Scientific sources - Case31
References
N. I. Shvetsov-Shilovski, M. Lein, L. B. Madsen, E. Räsänen, C. Lemell, J. Burgdörfer, D. G. Arbó, and K. Tőkési. 2016. Semiclassical two-step model for strong-field ionization. Physical Review A, 94, 013415. Source.
Coherent semiclassical outgoing distributions, independent SCTS/QTMC action identities and finite Coulomb remainder, 800-nm quantum comparison, launch sensitivity and wavelength-domain limits. Source nodes and external feasibility metrics are not exact 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. 013415-3-4, Eqs. (9)-(14) Instantaneous field magnitude, Stark-shifted binding and the outgoing parabolic exit define the launch. The field sign is not substituted for its magnitude in the tunneling weight. |
| F2, I3 | article pp. 013415-9-10, Eqs. (47)-(48), Fig. 6(a-c), Fig. 7 and discussion The nonzero-longitudinal-velocity 800-nm launch is an independent first-step change under the same transverse weight; candidate-presented contrast is needed for identification. |
| F3 | article pp. 013415-4 and 013415-6-7, Eq. (15), importance-sampling discussion and Eq. (41) The estimator sums amplitudes coherently with unbiased sampling/weights, not probabilities. Sampling the probability and then using unit amplitudes is not automatically equivalent. |
| F4 | article p. 013415-6, Sec. III.B, Eqs. (26)-(29) Outgoing Kepler asymptotic momentum differs from finite pulse-end momentum; a scattering-equivalent mapping is accepted. |
| O1, O2, I1 | article p. 013415-8, Fig. 1(a-c), Fig. 2, and baseline comparison text The 800-nm coherent QTMC/TDSE/SCTS objects share broad support and ATI structure but differ materially in low-energy interference; source layout and exact node positions are not targets. |
| O3, M5 | article pp. 013415-7-9, TDSE-method Eqs. (43)-(44), Figs. 1-2 and Fig. 4(a,b) The independent 800-nm quantum reference supports specific low-energy/interference comparisons, not universal quantitative superiority over all energies. |
| O4, M7 | article p. 013415-9, Fig. 4(a-f), Fig. 5(a-c) and wavelength/Keldysh discussion 800/1200/1600-nm transfer probes the changing domain. Peak-normalized energy and yield-normalized angular reductions are distinct; fewer wavelengths permit narrower domain claims only. |
| I2, M4 | article p. 013415-8, Fig. 3(a-d) and phase discussion; p. 013415-6, Eq. (40) Finite post-pulse Coulomb relative phase changes low-energy interference; the optional single-cycle panels and named phase-ablation layout are not compulsory. |
| M1 | article pp. 013415-5-6, Eqs. (18)-(25), (30)-(40) The mixed position-to-momentum generating function fixes endpoint sign, the doubled Coulomb integrand and the trajectory-dependent finite post-pulse part. |
| M2 | article p. 013415-6, Sec. III.B, Eqs. (30)-(40) and regularization derivation Only common same-bin divergences cancel; the angular-momentum-dependent finite Coulomb remainder survives. |
| M3 | article pp. 013415-4-5, Eq. (17) and paragraph comparing it with Eqs. (22),(25) QTMC is a separately defined comparator action, not a renamed SCTS result; equivalent phase bookkeeping requires equality of same-bin relative phases. |
| M6 | article pp. 013415-8-10, Fig. 3, Figs. 6-7 and Conclusion Continuum-action and launch-input changes are distinct physical causes and need separately discriminating evidence. |
| V1, V2 | article pp. 013415-2-3, tunneling/semiclassical assumptions; pp. 013415-9-10, domain and Conclusion Single-active-electron hydrogen and the tested pulse/launch/Keldysh domain bound the result. Material phase/launch/binning risks need a concrete trigger, not a fixed trajectory count. |
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.
For Coulomb $V=-Z/r$, the assigned SCTS action is $\Phi_{\rm SCTS}=-\mathbf v_0\cdot\mathbf r_0+I_pt_0-\int_{t_0}^{\infty}[p^2/2-2Z/r]dt$ (Eq. (22)); generally the integrand is $p^2/2+V-\mathbf r\cdot\nabla V$ (Eq. (25)). The QTMC comparator is $\Phi_{\rm QTMC}=I_pt_0-\int_{t_0}^{\infty}[p^2/2-Z/r]dt$ (Eq. (17)), under the assigned endpoint convention. Gauge/generating-function changes must prove equality of same-bin relative phases; renaming a different action is not equivalence.
For hydrogen $Z=1$, let $E>0$, $b=(2E)^{-1}$, $g=\sqrt{1+2EL^2}$. After removal of common same-bin divergences, the finite Coulomb remainder is $\widetilde\Phi_f^C=-Z\sqrt b[\ln g+\operatorname{arsinh}(\mathbf r_f\cdot\mathbf p_f/(g\sqrt b))]$ (Eq. (40)). It is trajectory dependent and cannot be discarded with the common divergent phase.
The estimator has $R(\mathbf k)\propto|\sum_{j\to\mathbf k}a_je^{i\Phi_j}|^2$ with an unbiased amplitude measure (Eq. (15), importance-sampling discussion). Outgoing energy obeys $k^2/2=p_f^2/2-1/r_f$ and the direction follows the outgoing Coulomb/Kepler map (Eqs. (26)-(29)); finite pulse-end momentum is not the asymptotic observable.
The launch weight is $w(t_0,v_\perp)\propto\exp[-2\kappa^3/(3F(t_0))]\exp[-\kappa v_\perp^2/F(t_0)]$, with the assigned Stark binding and $F=|\mathbf F|$ (Eqs. (9),(13)). The parabolic exit uses the outgoing side of Eqs. (10)-(12); changing longitudinal launch must not silently change this transverse weight or action branch.
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.