Knowledge Bank

In the range 0--45~cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ below the ionization limit, the separation between adjacent electronic states (Rydberg states with principal quantum number $n>50$) of atoms and molecules is smaller than 2~cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$. In order to resolve the fine or hyperfine structure of these states, it is necessary to combine high-resolution vacuum ultraviolet (VUV) laser radiation, which is required to access the Rydberg states from the ground state, with millimeter wave radiation.% , \emph{J. Phys. B: Atom. Mol. Phys.} \textbf{10}, L183--189 (1977). {F. Merkt, A. Osterwalder}, \emph{Int. Rev. Phys. Chem.} \textbf{21}, 385--403 (2002). {M. Schafer, M. Andrist, H. Schmutz, F. Lewen, G. Winnewisser, F. Merkt}, \emph{J. Phys. B: At. Mol. Opt. Phys.} \textbf{39}, 831--845 (2006).} Such double-resonance experiments have been used to study the hyperfine structure of high Rydberg states of $\mathrm{<mrow\; data-mjx-texclass="ORD">83</mrow>}$Kr , \emph{Phys. Rev. A}, \textbf{74}, 062506 (2006).}, H$2$ , \emph{J. Chem. Phys.}, \textbf{121}, 11810--11838 (2004).}, or D$2$ , \emph{Phys. Rev. A} \textbf{77}, 04502 (2008).}. Millimeter wave transitions (240--350 GHz) between $n\ell$ ($52\le n\le 64,\ell \le 3$) Rydberg states of different xenon isotopes were detected by pulsed field ionization followed by mass-selective detection of the cations. Because of the high polarizability of high-$n$ Rydberg states ($\propto n7$, $\sim 104$ MHz,cm$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$,V$\mathrm{<mrow\; data-mjx-texclass="ORD">-2</mrow>}$ for $n\approx 50$), it is necessary to reduce the electric stray fields to values of the order of mV/cm (or less) in order to minimize the (quadratic) Stark shift of the millimeter wave transitions. Some p and d Rydberg states of Xe are nearly degenerate and efficiently mixed by small stray fields, making it possible to observe transitions forbidden by the $\Delta \ell =\pm 1$ selection rule or transitions exhibiting a linear Stark effect, which is typical for the degenerate high-$\ell$ Rydberg states. Multichannel quantum defect theory (MQDT) was used to analyze the millimeter wave data and to determine the hyperfine structures of the $2$P$\mathrm{<mrow\; data-mjx-texclass="ORD">3<mrow\; data-mjx-texclass="ORD">/</mrow>2</mrow>}$ ground electronic states of $\mathrm{<mrow\; data-mjx-texclass="ORD">129</mrow>}$Xe$+$ and $\mathrm{<mrow\; data-mjx-texclass="ORD">131</mrow>}$Xe$+$.