Scientific sources - Case19
References
Maiku Yamaguchi and Katsuyuki Nobusada. 2016. Photodissociation path in H₂⁺ induced by nonuniform optical near fields: Two-step excitation via vibrationally excited states. Physical Review A, 93, 023416. Source.
Reduced non-Born-Oppenheimer nuclear dissociation, energy-selective nonuniform response and the state-resolved vibrationally mediated route. Absolute source yields, exact fits and one named state are not hidden numerical targets.
Criterion-to-source crosswalk
Locations refer to the article or named preprint/manuscript page, not a figure-file index. Source examples establish scientific identity and robust structure; the task defines required reporting, case coverage and risk-triggered validation. No original source images are reproduced.
| Criteria | Source locations, scientific use and limits |
|---|---|
| F1 | article pp. 023416-1-2, Eq. (1) and Sec. II The coupled electronic/nuclear Hamiltonian, reduced masses, soft-core constants and vibrational ground state specify a non-Born-Oppenheimer calculation. |
| F2 | article p. 023416-2, Eqs. (2)-(6) The first-order spatial field generates both electronic and nuclear nonuniform interaction terms under the shared finite pulse. |
| F3 | article p. 023416-2, final numerical-method paragraph; p. 023416-3, Fig. 2(c,d) Electronic-boundary loss and outgoing nuclear flow represent different processes. Equivalent nuclear flux or separated-channel constructions are allowed. |
| O1, I4, M1 | article pp. 023416-2-4, Fig. 1(a,b), Fig. 3(a,b) and the paragraph interpreting Fig. 3 The 2.0/3.6/8.0 eV branches have three-/two-/one-photon identities; the 2.0 and 8.0 eV controls are approximately insensitive to nonuniformity. |
| O2, I1, M4 | article pp. 023416-3-4, Eqs. (8)-(9), Fig. 3(b) The selective 3.6 eV nonuniform response has leading quadratic yield, not a linear probability law. |
| O3, I3, M5 | article pp. 023416-3-4, Fig. 2(e), and its continuation paragraph on p. 023416-4 Excited vibrational occupation establishes the first stage; the plotted state is representative, not a required state index. |
| O4, I2, M6 | article pp. 023416-3-4, Fig. 2(c,d), Fig. 1(a) blue pathway and surrounding text Outgoing nuclear motion follows vibrational excitation and coupling to the repulsive electronic surface; a final yield alone does not identify that sequence. |
| M2, M3 | article p. 023416-3, Eqs. (7)-(9); p. 023416-4, Fig. 3 discussion Same-surface electronic parity kills the uniform z matrix element while the even nonuniform terms allow vibrational excitation, explaining pathway selectivity. |
| M8 | article pp. 023416-3-4, Fig. 2(c-e), Eqs. (8)-(9) and Summary The causal answer combines selective response, direct excited-state evidence and subsequent nuclear dissociation; source narrative cannot replace submitted evidence. |
| V1, V2 | article p. 023416-2, first-order field-model and absorber paragraphs; p. 023416-4, Summary Finite-domain nuclear/electronic separation and the truncated spatial expansion bound the claim. Additional validation is required only for an actual material risk, not by source solver choice. |
Formula and convention notes
Source-numbered identities below are paraphrased mathematically. Explicit algebraic consequences and accepted model-conditioned representations are identified as such; they do not add a required solver, plot or validation recipe.
The interaction is $V_{\rm ext}=E_0f(t)\sin(\omega t)[z+\epsilon z^2-\epsilon R^2]$ (Eq. (5)). On the same even electronic surface, $\langle v^{\prime}|z|v\rangle=0$, while $\langle v^{\prime}|V_{\rm ext}|v\rangle\propto\epsilon$ generally survives through $z^2$ and $R^2$; hence $T_{v\to v^{\prime}}\propto\epsilon^2$ in the leading-response regime (Eqs. (7)-(9)), not universally at saturation.
A nuclear diagnostic may use $P(R,t)=\int dz,|\Psi(z,R,t)|^2$ and separated outgoing R-flux/loss; electronic z-loss alone is not dissociation. A direct state diagnostic is $P_{v^{\prime}}(t)=|\langle\phi_{v^{\prime}}|\Psi(t)\rangle|^2$ or an identified excited-subspace equivalent. Fig. 2(c-e) supplies canonical examples, not a compulsory absorber radius or state label.
Scope of the source anchors
Figure panels, displayed source coordinates, curve multipliers, numerical grids and named controls are reference examples, not compulsory submission layouts or hidden pointwise targets. Equivalent evidence must preserve the actual physical observable, case, relative scale and discriminating function. Correct data, candidate identification, causal explanation and risk resolution are separate evidential acts. Existing branch-local dependencies, applicability/N/A and descriptive Research Closure rules remain in the case rubric.