Scientific sources - Case27
References
Vladislav V. Serov, Alexander W. Bray, and Anatoli S. Kheifets. 2019. Numerical attoclock on atomic and molecular hydrogen. Physical Review A, 99, 063428. Source.
Atomic Coulomb-free SFA distribution and signal-to-saddle relation, plus two-site molecular root topology for three orientations. Molecular widths/distributions and Coulomb/TDSE/timing claims lie outside the assigned observable scope.
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. 063428-2, Eq. (3) and following pulse/intensity paragraph Finite circular-pulse support, intensity and ionization potential define the atomic reference case. |
| F2, F3, M2 | article p. 063428-2, Eqs. (4)-(7) Complex stationary contributions enter a coherent atomic amplitude; consistent action, prefactor and physical branch choices define the same SFA object. |
| F4, M3 | article pp. 063428-3-4, two-center LCAO paragraph and Eqs. (8)-(9) Translation phases produce opposite-sign site terms in the molecular stationary condition, not an unspecified molecular signal. |
| O1, I1 | article p. 063428-3, Fig. 1 lower SPM panel and caption; p. 063428-4, SFA/Coulomb comparison Atomic Coulomb-free support is a finite crescent/semicircle on the vector-potential scale; the upper TDSE panel is not the required SFA output. |
| O2, I2, I3, M4, M7 | article pp. 063428-3-4, Fig. 2 lower molecular panel, Eq. (9) and following orientation discussion Both site families split for in-plane orientations and coincide for the perpendicular orientation because E dot R vanishes. |
| O3, M1, M5 | article p. 063428-3, Fig. 1 c/f labels, Fig. 2 upper atomic panel and saddle-damping paragraphs Representative momenta must be bound to the candidate signal; relative action/damping identifies a dominant main-lobe saddle, without requiring a root map at every momentum. |
| M6 | article p. 063428-3, Fig. 2 upper atomic panel/insets and fringe-damping discussion Weaker features actually claimed require a coherent multipath/damping explanation; no hidden unclaimed fringe family is imposed. |
| V1, V2, V3 | article pp. 063428-2-4, Eqs. (4)-(9), SFA/TDSE comparison and molecular-stationarity discussion; stated task output boundary The assigned molecular conclusion ends at root topology. Molecular PMD, widths, Coulomb offsets and tunneling times do not follow from the commissioned saddle-only evidence. Risk checks remain conditional. |
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 atomic action is $S_{\mathbf k}(t)=\int^t{[\mathbf k+\mathbf A(t^{\prime})]^2/2+I_p}dt^{\prime}$, with $[\mathbf k+\mathbf A(t_s)]^2/2+I_p=0$ (Eq. (6)). A hydrogenic convention gives $D(\mathbf k)\propto\sum_s[S_{\mathbf k}^{\prime\prime}(t_s)]^{-1}e^{iS_{\mathbf k}(t_s)}$ (Eq. (7)), and $P(k_x,k_y,0)\propto|D|^2$. The action damping and prefactors, not root count alone, establish relative importance.
For two translated centers, $[\mathbf k+\mathbf A(t_{sj})]^2/2+I_p-(-1)^j\mathbf E(t_{sj})\cdot\mathbf R/2=0$ (Eq. (9)). Opposite site labels interchange signs; for $\mathbf R\parallel\mathbf e_z$ with in-plane field the site term vanishes. This establishes stationary-family topology, not an uncomputed molecular PMD or attoclock width.
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.