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 distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".