Ionization Energy Of The Metastable 2 S-1(0) State Of He-4 From Rydberg-Series Extrapolation

In a recent breakthrough in first-principles calculations of two-electron systems, Patkos, Yerokhin, and Pachucki [Phys. Rev. A 103, 042809 (2021)] have performed the first complete calculation of the Lamb shift of the helium 2 S-3(1) and 2 P-3(J) triplet states up to the term in alpha(7)m. Whereas their theoretical result of the frequency of the 2 P-3 <- 2 S-3 transition perfectly agrees with the experimental value, a more than 10 sigma discrepancy was identified for the 3 D-3 <- 2 S-3 and 3 D-3 <- 2 P-3 transitions, which hinders the determination of the He2+ charge radius from atomic spectroscopy. We present here a new measurement of the ionization energy of the 2 S-1(0) state of He [960 332 040.491(32) MHz] which we use in combination with the 2 S-3(1) <- 2 S-1(0) interval measured by Rengelink et al. [Nat. Phys. 14, 1132 (2018).] and the 2 P-3 <- 2 S-3(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 S-3(1) state [1152 842 742.640(32) MHz] and the 2 P-3 centroid energy [876 106 247.025(39) MHz]. These values reveal disagreements with the alpha(7)m Lamb shift prediction by 6.5 sigma and 10 sigma, respectively, and support the suggestion by Patkos et al. of an unknown theoretical contribution to the Lamb shifts of the 2 S-3 and 2 P-3 states of He.