Long-range additive and nonadditive potentials in a hybrid system: Ground-state atom, excited-state atom, and ion
Bibliographic record
Abstract
We report a theoretical study on the long-range additive and nonadditive potentials for a three-body hybrid atom-atom-ion system composed of one ground-$S$-state Li atom, one excited-$P$-state Li atom, and one ground-$S$-state ${\mathrm{Li}}^{+}$ ion, $\mathrm{Li}(2{\phantom{\rule{0.16em}{0ex}}}^{2}S)\text{\ensuremath{-}}\mathrm{Li}(2{\phantom{\rule{0.16em}{0ex}}}^{2}P)\text{\ensuremath{-}}{\mathrm{Li}}^{+}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S$). The interaction coefficients are evaluated with highly accurate wave functions calculated variationally in Hylleraas coordinates. For this hybrid system the three-body nonadditive interactions (appearing in second order) induced by the energy degeneracy and enhanced by the induction effect of the ${\mathrm{Li}}^{+}$ ion through the internal electric field can be strong and even stronger than the two-body additive interactions at the same order. We find that for particular geometries the two-body additive interactions of the system sum to zero, leaving only three-body nonadditive interactions, thus making the present system potentially a platform to explore quantum three-body effects. We also extract by first principles the leading coefficients of the long-range electrostatic, induction, and dispersion energies of ${\text{Li}}_{2}{}^{+}$ electronic states correlating to ${\text{Li}}^{+}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\ensuremath{-}\text{Li}(2{\phantom{\rule{0.16em}{0ex}}}^{2}P)$. The results should be especially valuable for the exploration of schemes to create trimers with ultracold atoms and ions in optical lattices.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".