Polarizabilities of Rn-like Th${}^{4+}$ from rf spectroscopy of Th${}^{3+}$ Rydberg levels

High-resolution studies of the fine-structure pattern in high-L n $=$ 37 levels of Th${}^{3+}$ have been carried out using radio-frequency (rf) spectroscopy detected with resonant excitation Stark ionization spectroscopy (RESIS). Intervals separating $L$ $=$ 9 to $L$ $=$ 15 levels have been measured, and the results analyzed with the long-range effective potential model. The dipole polarizability of Th${}^{4+}$is determined to be $\alpha$${}_{\mathrm{D}}$ $=$ 7.720(7) a.u. The quadrupole polarizability is found to be 21.5(3.9) a.u. Both measurements represent significant tests of a priori theoretical descriptions of this highly relativistic ion.

Figure 1

Diagram of the microwave RESIS apparatus. A beam of the Th${}^{4+}$ is produced using an ECR and charge and mass selected at (1). The beam then passes through a dense Rb target at (2) where it charge captures a highly excited Rydberg electron to become a beam of Th${}^{3+}$ Rydberg states. The beams are then charge analyzed at (3) to select just the Th${}^{3+}$ Rydberg beam. An electrostatic lens then focuses that beam and ionizes any weakly bound Rydberg states, (4). At (5) a Doppler-tuned CO${}_2$ laser excites transitions between a specific $\mathit{nL}$ level to the higher $n$′ level, depleting the population in the $\mathit{nL}$ level. Then the rf region, if on resonance with a transitions, will repopulate the $\mathit{nL}$ level at (6). A second Doppler-tuned CO${}_2$ laser then excites the population of the $\mathit{nL}$ level again the to the higher $n$′ level at (7). The n′ level is then Stark ionized and deflected into the channel electron multiplier at (8).

Figure 2

The figure illustrates a RESIS rf signal representing the transition between the $L$ $=$ 11 and $L$ $=$ 12 levels of the $n$ $=$ 37 state of Th${}^{3+}$. The rf electric field is propagating antiparallel to the ion beam velocity. Each data point represents 2 min of data taking. The width of the line is due to the transit time through the rf region and the unresolved spin splitting.

Figure 3

Plot of the scaled first-order energies measured in this study. The data are the solid black points with error bar; on some points the error bar lies inside the point itself. The dotted line is the linear fit of the data that clearly fails to account for the measurements. The solid line is a fit that includes terms proportional to $\langle r^{-8}\rangle$, as described in the text. This second fit matches the data within the measurement precision and gives the $y$ intercept shown by the open circle.