PHOTOELECTRON ANGULAR DISTRIBUTION PARAMETERS FOR ELEMENTS Z=1 TO Z=54 IN THE PHOTOELECTRON ENERGY RANGE 100–5000 eV

Abstract

Parameters of the angular distribution of photoelectrons along with the subshell photoionization cross sections calculated for all subshells of atoms with 1 ≤ Z ≤ 54 are presented in the Table for nine photoelectron energies in the range 100-5000 eV. Relativistic treatment of the photoeffect is used. The calculations have been performed within the quadrupole approximation with the central Dirac-Fock-Slater potential. The hole left by the emitted electron has been taken into account in the framework of the frozen orbital approximation. Applications of nondipolar parameters to photoelectron angular distribution in solids, to quantitative x-ray photoelectron spectroscopy analysis, and to the x-ray standing wave method are discussed. C INTRODUCTIONIn photoeffect studies it is common to consider the angular distribution of photoelectrons within the electric dipole approximation (see, for example, [1][2][3] and references given therein). In this case the differential photoionization cross section for circularly polarized and unpolarized photons can be written ascharacterized by the energy-and subshell-dependent asymmetry parameter β of the photoelectron angular distribution. Here σ i is the photoionization cross section for the ith atomic subshell, P 2 (cos θ ) is the second order Legendre polynomial, and θ is the angle between the vectors of photon (k) and photoelectron (p) propagation (Fig. 1).In keeping with Eq. (1), the currently available tables which may be used for estimation of the photoelectron angular distribution contain values of the photoionization cross sections σ i and of the dipole parameter β [3][4][5]. However, there exist many investigations [6][7][8][9][10][11][12][13][14][15][16][17] where the angular distribution has been shown to differ significantly from that calculated within the dipole approximation, even for low photoelectron kinetic energies just above the photoionization threshold. In [6][7][8][9][10][11] the influence of quadrupole terms on the angular distribution has been studied using a nonrelativistic treatment of the photoeffect. Relativistic calculations have been carried out for a number of atoms using the quadrupole approximation [14,15] as well as taking into account all multipoles of the radiation field [12,13]. The breakdown of the dipole approximation has also been demonstrated in recent experiments [18][19][20] where the photoionization of Ne, Ar, and Kr has been studied at photoelectron energies E ≤ 3000 eV. In Ref. [9], simple expressions have been presented which describe adequately the angular distribution in various cases of photon polarization by the use of two additional nondipolar parameters γ and δ along with the dipole parameter β. According to Ref. [9], the photoelectron angular distribution for circular polarized and unpolarized photons may be written asFor linearly polarized photons the angular distribution may be represented aswhere θ is the angle between the vector p and the photon polarization direction ε, the vector ε being coincident with the z axis; ϕ is ...

Hard X-ray photoelectron and X-ray absorption spectroscopy characterization of oxidized surfaces of iron sulfides

“…The VB spectra are dominated by non-bonding Fe 3d 6 orbital states in the vicinity of 2 eV below the Fermi level [5][6][7]. The relative intensity of this peak decreases with increasing the excitation energy owing to lower Fe 3d photoionization cross-section values [57]. The spectra from the chemically etched pyrite (lower panels) are quite similar to the abraded samples.…”

“…The spectra were acquired at photon energies from 2 keV to 6 keV and, in some cases, to 9 keV; the slit width was of 0.5 mm for all the excitation photon energies. Atomic ratios of elements (I i,h ) relative to S were calculated from the intensity area of the detail spectra for each energy (A i,h ) employing photoionization cross-sections ( i,h ) tabulated in [57,58] and the ones extrapolated for the higher energies, and taking into account IMFP ( (KE) i ) calculated for FeS 2 and Fe 9 S 10 employing TPP−2M formula [38] and analyzer's transmission function (T(KE) i ) [40][41][42] using following equation…”

Operando Analyses of Solar Fuels Light Absorbers and Catalysts

“…photoionization cross section on the electron energy [25,26] closer to the conduction band than the energy that is given by the doping level alone. In this case, electron accumulation occurs at the surface and, depending on the amount of negative polarization, a two-dimensional electron gas can be formed.…”

Enhanced electron correlations at theSrxCa1−xVO3surface

“…Indeed, this is reflected in theoretical tabulations of these cross-sections, which predict the Ca 4s, Sr 5s and V 4s cross-sections are between 13 and 21 times larger than the O 2p cross-section at 4 keV. 20 In order to more accurately assess the origin of the differences in the HAXPES spectra between CVO and SCVO, we turn to a more quantitative analysis, in which the relative photoionization cross-sections for each orbital are fitted to the experimental data, yielding approximate empirical relative cross-sections. The data are first corrected for inelastic scattering processes, leading to the Shirley-type background shown by the dashed line in Fig.…”

“…19 However, at such hard energies, there are several additional considerations. Most importantly, the cross section for photoionization drops off at higher energies, particularly for shallow binding energies at the valence band, 20 and practical instrument resolutions are poorer than at low energies. Additionally, the electron momentum distribution is focused into much tighter angles, meaning the coverage of the Brillouin zone of a typical HAXPES measurement is much broader, although recent technical advances have facilitated the momentum-resolved spectral function at hard x-ray energies.…”