$g$ Factor of Lithiumlike Silicon ${}^{28}\mathrm{Si}^{11\mathbf{+}}$

The $g$ factor of lithiumlike silicon ${}^{28}\mathrm{Si}^{11+}$ has been measured in a triple-Penning trap with a relative uncertainty of $1.1\times {10}^{-9}$ to be $g_{\exp }=2.0008898899(21)$. The theoretical prediction for this value was calculated to be $g_{\mathrm{th}}=2.000889909(51)$ improving the accuracy to $2.5\times {10}^{-8}$ due to the first rigorous evaluation of the two-photon exchange correction. The measured value is in excellent agreement with the theoretical prediction and yields the most stringent test of bound-state QED for the $g$ factor of the $1s^{2}2s$ state and the relativistic many-electron calculations in a magnetic field.

Figure 1

The trap arrangement consists of an electron beam ion trap (EBIT) for the creation of highly charged ions, an analysis trap where a ferromagnetic ring electrode is used to produce a magnetic inhomogeneity, and a precision trap with a very homogeneous magnetic field. In order to induce spin flips, microwaves are irradiated through a quartz glass window into the trap chamber.

Figure 2

Spin flip resonance of a single lithiumlike silicon ion. A Gaussian line shape (solid line) was fit to the data. The dark gray area is the confidence interval of the maximum-likelihood fit. Because of high microwave power, the resonance is saturated. The inset shows a discrete spin flip, which is monitored by a jump of 240 mHz within the absolute axial frequency of about 411.8 kHz.

Figure 3

Comparison of experimental and theoretical $g$ factor for ${}^{28}\mathrm{Si}^{11+}$. Three spin flip resonances have been recorded which are marked by the black points. Overall, the microwave power was varied by a factor of $\sim 50$. The solid line is the resulting weighted average with the corresponding experimental uncertainty in dark gray. The dashed line denotes the theoretical value and the hatched area its uncertainty.

Figure 4

Feynman diagrams representing the two-photon exchange correction to the $g$ factor. The wavy line indicates the photon propagator and the double line the electron propagators in the Coulomb field of the nucleus. The dashed line terminated with the triangle denotes the interaction with the constant magnetic field.