Scientific sources - Case32
References
Xue-Bin Bian and André D. Bandrauk. 2014. Probing Nuclear Motion by Frequency Modulation of Molecular High-Order Harmonic Generation. Physical Review Letters, 113, 193901. Source.
Full coupled electron-nuclear molecular HHG, fixed/moving and H/D contrasts, emission-timing frequency modulation and conditional nuclear retrieval. Only scientific task scope is stated here; computational resource limits are supplied separately.
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 p. 193901-2, Eq. (1) and initial-state/mass paragraphs The full non-Born-Oppenheimer R,rho,z Hamiltonian and cylindrical electronic measure are required; no 1+1D soft-core or frozen-nuclear production surrogate is equivalent. |
| F2, F3, V1 | article pp. 193901-2-3, acceleration-spectrum paragraph, Fig. 3(a,b) and caption All three cases use one radiation/transform convention. Full-spectrum display shifts in panel (a) are not physical yield ratios; unshifted panel (b) supports line shape and frequency comparison. |
| M8, M6 | article p. 193901-4, Eqs. (2)-(3), retrieval paragraphs The emission/ionization-weighting estimate links rising/falling pulse imbalance to frequency shift; inversion is conditional on an applicable R-dependent rate, not unique from one shift. |
| O1, I1, M3 | article pp. 193901-2-3, Fig. 2 and nuclear-motion discussion Moving H and D have different nuclear onset/growth timing; heavier D moves more slowly under the same pulse. |
| O2, I2, M1, M2 | article p. 193901-3, Fig. 3(a,b) and fixed-versus-moving discussion Nuclear motion changes both yield and line position/asymmetry. Frequency modulation is not merely amplitude modulation. |
| O3 | article pp. 193901-3-4, Fig. 3(a,b), isotope paragraphs Moving D has lower HHG yield yet a larger redshift/asymmetry than moving H in the source case; common observable and scale are necessary for comparison. |
| O4, I3 | article pp. 193901-3-4, wavelet paragraph and Fig. 4(a-c) caption Fixed-H timing is approximately symmetric; moving-H emission favors the falling pulse and moving-D occurs later. Top/middle/bottom panels are fixed H/moving H/moving D respectively. |
| M4, M5 | article pp. 193901-2-4, Fig. 1, Fig. 2, Fig. 4 and isotope/emission-weighting discussion R-dependent ionization weights later falling cycles more strongly; mass changes nuclear timing and hence the magnitude and sign of the spectral modulation. |
| M7, V2 | article pp. 193901-1-2, amplitude-versus-frequency and propagation discussion; pp. 193901-4-5, retrieval caveats and conclusion The single-molecule one-electron aligned finite-pulse calculation is not a macroscopic or unique inverse reconstruction. Additional discrimination is triggered by an actual material risk, not a fixed wavelet recipe. |
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 full coordinate dynamics are $i\partial_t\Psi=[-\partial_R^2/(2\alpha)-\nabla_e^2/(2\beta)+V_C-V_I]\Psi$, $\nabla_e^2=\rho^{-1}\partial_\rho(\rho\partial_\rho)+\partial_z^2$, $\alpha=M_1M_2/(M_1+M_2)$, $\beta=(M_1+M_2)/(M_1+M_2+1)$ (Eq. (1)). Expectations use the cylindrical volume element, with one consistent convention for the integrated azimuth; neither reduced-mass dynamics nor rho may be dropped.
Using the same acceleration signal, $S(\omega)\propto|\int dt,w(t)d_A(t)e^{i\omega t}|^2$. A declared peak/centroid or equivalent estimator must distinguish displacement and asymmetry from amplitude change; source Fig. 3(a) display shifts do not define intensity ratios.
The source approximate weighting relation is $\Delta\omega/\omega\simeq[\int_{-\tau/2}^{0}\Gamma(R(t),I(t))dt-\int_0^{\tau/2}\Gamma(R(t),I(t))dt]/\int_{-\tau/2}^{\tau/2}\Gamma(R_e,I(t))dt$ (Eq. (2)). Under average-rate assumptions it becomes $[\Gamma(\bar R_1,\bar I)-\Gamma(\bar R_2,\bar I)]/[2\Gamma(R_e,\bar I)]$ (Eq. (3)). Falling-side enhancement gives the source redshift; inferring R requires the appropriate rate relation and cannot uniquely reconstruct an arbitrary R(t).
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.