An alternative method to the density matrix formalism and based on the graphical technique of angular momentum theory is applied to derive the expression for the photoionization cross section of atoms. This expression is suitable for calculating the polarization parameters of the remaining ion and photoelectron in the case of the ionization of polarized atoms exposed to polarized radiation. The atom and ion are described by the quantum numbers LSJ and LSJIF (I is nuclear spin). The expressions are verified by the calculation of the asymmetry parameter β of the angular distribution of photoelectrons in single and shake-up photoionization of the 2p subshell of Na atoms.

The cross sections and asymmetry parameters β of the 2p electron single photoionization, shake-up and shake-down processes from Na atoms in the ground state and in a number of excited states 2p6nl (n = 3, 4, 5 and l ≤ n–1) are calculated using a single channel relaxed-orbital Hartree–Fock approximation. A strong dependence of the calculated cross sections on the atomic orbit of the valence electron is found. The asymmetry parameters β are sensitive to the excitation of the valence electron near the threshold of photoionization. The single photoionization of the 2p subshell of Na atoms in the 4d 2D, 5p 2P and 5f 2F states is found to be about 43, 150 and 105 times less probable respectively than the shake-up process.

In a plane-wave Born approximation the total cross sections of the 2p shell ionization by electrons are calculated for Na atoms in the ground and in a number of excited states 2p6nl (n = 3, 4, 5; l ≤ n - 1). The relaxed-orbital (RO) Hartree–Fock and sudden perturbation (SP) methods are applied within the plane-wave Born approximation. Very strong dependence of the calculated cross sections on the valence electron state has been found. Large difference between the cross sections of RO and SP approximations is noticed near the threshold of ionization which disappears with the increase of the impact electron energy. The relaxation probabilities of the Hartee–Fock calculation strongly deviate from the hydrogenic ones for the 2p6ns and 2p6np states and coincide with them for the 2p6nl (l ≥ 3) states.