Distinguishing State-of-the-Art Atomic Structure Calculations with a Measurement of the $3p_{1/2} \rightarrow 2s_{1/2}$ X-Ray Transition in Neonlike Germanium

We measured the $(2s_{1/2}2p^63p_{1/2})_{J=1} \to (2s^22p^6)_{J=0}$ line of neonlike germanium, which has been measured in multiple experiments with widely disparate results. Our measurement was performed at an electron beam ion trap using a very high resolution flat-crystal spectrometer. Our experimental setup attained the highest spectral resolving power ($E/\Delta E \approx 5800$) of any such measurement. This resulted in a relative measurement accuracy of $1\times10^{-5}$. Our new value not only enables us to distinguish among the past measurements, but our value also serves as a benchmark for evaluating two implementations of the many-body perturbation theory (MBPT) used for performing highly accurate theoretical calculations. Earlier work that focused on $n=2 \rightarrow n=2$ transitions of neonlike germanium found that the two implementations of MBPT gave divergent results. However, our measurement of the $n=3 \rightarrow n=2$ transition is reproduced by both calculations within $10^{-4}$, and one calculation even matches the spectroscopic accuracy of $10^{-5}$.