DETERMINATION OF THE IONIZATION ENERGY OF THE METASTABLE 2 <sup>1</sup>S<sub>0</sub> STATE OF <sup>4</sup>He THROUGH RYDBERG-SERIES EXTRAPOLATION
Bibliographic record
Abstract
\\noindent Helium, as one of the simplest few-electron atoms, is well suited to test fundamental interactions and QED calculations with a high precision. Its importance is underlined by recent advances in the determination of particle properties such as the $\\alpha$-particle charge radius\\footnote{J. Krauth et al., Nature 589, 527531 (2021)}. Yet, the most accurate theoretical\\footnote{K. Pachucki, V. Patk\\'o$\\check{\\mathrm{s}}$, and V. A. Yerokhin, Physical Review A 95, 062510 (2017)}$^,$\\footnote{G. W. Drake and Z. C. Yan, Canadian Journal of Physics 86, 45 (2008)}\n%\\footnote{ V. Patk\\'o$\\check{\\mathrm{s}}$, V. A. Yerokhin, and K. Pachucki, Physical Review A 103, 012803 (2021)}$^,$\nand experimental\\footnote{W. Lichten, D. Shiner, and Z.-X. Zhou, Physical Review A 43, 1663 (1991)}$^,$\\footnote{C. J. Sansonetti and J. D. Gillaspy, Physical Review A 45, R1 (1992)} data on the ionization energies of the low-lying electronic states show a significant discrepancy of more than 2 $\\sigma$ (about 3 MHz). We report on the determination of the ionization energy of the metastable 2 $^1\\mathrm{S}_0$ state of helium through Rydberg-series extrapolation with a relative uncertainty of $5 \\times 10^{-11}$ through the determination of 20 different $n\\mathrm{p} \\leftarrow2\\;^1\\mathrm{S}_0$ transition frequencies in the range of $n$ from 24 to 102, yielding quantum-defect parameters for the $n$p Rydberg states. A one-photon excitation scheme was employed, using the frequency-doubled output of a narrowband cw laser source (312 nm), calibrated to a frequency comb referenced to a GPS-disciplined Rb clock. The major sources of systematic uncertainties are minimized by (i) carrying out the experiment in a doubly skimmed, pulsed supersonic beam of metastable $^4$He atoms to minimize the Doppler broadening, (ii) compensating electric stray fields to below 0.7 mV/cm, and (iii) cancelling the first-order Doppler shift by monitoring two Doppler components resulting from two counter-propagating laser beams. The effects of residual stray electric fields are included as DC-Stark shifts in the analysis. Our new value of the ionization energy of the $2\\;^1\\mathrm{S}_0$ state of $^4$He, with an absolute uncertainty better than 50 kHz, represents an improvement by a factor of about five in precision. It also allows for a purely experimental determination of the ionization energies of several other low-lying electronic states of $^4$He, which were previously only accurately known through combination of measured and theoretical energy intervals.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".