Dipole photoelectron angular photoionization

The latter equation assumes a 100% linearly polarized ionizing radiation, a is the fine structure constant, Nni is the number of electrons in a nl subshell, Dni->ei l is a radial dipole photoionization amplitude, fini is the dipole photoelectron angular asymmetry parameter, and A i2 is the electric dipole-quadrupole interference term arising due to the correction term ikr in the above expression for Mab,... 

Calculated results for the Ar nondipole Is photoelectron angular-asymmetry parameter yis(< ) for free Ar, Ar C60, Ar C60 (-240 and Ar C6o C240 C540 are shown in Figure 15 (the nondipole parameter Sns vanishes, by definition, and the dipole parameter fins = 2, i.e., is constant, nonrelativistically for the photoionization of ns-states). 

Angular distribution parameters ft of photoelectrons Is photoionization in helium / = 2.0 (in dipole approximation)... 

Within the dipole approximation (jphoton = 1) and for the example of photoionizing an wp-electron from a closed-shell atom (J = 0), the photoelectron angular momentum is either t = 0 or 2 and, hence,... 

In Eq. (12), l,m are the photoelectron partial wave angular momentum and its projection in the molecular frame and v is the projection of the photon angular momentum on the molecular frame. The presence of an alternative primed set l, m, v signifies interference terms between the primed and unprimed partial waves. The parameter ct is the Coulomb phase shift (see Appendix A). The fi are dipole transition amplitudes to the final-state partial wave I, m and contain dynamical information on the photoionization process. In contrast, the Clebsch-Gordan coefficients (CGC) provide geometric constraints that are consequent upon angular momentum considerations. 

Note that m is an abbreviation for mf.) It can be seen that in general there exist two photoionization channels which differ in the orbital angular momentum ( of the photoelectron and can interfere. Equ. (2.9a) is the dipole selection rule for the... 

Ionization at a given photon energy may proceed in several channels. For example, the dipole selection rule, A l- 1, permits an initial electronic state of angular momentum / to decay into two degenerate ionization channels, the / +1 and / -I channels in which the photoelectrons have angular momenta (/ + 1) h and (/ - 1 )h. Since the parameters a and P contain the radial matrix elements for ionization into the two channels, and since these elements are proportional to the overlap of the electronic wavefunctions for the initial and final states of the ionization process, it follows that a and P are functions of these overlaps. Secondly, since the two photoelectron waves have different phase and nodal structures, they may interfere this interference is also determinative of o and p values. For atomic photoionization and LS coupling, one finds ... 

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