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

Nikulin²,

J. Phys. B: At. Mol. Opt. Phys.

et al. 2001

Relativistic calculations of the parameters β,γ and δ of the photoelectron angular distribution have been carried out using the quadrupole approximation for a number of atoms at photoelectron energies up to 10 000 eV. The calculations have been performed using the Dirac-Fock (DF) atomic model, the exchange interaction having been taken into account exactly for the interaction both between bound electrons and between bound and free electrons. The influence of approximations in the exchange treatment on the magnitude of the parameters is shown to be essential at small photoelectron energies and in the energy regions where parameters become small, changing sign. The comparison between the above relativistic and our nonrelativistic Hartree-Fock calculations is made. Peculiarities of the parameters' behaviour are discussed. The DF calculations of the combined nondipolar parameter γ + 3δ for the 2p shell of Kr are in good agreement with available experimental data.

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Section: Introductionmentioning

confidence: 99%

“…In [4][5][6][7][8][9] the influence of quadrupole terms on the angular distribution has been studied using the nonrelativistic treatment. The quadrupole approximation has also been used in relativistic computations [15][16][17]. Advantage has been taken of the next octopole approximation in [18].…”

Section: Introductionmentioning

confidence: 99%

Relativistic photoelectron angular distribution parameters in the quadrupole approximation

Nikulin²,

J. Phys. B: At. Mol. Opt. Phys.

et al. 2001

show abstract

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

Atomic Data and Nuclear Data Tables

Yarzhemsky

2001

355

218

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 ...

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Non-dipole second order parameters of the photoelectron angular distribution for elements Z=1–100 in the photoelectron energy range 1–10keV

Nikulin²,

Atomic Data and Nuclear Data Tables

et al. 2006

147