Properties of Fr-like Th${}^{3+}$ from spectroscopy of high-$L$ Rydberg levels of Th${}^{2+}$

Binding energies of high-$L$ Rydberg states ($L$ ⩾ 7) of Th${}^{2+}$ with $n$ $=$ 27–29 were studied using the resonant excitation Stark ionization spectroscopy (RESIS) method. The core of the Th${}^{2+}$ Rydberg ion is the Fr-like ion Th${}^{3+}$ whose ground state is a 5 ${}^2$$F$${}_{5/2}$ level. The large-core angular momentum results in a complex Rydberg fine-structure pattern consisting of six levels for each value of $L$ that is only partially resolved in the RESIS excitation spectrum. The pattern is further complicated, especially for the relatively-low-$L$ levels, by strong nonadiabatic effects due to the low-lying 6d levels. Analysis of the observed RESIS spectra leads to determination of five properties of the Th${}^{3+}$ ion: its electric quadrupole moment $Q$ $=$ 0.54(4); its adiabatic scalar and tensor dipole polarizabilities ${\alpha }_d$${}_{,0}$ $=$ 15.42(17) and ${\alpha }_d$${}_{,2}$ $=$ -3.6(1.3); and the dipole matrix elements connecting the ground 5 ${}^2$$F_{5/2}$ level to the low-lying 6  ${}^2$$D$${}_{3/2}$ and 6  ${}^2$$D$${}_{5/2}$ levels, $|\langle 5\hspace{0.5em}{}^2{F}_{5/2}|\left|D\right||6{}^2{D}_{3/2}\rangle |=1.435(10)$ and $|\langle 5{}^2{F}_{5/2}|\left|D\right||6{}^2{D}_{5/2}\rangle |=0.414(24)$. All are in atomic units. These are compared with theoretical calculations.

Figure 1

Diagram of the RESIS apparatus used in this work. An electron cyclotron resonance source produces a 75-keV beam of Th${}^{3+}$, charge and mass selected at (1) using a 20° magnet. The beam then passes through a Rb target at (2) where it charge captures a highly excite electron, becoming a beam of Th${}^{2+}$ Rydberg states. Then at (3) the beam passes through a 15° magnet where it is charge analyzed and the Th${}^{2+}$ Rydberg beam is selected, eliminating any remaining Th${}^{3+}$ beam. From there it passes through an einzel lens at (4) to remove any weakly bound Rydberg states from the beam. Rydberg transitions are then excited with a CO${}_2$ laser at (5), making transitions from one $n$ level to a higher $n$ level. Then at (6) the upper $n$ Rydberg state is Stark ionized and at (7) it is steered and focused into the channel electron multiplier (CEM).

Figure 2

RESIS spectra of Th${}^{2+}$ Rydberg states for three different transitions; each spectrum is labeled to identify the specific transition. The solid line on each graph is the original signal and the points with error on them are the signal times 20. The quasiquantum defect discussed in the text is on the $x$ axis. Each spectrum has a limited scan range. The large peak around zero is referred to as the high-$L$ peak because it is made up of all the transitions with little quantum defect, i.e., the higher-$L$ levels that are unresolved. Letters without parentheses denote transitions used during the fitting process, while letters with parentheses identify analogous lines not used in the fit.

Figure 3

This figure illustrates the importance of nonadiabatic effects in the second-order dipole perturbation energy. Shown on the left of each panel are the energy levels calculated using the adiabatic model with the theoretical values of $Q$, ${\alpha }_d$${}_{,0}$ and ${\alpha }_d$${}_{,2}$, for $n$ $=$ 27 and $L$ $=$ 9, 11, and 13. On the right of each panel are the nonadiabatic effects that were calculated and added to the model. In both cases only the first-order quadrupole energies and second-order dipole energies are included. It can be observed that these nonadiabatic effects drastically affect the order of the energy levels for $L$ $=$ 9, but by $L$ $=$ 13 the effect is limited to slight shifts in each level, which would likely be described by the nonadiabatic terms of the effect potential.

Figure 4

Comparison between observed and simulated spectra using the $n$ $=$ 29–72 spectrum. The top shows the simulated spectrum using the fitted properties. The bottom is the actual experimental observation for $n$ $=$ 29–72. The solid line in both is the signal and the line with points in both is the signal times 20. The $x$ axis is the transition's frequency minus the non-relativistic hydrogenic energy in gigahertz. The simulated spectrum shows good agreement with the observed spectrum, with only slight variation in areas of overlapping signals.