Toward resolving the discrepancy in helium-3 and helium-4 nuclear charge radii
Bibliographic record
Abstract
The discrepancy in the squared nuclear charge radius difference, Δ R 2 , between He 3 and He 4 , as determined from electronic and muonic atom energy levels, presents an unresolved puzzle. This paper shows that accounting for off-diagonal hyperfine mixing effects can substantially reduce this discrepancy. We find that hyperfine mixing with the n 3 S and n 1 S states ( n > 2 ) in He 3 introduces a correction of − 1.37 kHz to the isotope shift of the 2 1 S − 2 3 S transition, a factor of seven times larger than the current uncertainty. This correction modifies Δ R 2 by − 0.0064 fm 2 , shifting it from 1.0757 ( 15 ) fm 2 to 1.0693 ( 15 ) fm 2 , as initially reported by Werf []. This brings Δ R 2 closer to the value of 1.0636 ( 31 ) fm 2 obtained from muonic helium μ He + by Schuhmann [], narrowing the existing discrepancy from 3.6 σ to 1.7 σ . The adjusted value Δ R 2 also agrees well with the result of 1.069(3) fm 2 derived from the helium 2 3 S
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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 | 0.009 | 0.037 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.005 | 0.004 |
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".