Parts-per-million-accurate determination of the K$\alpha$ photoionization resonance of Be-like oxygen with resolution of its ${}^{16}$O-${}^{18}$O isotopic shift

We determine with high accuracy the energy of the inner-shell transition $1s^{2}2s^2{}^1{\mathrm{S}}_0\to 1s2s^{2}2p_{3\mathrm{/}2}{}^1{\mathrm{P}}_1$ ${}^{16}{\mathrm{O}}_{K\alpha }^{4+}$ at $554.372(3)\mathrm{e}\mathrm{V}$ ($\lambda$ = $22.36480(12)\text{unicode}x212B$) as well as its small shift of $2.2\pm 1.3\mathrm{m}\mathrm{e}\mathrm{V}$ ($\mathrm{\Delta }\lambda$ = $0.089(52)\mathrm{m}\text{unicode}x212B$) for the ${}^{18}\mathrm{O}$ isotope. This transition blends with a $K_{\alpha }$ line of ${\mathrm{O}}^{5+}$ used in astrophysical diagnostics, potentially affecting its reliability. In contrast to our experimental uncertainty of $\pm 3\mathrm{m}\mathrm{e}\mathrm{V}$, advanced electronic structure predictions for this four-electron system, including quantum electrodynamic (QED) corrections on the order of $100\mathrm{m}\mathrm{e}\mathrm{V}$, still scatter by more than $\pm 250\mathrm{m}\mathrm{e}\mathrm{V}$. Ions generated and stored in an electron beam ion trap were excited at the ELETTRA synchrotron facility with monochromatic soft x rays, with photon energies corrected by an additional spectrometer. Upon resonant excitation of ${\mathrm{O}}^{4+}$ and subsequent autoionization, we separate the photoions of each isotope by a time-of-flight measurement. This way, we resolve soft x-ray isotopic shifts of a few meV, obtain very accurate data on an essential astrophysical ion, and test calculations down to the level of QED contributions.