P of helium to test a 10σ discrepancy with experiment*

There is a 10σ discrepancy between theory and experiment for the ionization energy of the 1s2s³S₁ state of helium [1]. In order to provide an additional check, Clausen et al. [2] have performed measurements for the Rydberg P-states of helium from n = 24 to n = 100 and extrapolated to n = ∞ to find the ionization energy. In the present work, we extend previous high-precision variational calculations [3] up to n = 24 using triple basis sets in Hylleraas coordinates. With the inclusion of relativistic and QED corrections, the results provide a direct theoretical test against the Clausen measurement at n = 24. The results are in excellent agreement, thereby confirming the 10σ discrepancy between theory and experiment for the ionization energy of the 1s2s³S₁ state of helium.

[1] V. Patkos, V. A. Yerokhin and K. Pachucki, Phys. Rev. A 103, 042809 (2021).

[2] G. Clausen et al. Phys. Rev. Lett. 127, 093001 (2021).

[3] G. W. F. Drake, M. M. Cassar and R. A. Nistor, Phys. Rev. A, 65, 054501 (2002).