Angular Distribution Parameters Research Articles

Quadrupole Effects in the Photoionisation of Sodium 3s in the Vicinity of the Dipole Cooper Minimum

A procedure to obtain relativistic expressions for photoionisation angular distribution parameters using the helicity formulation is discussed for open-shell atoms. Electric dipole and quadrupole transition matrix elements were considered in the present work, to study the photoionisation dynamics of the 3s electron of the sodium atom in the vicinity of the dipole Cooper minimum. We studied dipole–quadrupole interference effects on the photoelectron angular distribution in the region of the dipole Cooper minimum. Interference with quadrupole transitions was found to alter the photoelectron angular distribution, even at rather low photon energies. The initial ground and final ionised state discrete wavefunctions of the atom were obtained in the present work using GRASP, and we employed RATIP with discrete wavefunctions, to construct continuum wavefunctions and to calculate transition amplitudes, total cross-sections and angular distribution asymmetry parameters.

Near-threshold Cooper minimum in the photoionisation of the 2p subshell of sodium atom and its impact on the angular distribution parameter

The present work reports the photoionisation studies of 2p subshell of Na atom, just above the threshold region. The calculations are performed in the framework of multiconfiguration Dirac–Hartree–Fock method (MCDHF). It unravels the effect of 3d orbital on the final state leading to the appearance of Cooper minimum (CM) in the region close to the threshold. Further, the impact of this CM on the angular distribution parameter is studied. It is found that CM not only modifies the cross section profile but also makes dramatic changes in the angular distribution.

Angular distribution parameters in two-photon double ionization of helium beyond the dipole approximation

We study nondipole effects in the two-photon double ionization of helium by solving the full-dimensional time-dependent Schr\"odinger equation (TDSE). The angular distributions of the photoelectrons in TDSE calculations are parametrized by several angular distribution parameters. The electron correlation effects are revealed and discussed by analyzing angular distribution parameters of the photoelectrons. Compared with the linearly polarized laser, the values of dipole angular parameters for circularly polarized laser pulses in the nonsequential double-ionization regime are closer to the pure dipole emission of the one-photon single ionization, which indicates a weaker electron correlation for circular pulses. For the nondipole angular parameters, in the sequential double-ionization regime, we find that the parameters show peak structures from the sequential ionization channel over the energy sharing between two electrons and these peak positions are slightly shifted by the electron correlation. In general, due to the nondipole effects, the angular distributions of photoelectrons are shifted towards the direction of laser propagation, due to the transfer of the photon linear momentum.

Photoelectron circular dichroism of O 1s-photoelectrons of uniaxially oriented trifluoromethyloxirane: energy dependence and sensitivity to molecular configuration.

The photoelectron circular dichroism (PECD) of the O 1s-photoelectrons of trifluoromethyloxirane (TFMOx) is studied experimentally and theoretically for different photoelectron kinetic energies. The experiments were performed employing circularly polarized synchrotron radiation and coincident electron and fragment ion detection using cold target recoil ion momentum spectroscopy. The corresponding calculations were performed by means of the single center method within the relaxed-core Hartree-Fock approximation. We concentrate on the energy dependence of the differential PECD of uniaxially oriented TFMOx molecules, which is accessible through the employed coincident detection. We also compare the results for the differential PECD of TFMOx to those obtained for the equivalent fragmentation channel and similar photoelectron kinetic energy of methyloxirane (MOx), studied in our previous work. Thereby, we investigate the influence of the substitution of the methyl group by the trifluoromethyl group at the chiral center on the molecular chiral response. Finally, the presently obtained angular distribution parameters are compared to those available in the literature.

Estimation of the influence of elastic neutron scattering anisotropy on the integral parameters of the model experiment

For the vast majority of isotopes presented in modern evaluated data libraries, the quality of description of elastic neutron scattering anisotropy is difficult to assess due to the lack of critical experiments that are sensitive to these data. This results in a large variation in these data, due to both the difference in the models used in the estimation, and the smoothing of the resonance peculiarities in representation of the energy dependence in the evaluated data files. This work estimates the effect of anisotropy of elastically scattered neutrons based on the model of a critical assembly with a reflector from the tested isotope. Direct estimates of the angular distributions in the evaluated data libraries were compared with the angular distributions, which were reconstructed from the resonance parameters by using Blatt-Biedenharn formula. The thickness of the reflector at which an assembly model became critical is used as a comparison value. The obtained integral characteristics of the elastic scattering anisotropy data, together with the performed comparisons of the detailed dependences of the angular distribution parameters, can serve as a basis for setting tasks to improve the quality of the evaluated data.

Photoionization of the I 4d and valence orbitals of methyl iodide

The photoabsorption and photoionization dynamics of the I 4d and valence orbitals in methyl iodide have been studied both experimentally and theoretically. Synchrotron radiation has been employed to measure the total ion yield in the vicinity of the I 4d ionization thresholds. The observed structure, due to excitations into Rydberg or valence states, has been assigned using transition energies and relative intensities computed with time-dependent density functional theory within the Tamm–Dancoff approximation. Photoelectron spectra, recorded with plane polarized radiation in two polarization geometries, have allowed the effect of autoionization on the valence electron angular distributions to be investigated. The spectra obtained at photon energies of 50.62 and 52.34 eV, coinciding respectively with the I 4d5/2 → σ* and 4d3/2 → σ* transitions, reveal, in addition to valence shell photoelectron bands, features not associated with simple photoionization of the parent molecule. High resolution photoelectron spectra of the I 4d main-lines display structure resulting from spin–orbit coupling and molecular field splitting. The binding energies of the five states contributing to the (I 4d)−1 ionization have been determined. The iodine (in CH3I) N45VV Auger spectrum has been measured and the observed structure has been assigned using the core hole binding energies derived in the present work together with established ionization energies of the doubly charged ion. The experimentally determined Auger electron angular distributions have been discussed in relation to the theoretical angular distribution parameter characterizing the spatial alignment of molecular axes in the (I 4d)−1 state.

Dirac–Fock photoionization parameters for HAXPES applications, Part II: Inner atomic shells

Presented here are the photoionization cross sections and parameters of the photoelectron angular distribution for inner atomic subshells with binding energies beyond 1.5 keV in the photon energy range from 2 keV to 12 keV. The calculations are an extension of our previous paper containing the photoionization parameters for comparatively outer shells with binding energies lower than 1.5 keV (Trzhaskovskaya and Yarzhemsky, 2018). The calculations are intended for use in the experimental HAXPES spectroscopy investigations. The up-to-date HAXPES activity tends to increase the photon energy to investigate the deep core levels resulting in a necessity of theoretical consideration of photoionization parameters for inner atomic shells. Our relativistic calculations have been performed by the Dirac–Fock method. The photoionization cross sections have been found including all multipoles of the radiative field while the photoelectron angular distribution parameters have been obtained in the quadrupole approximation. The effect of the hole resulting in the atomic subshell after photoionization has been taken into account using the frozen orbital model.

Interchannel mixing in the K-shell photoionization of CH4

Rearrangement of the electron shells accompanying inner-shell photoionization of the CH4 molecule is studied theoretically. For this purpose, the K-shell photoionization cross section σ1s (ω) and the respective photoelectron angular distribution (PAD) parameter βe1s(ω) are computed in different approximations using the single center method. It is obtained that a strong mixing of the partial ionization channels in the vicinity of the 1s ionization threshold, caused by the the non-spherical part of the molecular potential, results in a qualitative difference between the electronic rearrangement effects in molecules, as compared to atoms.

Lepton angular distributions of fixed-target Drell-Yan experiments in perturbative QCD and a geometric approach

The lepton angular distributions of the Drell-Yan process in fixed-target experiments are investigated by NLO and NNLO perturbative QCD. We present the calculated angular parameters $\lambda$, $\mu$, $\nu$ and the degree of violation of the Lam-Tung relation, $1-\lambda-2\nu$, for the NA10, E615 and E866 experiments. Predictions for the ongoing COMPASS and SeaQuest experiments are also presented. The transverse momentum ($q_T$) distributions of $\lambda$ and $\nu$ show a clear dependence on the dimuon mass ($Q$) while those of $\mu$ have a strong rapidity ($x_F$) dependence. Furthermore, $\lambda$ and $\nu$ are found to scale with $q_T/Q$. These salient features could be qualitatively understood by a geometric approach where the lepton angular distribution parameters are expressed in terms of the polar and azimuthal angles of the "natural axis" in the dilepton rest frame.

Many-electron character of two-photon above-threshold ionization of Ar

The absolute generalized cross sections and angular distribution parameters of photoelectrons for the two-photon above threshold $3p$-ionization of Ar were calculated in the exciting photon energy range from 15.76 to 36 eV. The correlation function technique developed earlier was extended for the case when an intermediate-state function is of a continuum-type. We show that two-photon ionization of Ar near the $3p^{4}$ threshold to a large extent is determined by the $(3p\dashrightarrow\varepsilon d)^{2}$ two-photon absorption via the giant resonance. This many-electron correlation causes (i) an increase of the photoionization cross sections by more than a factor of 3; (ii) the appearance of resonances in the exciting-photon energy range of the doubly-excited states. The predictions are supported by a good agreement between length and velocity results obtained after taking into account of the higher-order perturbation theory corrections.

Relativistic photoionization of H-isoelectronic series including plasma shielding effects

With plasma shielding effects of the Debye-H\"uckel model, we investigate the relativistic photoionization processes of H, Nb$^{40+}$ and Pb$^{81+}$ plasmas in the H-isoelectronic series. The shielded nuclear potential of Yukawa-type experienced by the electron is parameterized by Debye-length $D$. To account for relativistic effects non- perturbatively, we solve the Dirac equation for the bound as well as continuum wavefunctions. Contributions from multipole fields are calculated for high incident photon energies, while the angular distribution and spin polarization parameters of photoelectrons are provided in the electric-dipole approximation. Our results of photoionization cross sections for the H plasma agree with other available theoretical calculations. The interplay between the relativistic and plasma shielding effects on the photoionization parameters is also studied. \keywords{Photoionization, Multipole effect, Debye plasma, Hydrogen atom, Hydrogen-like ions

Calculations of photoionization and radiative recombination in warm dense plasmas by average-atom method

Peculiarities of photoionization and radiative recombination of ions in warm dense plasmas are studied with the average-atom model using the Dirac-Slater electron wave functions. Relativistic calculations of the photoionization and radiative recombination cross sections as well as the quadrupole photoelectron angular distribution parameters were performed for various shells of the oxygen, argon, iron, and germanium ions occurring in astrophysical and laboratory plasmas. When the results are compared with calculations for relevant free ions, it is apparent that taking into account the plasmas temperature and density in the average-atom approach affect the behavior and magnitude of the photoionization and radiative recombination cross sections as well as of angular parameters at photoelectron energies up to ∼ 1000 eV. In particular, the cross sections and angular parameters obtained with the average-atom model are demonstrated to oscillate distinctly at photoelectron energies ≲ 100 eV. The occurrence of the oscillations is shown to be associated with a behavior of the continuum function normalization factor in the average-atom potential.

Photoelectron angular distributions from rotationally resolved autoionizing states of N2

The single-photon, photoelectron-photoion coincidence spectrum of N2 has been recorded at high (∼1.5 cm-1) resolution in the region between the N2+ X Σg2+, v+ = 0 and 1 ionization thresholds by using a double-imaging spectrometer and intense vacuum-ultraviolet light from the Synchrotron SOLEIL. This approach provides the relative photoionization cross section, the photoelectron energy distribution, and the photoelectron angular distribution as a function of photon energy. The region of interest contains autoionizing valence states, vibrationally autoionizing Rydberg states converging to vibrationally excited levels of the N2+ X Σg2+ ground state, and electronically autoionizing states converging to the N2+A2Π and B 2Σu+ states. The wavelength resolution is sufficient to resolve rotational structure in the autoionizing states, but the electron energy resolution is insufficient to resolve rotational structure in the photoion spectrum. A simplified approach based on multichannel quantum defect theory is used to predict the photoelectron angular distribution parameters, β, and the results are in reasonably good agreement with experiment.

Rotational Magnetization Lag-Angle Plots Using the Anisotropic Stoner–Wohlfarth Model

A numerical implementation of the classical Stoner-Wohlfarth (SW) model to simulate the magnetization angle of an assembly of SW particles with an effective axis of anisotropy under a rotating applied field is presented. Using an angular distribution for the angle each SW particle is making with the medium's reference axis, the proposed model successfully simulated lag-angle plots exhibiting the same rotational magnetization behavior measured for different ellipsoidally magnetizable media in the literature. The developed algorithm provides a simple tool for rotational-energy-loss calculations, preserves the physical intuition of the classical SW model, and is computationally faster compared to the Preisach-Stoner-Wohlfarth models. The effect of the angular distribution parameters on the switching transition angle and the algorithm's potential for modeling additional anisotropies through using different angular distributions are discussed.

Photoionization of atomic Ba in the region of the excitations

We investigate the angular distribution parameters and partial photoionization cross sections of the atomic barium mainline and the , and satellites in the region of the excitations. Our measurements cover the photon energy range from 19.0 eV to 23.0 eV. They are in good qualitative agreement with early experimental investigations of these partial cross sections but were recorded with a significantly improved monochromator resolution detailing the complicated resonance structure in this energy regime. The angular distribution measurements reported here are a significant improvement over the only other angular distribution measurement to date in this resonance region.

Relativistic, correlation, and polarization effects in two-photon photoionization of Xe

Two-photon ionization of xenon was investigated theoretically for exciting-photon energies from 6.7 to 11.5 eV, which results in the ionization of Xe between $5{p}_{1/2}$ (13.43 eV) and $5s$ (23.40 eV) thresholds. We describe the extension of a previously developed computational technique for the inclusion of relativistic effects to calculate energies of intermediate resonance state and cross sections for two-photon ionization. Reasonable consistency of cross sections calculated in length and velocity form was obtained only after considering many-electron correlations. Agreement between calculated and measured resonance energies is found when core polarization was additionally included in the calculations. The presently computed two-photon photoionization cross sections of Xe are compared with Ar cross sections in our previous work. Photoelectron angular distribution parameters calculated here indicate that intermediated resonances strongly influence photoelectron angular distribution of Xe.

Dirac–Fock photoionization parameters for HAXPES applications

Presented here are the photoionization cross sections and parameters of the photoelectron angular distribution for atomic subshells with binding energies lower than 1.5 keV of all elements with 1≤Z≤100 in the photon energy range 1.5–10 keV. The calculations were performed in an effort to provide handy theoretical data for experimental studies by hard X-ray photoelectron spectroscopy (HAXPES). We used the relativistic treatment of atomic photoeffect and the Dirac–Fock method with proper consideration of the electron exchange for computing the electron wave functions. The photoionization cross sections were determined including all multipoles of the radiative field while the photoelectron angular distribution parameters were obtained within the quadrupole approximation. The effect of the hole resulting in the atomic subshell after photoionization was taken into account by the use of the frozen orbital model.

Study on angular variation of cosmic ray secondary particles with atmospheric depth using CORSIKA code

The distribution of the secondary cosmic ray charged particles in the atmosphere as a function of zenith angle of the primary particle depends on various factors such as atmospheric depth, latitude and longitude of the place of observation and possibly other atmospheric conditions. This work is focussed on the investigation of atmospheric attenuation of an Extensive Air Shower using the zenith angle distribution of the secondary charged particles, at different atmospheric depths for pure primary compositions (gamma, proton and iron nucleus) and mixed compositions employing the Monte Carlo Simulation code CORSIKA (versions 6.990 and 7.3500) in the energy range 10 TeV–1 PeV. The secondary charged particles in different zenith angle bins are fitted with a differential distribution dN sp /dθ = A(X)sinθcos n(X)θ, where the power index n(X) is a function of atmospheric depth X. For a given zenith angle θ, the frequency of the showers with secondary charged particle intensity higher than a threshold is also fitted with a relation F(θ,X0) = F(0,X0)exp[−X0(secθ − 1)/λ], where X0 is the vertical atmospheric depth and λ is the attenuation length. Further, the angular distribution parameter n(X) and attenuation co-efficients (λ) from our simulation result for different primaries are compared with available experimental data.

Theoretical calculation of the photoelectron angular distribution of neon

The general formula of the angular distribution of photoelectron is derived by using the density matrix theory and Racah algebra method. For comparing with the experimental data, the general formula in this paper is matched to the parametric formula and the non-dipole parameters of the photoelectron angular distribution associated with the terms of the second order for both unpolarized and polarized incident light are given explicitly. From the formula of these parameters we can see that the contribution to the non-dipole parameter is from the interference between dipole amplitude and multipole amplitude. And then, the relativistic calculation program for photoelectron angular distribution is further developed with the help of the program packages GRASP2K and RATIP which are based on the multi-configuration Dirac-Fock method. By using this program, the dipole and non-dipole angular-distribution parameters for neon 2s and 2p photoelectrons are calculated concretely. The good agreement between the results of this paper and the available theoretical data is obtained in a 50-5000 eV photoelectron-energy range studied. On this basis, the angular photoelectron distributions for neon 2s and 2p are calculated with and without considering the second non-dipole terms at the photoelectron energy E=600 eV and E=5000 eV, respectively. Special attention is paid to the effects of the polarization property of incident light and the non-dipole terms of photo-electron interaction on the angular distribution of photoelectrons. The results show that 1) the dipole and non-dipole parameters of the photoelectron angular distribution are sensitive to the ionized electron orbital, it can bring out considerable diversities among the photoelectron angular distributions of the different shells; 2) non-dipole effects make the photoelectron forward distribution in the direction of incident light, the polarization property of incident light will strengthen the asymmetric distribution of photoelectrons.

Dynamics of the C1s→π*excitation and decay inCO2probed by vibrationally and angularly resolved Auger spectroscopy

Participator resonant Auger decay spectra populating the $X, A, B$, and $C$ states of ${\mathrm{CO}}_{2}{}^{+}$ are recorded with angular and vibrational resolution for selected photon energies in the vicinity of the C $1s\ensuremath{\rightarrow}{\ensuremath{\pi}}^{*}$ resonance of ${\mathrm{CO}}_{2}$ using a narrow photon bandwidth and a high-resolution electron spectrometer. The measured electron spectra and the corresponding angular distribution parameters exhibit significant changes as functions of the photon energy across the resonance and with respect to the vibrational sublevels of a final ionic state. The measured spectra are interpreted by ab initio electronic structure and nuclear dynamics calculations which attribute observed variations to the effects of lifetime vibrational interference and of electronic state interference between the direct ionization amplitude and the resonant amplitudes for the excitation and decay of two overlapping resonant states of different symmetry. The present results provide deeper insight into the femtosecond relaxation dynamics of the core-excited ${\mathrm{CO}}_{2}$, which is not achievable with lower resolution, angle-averaged measurements.