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The Born Oppenheimer wave function near level crossing

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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J. E. Avron, A. Gordon

Quantum Physics · Submitted 18 Jun 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We find that, at low angular momenta, the mixing due to crossing is surprisingly large, scaling like \mu^(1/6), where \mu is the electron to nuclear mass ratio.

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arXiv IDquant-ph/0006078 (version 2)
Pith IDYXPDA3TU, Pith's permanent record of this paper and its review
CitationA. Gordon, J. E. Avron. "The Born Oppenheimer wave function near level crossing." arXiv:quant-ph/0006078 (2000). https://pith.science/paper/YXPDA3TU
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,608 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.09 · randomized assignment 0.01 · states quantitative result 0.90 · compares with prior results 0.71 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

The standard Born Oppenheimer theory does not give an accurate description of the wave function near points of level crossing. We give such a description near an isotropic conic crossing, for energies close to the crossing energy. This leads to the study of two coupled second order ordinary differential equations whose solution is described in terms of the generalized hypergeometric functions of the kind 0F3(;a,b,c;z). We find that, at low angular momenta, the mixing due to crossing is surprisingly large, scaling like \mu^(1/6), where \mu is the electron to nuclear mass ratio.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The standard Born Oppenheimer theory does not give an accurate description of the wave function near points of level crossing. background 0.51 0.08 0.09 asserted 1.00
s1 We give such a description near an isotropic conic crossing, for energies close to the crossing energy. contribution 1.00 0.95 0.20 asserted 1.00
s2 This leads to the study of two coupled second order ordinary differential equations whose solution is described in terms of the generalized hypergeometric functions of the kind 0F3(;a,b,c;z). method 0.73 0.86 0.13 asserted 1.00
s3 We find that, at low angular momenta, the mixing due to crossing is surprisingly large, scaling like \mu^(1/6), where \mu is the electron to nuclear mass ratio. result 1.00 0.96 0.46 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • references and citing sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The standard Born Oppenheimer theory does not give an accurate description of the wave function near points of level crossing. We give such a description near an isotropic conic crossing, for energies close to the crossing energy. This leads to the study of two coupled second order ordinary differential equations whose solution is described in terms of the generalized hypergeometric functions of the kind 0F3(;a,b,c;z). We find that, at low angular momenta, the mixing due to crossing is surprisingly large, scaling like \mu^(1/6), where \mu is the electron to nuclear mass ratio.

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