Anisotropic interactions in autoionizing Rydberg systems

Abstract

We present an improved theoretical description of Rydberg electron motion in the presence of an arbitrary ionic core. Through the use of a generalized eigenvalue equation involving Coulomb, multipole, and polarization interactions we are able to describe accurately the physics of the autoionizing Mg $3pnf$ Rydberg states. The vector hyperpolarizability ${\ensuremath{\beta}}_{v},$ the proportionality constant for an interaction term with the operator structure $\stackrel{\ensuremath{\rightarrow}}{{L}_{c}}\ensuremath{\cdot}\mathcal{l}\ensuremath{\rightarrow}{/r}^{6}$, where $\stackrel{\ensuremath{\rightarrow}}{{L}_{c}}$ and $\mathcal{l}\ensuremath{\rightarrow}$ are the orbital momenta of the ionic core and the Rydberg electron, is found to be 1.885 a.u., roughly two orders of magnitude larger than in ground-state Ne${}^{+}$. The effects of nonadiabatic radial interactions now emerge clearly. Comparisons with measured autoionization energies and rates, and with those computed using $R$-matrix and multichannel quantum defect theory methods, confirm the accuracy of this approach. The concept of adiabatic torquing of orbital planes is introduced and explored in Rydberg magnesium.