Polarization studies in the photoionization of atoms using a graphical technique

Abstract

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.

Properties of Auger electrons following ionization of polarized atoms by polarized electrons

“…To obtain the special cases, one needs to integrate over the angles of one or both escaping and Auger electrons and to sum over the magnetic components of some angular momenta. The following summation and integration formulae from [8] make this easy to do:…”

“…For the calculation of polarized line emission, the method based on a collisional-radiative kinetic model of magnetic sublevel populations was recently used by Hakel et al [6]. Another method applied as an alternative approach with respect to the usual density matrix formalism was based on the methods developed in the atomic theory [7][8][9]. In the latter method, the probability or cross-section of the interaction was expressed as multiple expansion over the multipoles (irreducible tensors) of the state of all particles taking part in the process both in initial and final states.…”

“…Then the ion formed can be specified by the total angular momentum J of electronic shells. The modifications enabling one to take into account hyperfine structure splitting can be easily made [8,9].…”

Investigation of fluorescence radiation following radiative recombination of ions and electrons

“…The aim of the present work is the derivation of a general expression for the differential cross section of PRF following PR of polarized ions and polarized electrons by using atomic theory methods [3][4][5][6] that are alternative to the density matrix formalism [7].…”

Atomic theory methods for the polarization in photon and electron interactions with atoms

“…A further development of the ideas of Fano and Macek [15] was accomplished by Kupliauskienė et al [25,26]. They have used the method based on the atomic theory [1,2,27] to derive the expressions for the photoionization cross-sections of polarized atoms by polarized radiation.…”