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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The method of construction of the wavefunction of a Cooper pair based on the Pauli exclusion principle and the Mackey-Bradley theorem is developed. Tables of symmetrized and antisymmetrized Kronecker squares of single- and double-valued irreducible representations of the groups Oh6 and D6h4 are obtained. The tables are used to search for points in the Brillouin zone where totally symmetric Cooper pairs can exist. It is shown that, in the symmetrical points and directions in a Brillouin zone, a direct connection between the multiplicity and parity of the Cooper pair wavefunction does not exist.

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The nodal structure of the superconducting order parameter (SOP) in D 4 6h symmetry (crystal symmetry of UPt 3 ) is investigated making use of the space-group approach to the wave function of a Copper pair. It is shown that the lines of nodes of odd SOP appear in strong spin±orbit coupling case if the time-reversal symmetry is violated. The nodal structure of the SOP is defined by the space±time symmetry of the crystal and does not depend on any choice of basis functions. The theoretical nodal structure of the E 1u in D 4 6h symmetry agrees with the experimental data on UPt 3 .

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