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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2606.00814 |
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| _version_ | 1866914620553297920 |
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| author | Drake, G. W. F. Bondy, Aaron T. |
| author_facet | Drake, G. W. F. Bondy, Aaron T. |
| contents | High precision variational calculations for helium in Hylleraas coordinates are used to obtain a combination of quantum defect expansions for the nonrelativistic energy and $1/n$ expansions for the relativistic and quantum electrodynamic (QED) corrections. The extrapolations based on direct calculations for the singlet and triplet $P$-states up to principal quantum number $n = 35$ provide ionization energies of the $1snp\;^1P_1$ and $^3P_c$ (centroid) states up to $n=102$ with accuracies better than $\pm$1 kHz. The calculated ionization energies are combined with 28 measured transition frequencies to obtain values for the ionization energy of the $1s2s\;^3S_1$ state. The final result of 1152 842 742.705(16) MHz differs from theory by $0.474\pm 0.052$ MHz, and provides a strong confirmation of the 9$σ$ disagreement between theory and experiment obtained previously by quantum defect extrapolation of experimental data to the series limit. An analysis of the quantum defect method is presented, and second-order mass polarization (recoil) terms are identified that vary as $1/n^2$ in lowest order. The nonrelativistic part provides a theoretical justification for the effective reduced-mass Rydberg $R_M^{(+)}$ based on the phenomenological model of a Rydberg electron scattering from a He$^+$ core. The Ritz expansion for the nonrelativistic energy is verified to an unprecedented 20-figure accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00814 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Theory for the Rydberg states of helium: quantum defect extensions and comparison with experiment up to $n = 102$ for the singlet and triplet $P$-states Drake, G. W. F. Bondy, Aaron T. Atomic Physics High precision variational calculations for helium in Hylleraas coordinates are used to obtain a combination of quantum defect expansions for the nonrelativistic energy and $1/n$ expansions for the relativistic and quantum electrodynamic (QED) corrections. The extrapolations based on direct calculations for the singlet and triplet $P$-states up to principal quantum number $n = 35$ provide ionization energies of the $1snp\;^1P_1$ and $^3P_c$ (centroid) states up to $n=102$ with accuracies better than $\pm$1 kHz. The calculated ionization energies are combined with 28 measured transition frequencies to obtain values for the ionization energy of the $1s2s\;^3S_1$ state. The final result of 1152 842 742.705(16) MHz differs from theory by $0.474\pm 0.052$ MHz, and provides a strong confirmation of the 9$σ$ disagreement between theory and experiment obtained previously by quantum defect extrapolation of experimental data to the series limit. An analysis of the quantum defect method is presented, and second-order mass polarization (recoil) terms are identified that vary as $1/n^2$ in lowest order. The nonrelativistic part provides a theoretical justification for the effective reduced-mass Rydberg $R_M^{(+)}$ based on the phenomenological model of a Rydberg electron scattering from a He$^+$ core. The Ritz expansion for the nonrelativistic energy is verified to an unprecedented 20-figure accuracy. |
| title | Theory for the Rydberg states of helium: quantum defect extensions and comparison with experiment up to $n = 102$ for the singlet and triplet $P$-states |
| topic | Atomic Physics |
| url | https://arxiv.org/abs/2606.00814 |