Accurate long-range coefficients for two excited like isotope He atoms:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">He</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mspace width="0.2em"/><mml:mmultiscripts><mml:mi>P</mml:mi><mml:mprescripts/><mml:none/><mml:mn>1</mml:mn></mml:mmultiscripts><mml:mo>)</mml:mo></mml:mrow><mml:mo>–</mml:mo><mml:mi mathvariant="normal">He</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mspace width="0.2em"/><mml:mmultiscripts><mml:mi>P</mml:mi><mml:mprescripts/><mml:none/><mml:mn>1</mml:mn></mml:mmultiscripts><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">He</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mspace width="0.2em"/><mml:mmultiscripts><mml:mi>P</mml:mi><mml:mprescripts/><mml:none/><mml:mn>1</mml:mn></mml:mmultiscripts><mml:mo>)</mml:mo></mml:mrow><mml:mo>–</mml:mo><mml:mi mathvariant="normal">He</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mspace width="0.2em"/><mml:mmultiscripts><mml:mi>P</mml:mi><mml:mprescripts/><mml:none/><mml:mn>3</mml:mn></mml:mmultiscripts><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">He</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mspace width="0.2em"/><mml:mmultiscripts><mml:mi>P</mml:mi><mml:mprescripts/><mml:none/><mml:mn>3</mml:mn></mml:mmultiscripts><mml:mo>)</mml:mo></mml:mrow><mml:mo>–</mml:mo><mml:mi mathvariant="normal">He</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mspace width="0.2em"/><mml:mmultiscripts><mml:mi>P</mml:mi><mml:mprescripts/><mml:none/><mml:mn>3</mml:mn></mml:mmultiscripts><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>
Bibliographic record
Abstract
A general formalism is used to express the long-range potential energies in inverse powers of the separation distance between two like atomic or molecular systems with $P$ symmetries. The long-range molecular interaction coefficients are calculated for the molecular symmetries $\ensuremath{\Delta}$, $\ensuremath{\Pi}$, and $\ensuremath{\Sigma}$, arising from the following interactions: $\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{1}P)--\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{1}P)$, $\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{1}P)--\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}P)$, and $\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}P)--\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}P)$. The electric quadrupole-quadrupole term ${C}_{5}$, the van der Waals (dispersion) term ${C}_{6}$, and higher-order terms ${C}_{8}$ and ${C}_{10}$ are calculated ab initio using accurate variational wave functions in Hylleraas coordinates with finite nuclear mass effects. A comparison is made with previously published results where available.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.054 | 0.025 |
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".