 keV from a bare nucleus of uranium and from uranium ions with closed shells is considered in terms of nonrelativistic and relativistic quantum theory. The appearance of Coulomb glory in collisions with multiply charged ions is caused by nucleus charge screening by filled electron shells. In scattering from a bare nucleus, the effect appears because of the screening properties of the vacuum polarization potential.

The forward glory effect in the differential cross sections measured below Elab = 50 eV for the one-electron capture process in N5+–He collisions

A crossed-beam apparatus was used to measure the relative state-selective differential cross sections for the one-electron capture process in the N5+–He system from θlab = −3° to 21° at Elab = 27.5 and 47.5 eV. The main reaction channel was found to be N5+ (1s2 1S) + He → N4+ (1s23s 2S) + He+ + 16.8 eV. The differential cross section for this channel is pronounced at θcm = 0, and it shows another peak at a certain angle that depends on the collision energy. The O5+–He system at Elab = 47.5 eV was measured for comparison. The differential cross section for the main reaction channel O5+ (1s22s 2S) + He → O4+ (1s22s3p 1,3P) + He+ + 17 eV is zero at θcm = 0, and it shows only a single peak at θcm = 0.314 rad. The structures observed in the N5+–He system were analysed using the classical deflection function based on ab initio potentials. The peak observed at θcm = 0 is assigned to the forward glory effect and the second peak to the inelastic rainbow effect.

Tests of fundamental theories with heavy ions at low-energy regime

The current status of theoretical investigations of spectroscopic properties and fundamental interactions in highly charged ions is reviewed. Laying special attention on tests of quantum electrodynamics at strong fields recent progress in calculations of energy levels, hyperfine splitting and g factor values is reported. The parity nonconservation effect on the laser-induced \(2^3S_1-2^1S_0\) transition in heavy He-like ions is studied, which could serve as test scenario for the Standard Model in low-energy atomic physics. The Coulomb glory effect in collisions of antiprotons with heavy ions is considered. It is emphasized that observation of this effect in collisions of antiprotons with bare nuclei would exhibit the screening properties of the vacuum polarization potential. A new approach to the description of dynamic atomic processes in low-energy heavy-ion collisions is presented. As a first application of this approach, the charge transfer probabilities for the U91 + (1s) – U92 + collision are evaluated.

The Coulomb glory effect in collisions of antiprotons with heavy nuclei: relativistic theory

Collisions of antiprotons with bare uranium nuclei are studied for scattering angles near 180° in the framework of relativistic theory. The Coulomb glory phenomenon is investigated at antiproton energies in the range 100 eV–2.5 keV. The vacuum polarization effect and the anomalous magnetic moment of the antiproton are taken into account. Estimations of possible influence of such effects as radiative recombination and antiproton annihilation are given.

Cross sections for single electron capture in collisions of N2+ with He at low energies

The absolute cross sections of single electron capture during the collision of N2+ with He have been measured over the energy range 0.1-300 eV/u. From the plot showing the dependence of cross sections on energy, the following three remarkable observations can be made: (1) the cross sections exhibit an oscillatory structure below 1eV/u, (2) a bend in the cross sections appears at approximately 1 eV/u and (3) there is a dip in the cross sections at approximately 70 eV/u. The formation of an oscillatory structure is attributed to the glory effect. The bend in the cross sections occurs owing to the attractive potential part of a l2n state of quasimolecule NHe2+. The dip in the cross sections appears as a result of opening a new reaction path above 70eV/u. The glory effect can be observed for the first time on a total cross section even for slow ion-neutral collisions. The objective of this study is to explore the possibilities of providing a detailed explanation of energy dependence measurements in order to study reaction dynamics for a charge changing process.

Backward scattering of low-energy antiprotons by highly charged and neutral uranium: Coulomb glory

Collisions of antiprotons with He-, Ne-, Ni-like, bare, and neutral uranium are studied theoretically for scattering angles close to $180\ifmmode^\circ\else\textdegree\fi{}$ and antiproton energies in the interval from $100\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ to $10\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$. We investigate the Coulomb glory effect which is caused by a screening of the Coulomb potential of the nucleus and results in a prominent maximum of the differential cross section in the backward direction at some energies of the incident particle. We found that for larger numbers of electrons in the ion the effect becomes more pronounced and shifts to higher energies of the antiproton. On the other hand, a maximum of the differential cross section in the backward direction can also be found in the scattering of antiprotons on a bare uranium nucleus. The latter case can be regarded as a manifestation of the screening property of the vacuum-polarization potential in nonrelativistic collisions of heavy particles.

Radiative quenching and excitation of metastable states upon differential scattering of atoms: II. The He(11 S–21 S)-Ne molecule

The differential cross sections of radiative-collisional quenching (absorption) of a metastable state of a colliding atom are calculated for the first time. As a particular example, the reaction of quenching (excitation) of the metastable state He(21S) in collisions with Ne atoms in the ground state is considered. The calculations are performed for the thermal collisional energy E = 10−3 au for a wide range of radiation frequencies, including both wings and the center of the line of a forbidden atomic transition, and are based on the uniform quasi-classical approximation, which generalizes the Franck-Condon approximation to the case of an exponential dependence of the transition dipole moment on the internuclear distance, as well as to the case of nonintersecting terms. The calculated differential cross sections have an oscillating structure, which, for the blue wing of the forbidden spectral line, is interpreted as Stuckelberg oscillations. At a radiation frequency close to the frequency of the forbidden atomic transition, a sharp maximum in the differential cross section—the giant glory effect—is observed in the range of small scattering angles. This effect is shown to occur as a result of superimposition of the rainbowlike feature of the differential cross section on the glory feature.

Regge Oscillations in Integral Cross Sections for Proton Impact on Atomic Hydrogen

The integral cross sections for elastic scattering and spin exchange for proton impact on atomic hydrogen show several oscillations in the energy range 0.01-1.0 eV that cannot be associated with resonances or the glory effect. A complex angular momentum analysis using computed Regge trajectories shows that each peak of the oscillatory structure is predominantly associated with at most three trajectories. In this way, the peaks are related to the L=0 bound states of H+ 2. The complex angular momentum theory for integral cross sections that we introduce shows that such oscillations are a general feature of potential scattering.

Glory and thresholds effects in H+D 2 reactive angular scattering

We analyse H+D 2 reactive angular scattering using the S-matrix elements obtained by Aoiz et al. and Althorpe et al. Enhancement of small angle scattering in the v ′=3← v=0 H+D 2 delayed reaction is attributed to a glory effect caused by threshold resonances in the v=3 vibrationally adiabatic channel. The oscillatory structures in the reactive angular distributions are shown to be of nearside–farside (NP) origin and are likely to arise from capture in a number of relatively short-lived barrier Regge states at large angular momenta. Padé reconstruction of the reactive matrix element is discussed in detail.

Scattering ofscalar waves by rotating black holes

We study the scattering of massless scalar waves by a Kerr black hole byletting plane monochromatic waves impinge on the black hole. Wecalculate the relevant scattering phase-shifts using the Prüferphase-function method, which is computationally efficient and also reliablefor high frequencies and/or large values of the angular multipoleindices (l, m). We use the obtained phase-shifts and the partial-waveapproach to determine differential cross sections and deflectionfunctions. Results for off-axis scattering (waves incident alongdirections misaligned with the black hole's rotation axis) are obtained forthe first time. Inspection of the off-axis deflection functions reveals thesame scattering phenomena as in Schwarzschild scattering. In particular,the cross sections are dominated by the glory effect and the forward(Coulomb) divergence due to the long-range nature of the gravitationalfield. In the rotating case the overall diffraction pattern is`frame-dragged' and as a result the glory maximum is not observed in theexact backward direction. We discuss the physical reason for thisbehaviour, and explain it in terms of the distinction between prograde andretrograde motion in the Kerr gravitational field. Finally, we also discussthe possible influence of the so-called superradiance effect on thescattered waves.

Nuclear forward glory,σRandfN(0°)in the scattering of6Heby carbon

Using the generalized optical theorem for charged particles, the total reaction cross section ${\ensuremath{\sigma}}_{R}$ and the nuclear scattering amplitude ${f}_{N}$ at $0\ifmmode^\circ\else\textdegree\fi{}$ have been determined model independently for the first time in the ${}^{6}\mathrm{He}{+}^{12}\mathrm{C}$ system. A large fraction of ${\ensuremath{\sigma}}_{R}$ is accounted for by ${f}_{N}(0\ifmmode^\circ\else\textdegree\fi{})$ --- a manifestation of the nuclear forward glory effect. A comparison with the ${}^{6}\mathrm{Li}{+}^{12}\mathrm{C}$ system supports the prediction that the high break-up probability of ${}^{6}\mathrm{He}$ reduces the fraction of the total reaction cross section accounted for by the nuclear scattering amplitude at $0\ifmmode^\circ\else\textdegree\fi{}.$

Kinematical rainbow and elastic focusing effects in atom-surface scattering

In this work two general anomalous singularity effects in elastic surface diffraction are reported. First, a kinematical rainbow (KR) condition, a special case of the well-known rainbow singularity, is examined and shown to be a two-dimensional counterpart of the glory effect in gas-phase scattering. Second, an elastic focusing (EF) effect is presented as the elastic counterpart of a general effect called inelastic focusing recently observed in the inelastic scattering of He atoms from a NaCl(001) surface. Both effects occur under conditions in which the angular positions of the diffraction channels are degenerate in pairs. In the vicinity of the KR the coupling among diffraction channels is strongly rearranged and noticeable changes in the diffraction pattern intensities are expected, whereas the EF enhances the observed intensity of only the affected diffraction peak. As an illustration of these general phenomena in surface scattering, calculations are presented demonstrating that both of these new effects should be observable for He atom scattering from stepped metal surfaces.

Glory effect in pion-proton elastic scattering

A surface-wave model is presented for interpreting the large-angle peak in elastic π+p differential cross-section at momenta up to 70 GeV/c. One fits the angular distributions at various momenta. Furthermore, the fit parameters so found are in turn fitted by means of theoretical functions which reproduce their behaviour at varying momentum. In particular the model is able to reproduce quantitatively the behaviour, at varying momentum, of the «slope» of the backward differential cross-section.

Analysis ofπ±−C12elastic scattering

We present an analysis of ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{-}^{12}\mathrm{C}$ elastic scattering by using a phenomenological ansatz for the pure hadronic amplitude; in addition a careful treatment of Coulomb effects has turned out to be essential. The resulting phase shifts and inelasticity parameters show a smooth behavior in the entire energy region between ${T}_{\ensuremath{\pi}}=30$ and 230 MeV. The rapid increase of the differential cross sections at backward angles (${T}_{\ensuremath{\pi}}=162$ MeV) is discussed in terms of a semiclassical theory of the nuclear glory effect and is well reproduced by using additional information on analytic structure of the $\ensuremath{\pi}\ensuremath{-}^{12}\mathrm{C}$ elastic scattering amplitude in the complex $t$ plane.[NUCLEAR REACTIONS $^{12}\mathrm{C}({\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}},{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}})^{12}\mathrm{C}$, $E=30\ensuremath{-}226$ MeV.]

Backscattering of light from a water droplet: The glory effect

We discuss the theoretical attempts at explaining the glory effect and describe a simple setup that permits visualization of the glory ray.

Back-angle anomalies in elastic and inelastic scattering of16O

The elastic and inelastic scattering of 6O+28Si at ECM=35 MeV (over the angular range 20 degrees < theta <180 degrees ) has been analysed by the method of the parametrised smooth cut-off S matrix (S(l)) and the derivative relation of Austern and Blair for the single-phonon excitation mechanism. The dominant pole of S(l) (the nearest to the real axis) is allocated to the rainbow scattering region of the complex l plane. Agreement between theoretical and experimental results for the nuclear rainbow angle is obtained. These results indicate that the backward oscillation observed in the elastic scattering angular distribution cannot be identified with the glory effect or orbiting (spiral) phenomena. The reduced matrix element and deformation length are determined for the 2+, 1.78 MeV state in 28Si.