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 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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 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".