Effects of anisotropic electron-ion interactions in atomic photoelectron angular distributions

The photoelectron asymmetry parameter $\beta$ in $\mathrm{LS}$ coupling is obtained as an expansion into contributions from alternative angular-momentum transfers $j_t$. The physical significance of this expansion of $\beta$ is shown to be that (i) the electric-dipole interaction transfers to the atom a characteristic single angular momentum $j_t=l_0$, where $l_0$ is the photoelectron's initial orbital momentum, whereas (ii) angular-momentum transfers $j_t\ne l_0$ indicate the presence of anisotropic (i.e., term-dependent) interaction of the outgoing photoelectron with the residual ion. For open-shell atoms the photoelectron-ion interaction is generally anisotropic; photoelectron phase shifts and electric-dipole matrix elements depend on both the multiplet term of the residual ion and the total orbital momentum of the ion-photoelectron final-state channel. Consequently, $\beta$ depends on the term levels of the residual ion and contains contributions from all allowed values of $j_t$. These findings contradict the independent-particle-model theory for $\beta$, which ignores the final-state electron-ion interaction and to which our expressions reduce in the limiting cases for which only $j_t=l_0$ is allowed, namely (a) spherically symmetric atoms (e.g., closed-shell atoms) and (b) open-shell atoms for which the electron-ion interaction is isotropic (e.g., very light elements). Numerical calculations of the asymmetry parameters and partial cross sections for photoionization of atomic sulfur are presented to illustrate the theory and to demonstrate the information on electron-ion dynamics that can be obtained from the theoretical and experimental study of $\beta$ for open-shell atoms.