Calculation of the photoionization cross sections for the ions of the rubidium isoelectronic sequence by the Dirac-Fock method

The photoionization cross sections for the ground and some excited states of 11 ions of the rubidium isoelectronic sequence from Rb through Ag¹⁰⁺ are calculated by the relativistic Dirac-Fock self-consistent field method. The energy dependence of the photoionization cross sections and the changes in the threshold values along the isoelectronic sequence are considered. The influence of the exchange effect and the choice of gauge on the calculated values of photoionization cross sections is examined. For practical use, the calculated cross sections are approximated by an analytical expression. Along with the total photoionization cross sections, the asymmetry parameter in the angular distribution of photoelectrons and the degree of their polarization are also calculated.     

Effect of relativistic many-electron interactions on photoelectron partial wave probabilities

We obtain relative cross sections for the production of photoelectrons with specific angular momentum quantum numbers. These cross sections are obtained from the polarization analysis of the visible fluorescence of ions produced when circularly polarized vacuum ultraviolet radiation photoionizes ground state Ar. The ratio of cross sections for the production of photoelectrons with the same orbital angular momentum but different total angular momenta shows strong deviations from the statistical ratio, demonstrating the importance of relativistic interactions in many-electron photoionization dynamics.     

Experimental verification of quadrupole-dipole interference in spin-resolved photoionization

We have measured the spin polarization of Xe (4p)(-1) photoelectrons after ionization with circularly polarized light at photon energies close to the ionization threshold where a resonant enhancement of quadrupole transitions has recently been predicted. At a reaction angle of 90 degrees a nonvanishing longitudinal spin polarization component of about 4% clearly indicates a quadrupole contribution to the photoexcitation. This is the first experimental evidence for the influence of nondipole transitions on the photoionization process at excitation energies much below 1 keV in an observable other than the intensity angular distribution.     

Spectroscopy of He–Ne afterglow plasma

Implementation of promising control schemes for the intensity and position of X-ray-laser beams with a photon energy up to several tens of kiloelectronvolts requires knowledge of the angular dependence of cross sections for photoionization of noble gas atoms by hard photons. Estimates of quadrupole corrections to the cross section for photoionization of a Kr atom by X-ray photons with an energy of about 25 keV are reported in this paper. An analytic expression for the cross section of the process is parameterized in a compact form convenient for analyzing angular distributions with an arbitrary polarization of a photon beam.     

The scattering of partially polarized light by oriented atoms

A compact expression is derived for the cross section of scattering of arbitrarily polarized light by oriented atomic systems, in which the dependence on the geometric parameters and on the Stokes parameters preassigning the state of partial polarization of incident radiation is explicitly separated. It is found that the cross section of any photoprocess accompanied by photon absorption (stimulated emission) contains the sum of the products of the circular and linear dichroisms of the process by the respective Stokes parameters. The effect of the atomic orientation and of the dissipation of light energy on the polarization singularities and angular distribution of scattered light is investigated. In particular, it is demonstrated that, in the case of an open dissipation channel, the angular distribution remains dependent on the atomic orientation even in the case of zero degree of circular polarization of scattered radiation.     

Double photoionization of rotating linear molecules

This communication presents a theoretical study of the angular distribution of one or both of the two electrons emitted in one-photon, one-step double ionization of a linear molecule. Experiments which do or do not detect spin of the photoelectrons have been considered. Effects of molecular rotation on double photoionization have been studied in both Hund's coupling schemes (a) and (b) by using parity-adapted states. Selection rules obtained in this paper are very different from those derived earlier for single photoionization and for Auger decay following the absorption of a photon in a rotating linear molecule. It is shown that complete specification of the spin-unresolved and of spin-resolved angular distributions of both photoelectrons require, respectively, three and seven parameters which depend, among other things, on their energies as well as directions of emission. The approach developed in this paper has been used to analyze spin-unresolved double photoionization in the shell of the molecule. The angular distribution is quite different depending on whether or not molecular rotation has been taken into account. Also, it is found to change significantly for different rotational transitions. Effects of electron-electron correlation are clearly manifested even in non-coincident, both rotationally resolved--as well as unresolved--double photoionization. Received: 7 August 1998     

The Photoionization of Atomic Hydrogen in an Intense Circularly Polarized Laser Field

We calculate nonperturbatively the irfluence of a strong circularly polarized laser beam on the hydrogen atom energy levels by making use of the time-independent formalism proposed by one of us. The photoionization cross section of the hydrogen atom irradiated by this laser beam and the angular distribution of photoelectrons are also calculated. From the numerical results we clearly see the intensity dependence of the whole photoionization process,including the intensity dependence of the photoelectron energies.     

The Photoionization of Atomic Hydrogen in an Intense Circularly Polarized Laser Field

We calculate nonperturbatively the irfluence of a strong circularly polarized laser beam on the hydrogen atom energy levels by making use of the time-independent formalism proposed by one of us. The photoionization cross section of the hydrogen atom irradiated by this laser beam and the angular distribution of photoelectrons are also calculated. From the numerical results we clearly see the intensity dependence of the whole photoionization process,including the intensity dependence of the photoelectron energies.     

Sudden interchannel interaction in the Tl 6p ionization above the 5d threshold

The linear magnetic dichroism in the angular distribution of Tl 5d and 6p photoelectrons and their dynamical spin polarization have been measured between hnu = 30 and 50 eV. In contrast to the Xe 5p photoionization at the 4d threshold, our results show that above the Tl 5d threshold strong interchannel coupling effects induce a sudden increase in the asymptotic phase difference of the s and d waves for the Tl 6p ionization. This shows that the valence excitation is different for resonant (Xe 4d) and nonresonant (Tl 5d) excitation from subvalence shells.     

A simple analytical model of the angular momentum transformation in strongly focused light beams

A ray-optics model is proposed to describe the vector beam transformation in a strongly focusing optical system. In contrast to usual approaches based on the focused field distribution near the focal plane, we use the beam pattern formed immediately after the exit aperture. In this cross section, details of the output field distribution are of minor physical interest but proper allowance is made for transformation of the beam polarization state. This enables the spin and orbital angular momentum representations to be obtained, which are valid for any cross section of the transformed beam. Simple analytical results are available for a transversely homogeneous, circularly polarized incident beam confined by a circular aperture. Variations of the spin and orbital angular momenta of the output beam with change of the focusing strength are analyzed. The analytical results are in good qualitative and reasonable quantitative agreement with the results of numerical calculations performed for the Gaussian and Laguerre-Gaussian beams. The model supplies an efficient and physically transparent means for qualitative analysis of the spin-to-orbital angular momentum conversion. It can be generalized to incident beams with complex spatial and polarization structure.     

Study of parameters of the angular distribution of photoelectrons in the relativistic quadrupole approximation

Relativistic calculations of differential cross sections for photoionization are performed and the behavior of parameters β, γ, and δ describing the angular distribution of photoelectrons in the quadrupole approximation is studied. The calculations were carried out for a number of atoms for kinetic energies of photoelectrons E _k ≈50 000 eV. The electronic wave functions of the initial and final states are calculated by the Dirac-Fock method taking into account the exchange interaction and a hole produced in the atomic shell upon photoionization. The dependence of parameters β, γ, and δ on the physical assumptions used in the calculations is studied. Comparison with nonrelativistic calculations shows that relativistic values of the nondipole parameters γ and δ can be substantially different even at low energies of photoelectrons. Our calculations of nondipole parameters γ and δ for the 2p-shell of the Kr atom better agree with the recent experimental data than nonrelativistic calculations performed earlier taking approximately into account the exchange interaction and neglecting a hole.     

Al原子K壳层光电离的理论研究

基于多组态Dirac-Fock理论方法及其相应的GRASP2K和修改后的RATIP2012程序包,计算了极化光子入射Al原子K壳层光电离截面,并利用最新发展的RPI-E计算程序研究了K壳层光电子角分布,重点讨论了辐射场的非偶极项对光电离截面和光电子角分布的影响.结果表明,在入射光子5000 e V能量范围内,辐射场的非偶极效应对光电离总截面的影响可以忽略不计.随着入射光子能量的增加,辐射场的非偶极效应对光电子角分布的影响越来越大,入射光子能量在5000 eV,一级非偶极参数γ的数值达到1.5.     

Angular electron distribution in photoionization of spatially oriented linear molecules for different geometries of the experiment

Starting from the general expression for the angular distribution of electrons produced through photoionization of spatially oriented molecules, simpler formulas for photoionization of linear molecules with an inversion center found in the Σ state, accompanied by the production of molecular ions in Σ and Π states, are obtained. For different geometric arrangements of the vectors determining the angular distribution, simple formulas are derived and their comparative analysis is made. It is shown that one can determine for different conditions of the experimental measurement of the angular dependences of ejected electrons the values of matrix elements and phase differences and separate the processes responsible for the production of ions in states with different symmetries.     

Spin-orbit-induced photoelectron spin polarization in angle-resolved photoemission from both atomic and condensed matter targets

The existence of highly spin polarized photoelectrons emitted from non-magnetic solids as well as from unpolarized atoms and molecules has been found to be very common in many studies over the past 40 years. This so-called Fano effect is based upon the influence of the spin-orbit interaction in the photoionization or the photoemission process. In a non-angle-resolved photoemission experiment, circularly polarized radiation has to be used to create spin polarized photoelectrons, while in angle-resolved photoemission even unpolarized or linearly polarized radiation is sufficient to get a high spin polarization. In past years the Rashba effect has become very important in the angle-resolved photoemission of solid surfaces, also with an observed high photoelectron spin polarization. It is the purpose of the present topical review to cross-compare the spin polarization experimentally found in angle-resolved photoelectron emission spectroscopy of condensed matter with that of free atoms, to compare it with the Rashba effect and topological insulators to describe the influence and the importance of the spin-orbit interaction and to show and disentangle the matrix element and phase shift effects therein.The relationship between the energy dispersion of these phase shifts and the emission delay of photoelectron emission in attosecond-resolved photoemission is also discussed. Furthermore the influence of chiral structures of the photo-effect target on the spin polarization, the interferences of different spin components in coherent superpositions in photoemission and a cross-comparison of spin polarization in photoemission from non-magnetic solids with XMCD on magnetic materials are presented; these are all based upon the influence of the spin-orbit interaction in angle-resolved photoemission.     

Second-order orientation effects in light scattering by polarized atoms

A compact expression is derived for the part of the cross section for light scattering by axisymmetrically polarized atomic systems proportional to the third-rank state multipole. The effect of the second-order orientation determined by this state multipole on the polarization and angular distribution of the scattered light is studied. The polarization of the incident light can be arbitrary and is specified by the Stokes parameters. A number of orientation effects in the scattering process are shown to be induced precisely by the second-order orientation. In particular, when nonpolarized light is scattered by an oriented atom, the scattering intensity in the perpendicular direction depends on the second-order orientation alone. The second-order orientation also preserves circular dichroism in the linear polarization of the forward-and back-scattered light.     

Interferences from fast electron emission in molecular photoionization

We present a theoretical study of fast-electron emission produced in H2 and H2+ photoionization. We show that, when the electron wave length is comparable to the molecular size, the electron angular distributions arising from fixed-in-space molecules exhibit pronounced interference effects that critically depend on orientation and energy sharing between electrons and nuclei. In particular, for molecules oriented parallel to the polarization direction, the angular patterns reveal a complex nodal structure, while for molecules oriented perpendicularly, typical Young's double-slit interferences are observed. These patterns change dramatically as the molecule vibrates.     

Influence of nondipolar effects on the photoelectron angular distribution upon photoionization of 2p and 3d atomic shells

Relativistic calculations of the angular distribution of photoelectrons upon photoionization of 2p and 3d shells in the range of photoelectron energies from 1 to 10 keV are carried out for unpolarized and linearly polarized radiation. An exact expression for the angular distribution of photoelectrons that takes into account nondipolar terms of the order of O[(kr)²] (k is the photon energy and r is the radius of the ionized shell) is obtained in the case of unpolarized radiation. It is shown that the contribution of the O[(kr)²] terms to the differential cross section can be considerable, reaching 24% at the maximum energy considered. Accounting for such terms in the calculation of the ratio of differential cross sections, which is experimentally measured at a certain geometry of angles in the case of linearly polarized radiation, can change this ratio twofold. The parameters of the angular distribution, which are necessary for the conduction of a quantitative x-ray photoelectron analysis, are given for the 2p _1/2 and 2p _3/2 shells of elements with 11≤Z≤29 and for the 3d _3/2 and 3d _5/2 shells of elements with 30≤Z≤54.     

Ionization of ytterbium atoms from an excited state

The cross sections of the photoionization and the electron impact-induced ionization of Yb atoms from the excited 6s6p(³ P ₁) state are numerically calculated. Matrix elements are computed in multielectron relativistic and nonrelativistic approximations with allowance for the superposition of configurations and a relaxation effect. The radial part of the electron wavefunction in a continuous spectrum is calculated using the solutions to one-configuration Hartree-Fock and Dirac-Fock equations. The cross sections calculated by a relativistic method are compared to those for a nonrelativistic approximation. The ratios of the radiation reduced matrix elements and the phase shifts of the wavefunctions of a continuous spectrum calculated for the 6p ɛs and 6p → ɛd transitions are compared to the values obtained by approximating the experimental dependences of the angular distribution of photoelectrons for the photoionization by ultraviolet radiation from an oriented excited state.     

Calculation of electron-spin polarization in photoemission from Au(110)

We have calculated the spin polarization of electrons photoemitted by circularly polarized light from Au(110). Results for the spin polarization of the angular resolved photoyield are given for clean and contaminated surfaces for photon energies ?Ω up to 10 eV. In addition we calculated the spectrum for energy resolved photoelectrons for $\text{?Ω = 8.5 eV}$. Our calculations demonstrate that from an analysis of the spin polarization of energy resolved photoelectrons detailed information on the electronic structure of solids follows.