Hyperfine Splitting of the $2s_{1/2}$ and $2p_{1/2}$ Levels in Li- and Be-like Ions of ${}_{59}{}^{141}\mathrm{Pr}$

High-resolution spectroscopy of the $2s_{1/2}-2p_{1/2}$ transition in the extreme ultraviolet region is shown to resolve the level splitting induced by the nuclear magnetic field of both the $2s_{1/2}$ and the $2p_{1/2}$ levels in lithiumlike ${{}^{141}\mathrm{Pr}}^{56+}$ and of the $2s_{1/2}2p_{1/2}$ ${}^3{P}_1$ level in berylliumlike ${{}^{141}\mathrm{Pr}}^{55+}$. The ${}^{141}\mathrm{Pr}$ ions are an ideal test of this measurement approach because their energy levels are known well from first principles and are unaffected by small energy contributions from QED and nuclear magnetization effects. The accuracy attained in the measured $196.5\pm 1.2\mathrm{meV}$ $2s_{1/2}$ splitting is more than an order of magnitude better than that achieved before using crystal spectroscopy of the $2s_{1/2}-2p_{3/2}$ x-ray transition and at the level needed to implement a proposed scheme for disentangling the contributions from QED and nuclear magnetization effects in higher-$Z$ ions, such as ${}^{209}\mathrm{Bi}$.

Figure 1

Spectrum showing 14 h of co-added data: (a) four lines corresponding to the split $2s_{1/2}-2p_{1/2}$ transition array of ${{}^{141}\mathrm{Pr}}^{56+}$; (b) three lines corresponding to the $2s^2{}^1{S}_0-2s2p{}^3{P}_1$ transition array of ${{}^{141}\mathrm{Pr}}^{55+}$.

Figure 2

Schematic of the five lowest levels in berylliumlike ${\mathrm{Pr}}^{55+}$ and their splittings (far right) due to the hyperfine interaction with the nuclear magnetic field. The transition between the $2s^2$ ground state and the $2s2p{}^3{P}_1$ upper level splits into three components. Transitions are denoted by their multipole order, where $E1$ and $E2$ ($M1$ and $M2$) denote electric (magnetic) dipole and quadrupole transitions, respectively.

Figure 3

Hyperfine splittings derived from data sets collected on different days: (a) ${{}^{141}\mathrm{Pr}}^{56+}$ hyperfine splitting of the $2s_{1/2}$ ground level (yellow crosses and open orange circles) from the $2s_{1/2}-2p_{1/2}$ line separations between $F=2–2$ and 3–2 lines as well as between $F=2–3$ and 3-3 lines, and (b) of the $2p_{1/2}$ excited level (green crosses and open blue circles) between $F=2–2$ and 2–3 as well as between $F=3–2$ and 3–3; (c)–(e) ${{}^{141}\mathrm{Pr}}^{55+}$ hyperfine splittings of the $2s2p{}^3{P}_1$ excited level (solid blue circles) between $F=3/2–5/2$, $5/2–7/2$, and $3/2–7/2$. The solid horizontal lines represent the weighted averages for each measured splitting.