High-precision variational calculations in Hylleraas coordinates are presented for all singlet and triplet $P$ states of helium up to principal quantum number $n=35$ with a uniform accuracy of 1 part in ${10}^{22}$ for the nonrelativistic energy. Mass polarization, relativistic, and quantum electrodynamic effects are included to achieve a final accuracy of $\pm 1\mathrm{kHz}$ or better for the ionization energy of the Rydberg states of ${}^4\mathrm{He}$ in the range $24\le n\le 35$. The results are combined with 11 transition frequency measurements of Clausen et al. [Phys. Rev. A 111, 012817 (2025)] to obtain complementary measurements of the ionization energy of the $1s2s{}^3{S}_1$ state that do not depend on quantum-defect extrapolations to the series limit. The result from the triplet spectrum yields an ionization energy of 1 152 842 742.728(6) MHz, which agrees with but is larger than the experimental value by $14\pm 17\mathrm{kHz}$. However, it confirms a much larger $9\sigma$ discrepancy of $0.468\pm 0.055\mathrm{MHz}$ with the theoretical ionization energy of Patkóš et al. [Phys. Rev. A 103, 042809 (2021)]. The results provide a test of the quantum-defect-extrapolation method at the level of $\pm 17\mathrm{kHz}$.

Close

PrevNext

View figure in article

• Rydberg atoms & molecules
• Atomic Properties
• First-principles calculations
• Perturbative methods
• Schroedinger equation