Isotope shifts of the $6d{{}^{2}D}_{3/2}$–$7p{}^2{P}_{1/2}$ transition in trapped short-lived ${}^{209-214}$Ra${}^{+}$

Laser spectroscopy of short-lived radium isotopes in a linear Paul trap has been performed. The isotope shifts of the $6d{{}^{2}D}_{3/2}$–$7p{{}^{2}P}_{1/2}$ transition in ${}^{209-214}$Ra${}^{+}$, which are sensitive to the short-range part of the atomic wave functions, were measured. The results are essential experimental input for improving the precision of atomic structure calculations. This is indispensable for parity violation in Ra${}^{+}$ aiming at the determination of the weak mixing angle.

Figure 1

Level scheme of ${}^{209,211}$Ra${}^{+}$ with nuclear spin $I=5/2$. The hyperfine structure splitting is enlarged for visibility.

Figure 2

Schematics for ion trapping and laser spectroscopy. Repump laser I (auxiliary laser) is continuously locked to the wavelength meter. This is also cross-referenced to the frequency comb and serves as a reference laser. Repump laser II is used for spectroscopy. Both the pump lasers are used for spectroscopy and they are monitored with a tellurium (Te${}_2$) molecular reference.

Figure 3

$6d{{}^{2}D}_{3/2}$–$7p{{}^{2}P}_{1/2}$ transitions in ${}^{209-214}$Ra${}^{+}$. The horizontal axis shows the laser-frequency offset from the frequency of comb line $1111032$. The solid lines represent fits with one or three Gaussian functions. (a) Isotopes with $I=0$. (b) Isotope with $I=1/2$: The $6d{{}^{2}D}_{3/2}$$(F=1)$–$7p{{}^{2}P}_{1/2}$$(F=0)$ transition is shown. (c) Isotopes with $I=5/2$: The $6d{{}^{2}D}_{3/2}$$(F=4,3,2)$–$7p{{}^{2}P}_{1/2}$$(F=3)$ transitions are shown, where all peaks at low frequency correspond to the $6d{{}^{2}D}_{3/2}$$(F=4)$–$7p{{}^{2}P}_{1/2}$$(F=3)$ transitions.

Figure 4

King plot of the transformed isotope shifts [Eq. (3b) and (4)] of measured $6d{{}^{2}D}_{3/2}$–$7p{{}^{2}P}_{1/2}$ transition (1079 nm) for the isotope chain ${}^{209-214}$Ra${}^{+}$ against corresponding shifts of $7s^2{{}^{1}S}_0$–$7s7p{{}^{1}P}_1$ transition (482 nm) in neutral radium isotopes. The uncertainties of the measured isotope shifts of the $7s^2{{}^{1}S}_0$–$7s7p{{}^{1}P}_1$ transition are between 3 to 8 MHz, leading to error bars which are smaller than the size of markers in the plot.