Ionization Energy of the Metastable 2 ^{1}S_{0} State of ^{4}He from Rydberg-Series Extrapolation.

In a recent breakthrough in first-principles calculations of two-electron systems, Patk\\'o\\ifmmode \\acute{s}\\else \\'{s}\\fi{}, Yerokhin, and Pachucki [Phys. Rev. A 103, 042809 (2021)] have performed the first complete calculation of the Lamb shift of the helium $2\\text{ }^{3}{\\mathrm{S}}_{1}$ and $2\\text{ }^{3}{\\mathrm{P}}_{J}$ triplet states up to the term in ${\\ensuremath{\\alpha}}^{7}m$. Whereas their theoretical result of the frequency of the $2\\text{ }^{3}\\mathrm{P}\\ensuremath{\\leftarrow}2\\text{ }^{3}\\mathrm{S}$ transition perfectly agrees with the experimental value, a more than $10\\ensuremath{\\sigma}$ discrepancy was identified for the $3\\text{ }^{3}\\mathrm{D}\\ensuremath{\\leftarrow}2\\text{ }^{3}\\mathrm{S}$ and $3\\text{ }^{3}\\mathrm{D}\\ensuremath{\\leftarrow}2\\text{ }^{3}\\mathrm{P}$ transitions, which hinders the determination of the ${\\mathrm{He}}^{2+}$ charge radius from atomic spectroscopy. We present here a new measurement of the ionization energy of the $2\\text{ }^{1}{\\mathrm{S}}_{0}$ state of He [960 332 040.491(32) MHz] which we use in combination with the $2\\text{ }^{3}{\\mathrm{S}}_{1}\\ensuremath{\\leftarrow}2\\text{ }^{1}{\\mathrm{S}}_{0}$ interval measured by Rengelink et al. [Nat. Phys. 14, 1132 (2018).] and the $2\\text{ }^{3}\\mathrm{P}\\ensuremath{\\leftarrow}2\\text{ }^{3}{\\mathrm{S}}_{1}$ interval measured by Zheng et al. [Phys. Rev. Lett. 119, 263002 (2017)] and Cancio Pastor et al. [Phys. Rev. Lett. 92, 023001 (2004)] to derive experimental ionization energies of the $2\\text{ }^{3}{\\mathrm{S}}_{1}$ state [1152 842 742.640(32) MHz] and the $2\\text{ }^{3}\\mathrm{P}$ centroid energy [876 106 247.025(39) MHz]. These values reveal disagreements with the ${\\ensuremath{\\alpha}}^{7}m$ Lamb shift prediction by $6.5\\ensuremath{\\sigma}$ and $10\\ensuremath{\\sigma}$, respectively, and support the suggestion by Patk\\'o\\ifmmode \\check{s}\\else \\v{s}\\fi{} et al. of an unknown theoretical contribution to the Lamb shifts of the $2\\text{ }^{3}\\mathrm{S}$ and $2\\text{ }^{3}\\mathrm{P}$ states of He.