cases/case03/sources.md

Scientific Sources — Case03

References

Xiang-Ru Xiao, Mu-Xue Wang, Wei-Hao Xiong, and Liang-You Peng. 2016. Efficient time-sampling method in Coulomb-corrected strong-field approximation. Physical Review E, 94, 053310. Source

Efficient time-sampling method in Coulomb-corrected strong-field approximation

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

Standard post-pulse Coulomb/Kepler asymptotic-momentum map and finite regularized Coulomb phase; equivalent declared converged continuations remain accepted.

Criterion-to-source crosswalk

Article page identifiers below are journal pages, not PDF viewer indices. Supplemental pages are explicitly marked. The crosswalk distinguishes direct source facts, mathematical entailments and task-defined evidence duties. Original images and PDFs are referenced only; none are reproduced.

Criteria	Source locations, scientific use and limits
F1, M1, M2	Xiao et al. (2016), article pp.053310-3-5, Eqs.(18)-(21),(37),(38) and Sec.III.A: complex-time-to-momentum sampling and Jacobian compensation. Absolute area and separate proposal/cell bookkeeping are mathematical/task clarifications, not determinant-sign phases.
F2	Xiao et al. (2016), article pp.053310-2-4, Eqs.(7)-(16),(22)-(28),(33)-(36): direct amplitude, nonadiabatic launch, Coulomb dynamics and -2/r action. Operational finite asymptotic/tail closure is supplied by Shvetsov-Shilovski et al. (2016), Sec.III.B, article p.013415-6, Eqs.(26)-(40), not explicitly by Xiao et al.
O1, O2, O3, I1, M5	Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations.
O4	Xiao et al. (2016), article pp.053310-4,6, Eqs.(33),(34),(36), Fig.2(b): adiabatic planar QTMC with coherent final-momentum accumulation. The signed planar reduction and finite tail/asymptotic implementation follow the stated task and standard-method equivalence class.
O5, O6, I2, M3	Xiao et al. (2016), article pp.053310-3-6, Eqs.(22)-(28),(37),(38), Fig.2(c,d): ordinary and time-sampled CCSFA represent the same nonadiabatic launch family. In Coulomb propagation the sampled saddle label q is not the reached asymptotic momentum; this distinction is task-explicit.
I3, M4, M6, M7	Xiao et al. (2016), article p.053310-6, Sec.III.B paragraph beginning "In the present work" and Fig.2(b,c) boxed region: local larger-final-momentum CCSFA shift is linked to nonzero longitudinal launch. Extension to Fig.2(d) requires demonstrated c/d agreement. Article p.053310-7, Fig.3 is optional fine-trajectory context, not mandatory fringe matching.
V1, V2	Xiao et al. (2016), article p.053310-6, Sec.III.A sampling/bin-error discussion and p.053310-7 Table I (efficiency context only); Shvetsov-Shilovski et al. (2016), Sec.III.B, article p.013415-6, Eqs.(26)-(40) for finite post-pulse treatment. Reproduction records, compatible complex-estimator replica aggregation and risk-triggered checks are task-defined; no source sample count or runtime is a scoring target.

Formula and convention notes

For F1-F2/O1-O6/M1-M4, use article pp.053310-2-4, Eqs.(7),(8),(18)-(28),(33),(34),(36)-(38), with $\mathbf q$ denoting the launch/saddle label in the Coulomb branches: $$[q_z+A_z(t_s){]}^2+q_x^2+2I_p=0,q_z=-\mathrm{\Re }{A}_z(t_s),q_x=\pm \sqrt{[\mathrm{\Im }{A}_z(t_s){]}^2-2I_p},[q\_z+A\_z(t\_s)]^2+q\_x^2+2I\_p=0,\backslash quad\; q\_z=-\backslash Re\; A\_z(t\_s),\backslash quad\; q\_x=\backslash pm\backslash sqrt\{[\backslash Im\; A\_z(t\_s)]^2-2I\_p\},$$ $${\mathbf{v}}_0=\mathbf{q}+\mathbf{A}(t_r),{\mathbf{r}}_0=\mathrm{\Re }{\int }_{t_s}^{t_r}[\mathbf{q}+\mathbf{A}(s)]ds,J_q=\mid \det \frac{\mathrm{\partial }(q_x,q_z)}{\mathrm{\partial }(t_r,t_i)}\mid \mathrm{.}\backslash mathbf\; v\_0=\backslash mathbf\; q+\backslash mathbf\; A(t\_r),\backslash quad\; \backslash mathbf\; r\_0=\backslash Re\backslash int\_\{t\_s\}^\{t\_r\}[\backslash mathbf\; q+\backslash mathbf\; A(s)]ds,\backslash quad\; J\_q=\backslash left|\backslash det\backslash frac\{\backslash partial(q\_x,q\_z)\}\{\backslash partial(t\_r,t\_i)\}\backslash right|.$$ For the no-Coulomb map replace q by final p. Both signed transverse branches must be represented. Subsequent Coulomb equations are $\dot{\mathbf r}=\mathbf v$, $\dot{\mathbf v}=-\mathbf E-\mathbf r/r^3$. The retained continuum action uses $-\int(v^2/2-2/r+I_p)dt$, rather than the source's $-1/r$ action. Its infinite tail must be replaced by a declared finite regularized phase. For a post-pulse outgoing Coulomb trajectory, $p_\infty=\sqrt{v_f^2-2/r_f}$; an analytic Kepler vector map or demonstrated equivalent continuation fixes direction. The q-to-p_infinity propagation map is not the time-to-q sampling Jacobian. The specified pulse antiderivatives, rather than the misprinted source Eqs.(31)-(32), determine the vector potential; directly integrating the stated pulse is equivalent.

For the standard post-pulse example, Shvetsov-Shilovski et al. (2016), article p.013415-6, Sec.III.B, Eqs.(26)-(40), gives for unit Coulomb charge $$\mathbf{L}={\mathbf{r}}_f\times {\mathbf{v}}_f,\mathbf{a}={\mathbf{v}}_f\times \mathbf{L}-{\mathbf{r}}_f\mathrm{/}{r}_f,{\mathbf{p}}_{\mathrm{\infty }}=p_{\mathrm{\infty }}\frac{p_{\mathrm{\infty }}(\mathbf{L}\times \mathbf{a})-\mathbf{a}}{1+p_{\mathrm{\infty }}^2{L}^2}\mathrm{.}\backslash mathbf\; L=\backslash mathbf\; r\_f\backslash times\backslash mathbf\; v\_f,\backslash quad\backslash mathbf\; a=\backslash mathbf\; v\_f\backslash times\backslash mathbf\; L-\backslash mathbf\; r\_f/r\_f,\backslash quad\; \backslash mathbf\; p\_\backslash infty=p\_\backslash infty\backslash frac\{p\_\backslash infty(\backslash mathbf\; L\backslash times\backslash mathbf\; a)-\backslash mathbf\; a\}\{1+p\_\backslash infty^2L^2\}.$$ Writing $E=p_\infty^2/2>0$, $b=1/(2E)$ and $g=\sqrt{1+2EL^2}$, one finite Coulomb tail contribution after removal of common divergent phases is $${\tilde{\mathrm{\Phi }}}_C=-\sqrt{b}[\ln g+\mathrm{arsinh}\frac{{\mathbf{r}}_f\cdot {\mathbf{v}}_f}{g\sqrt{b}}]\mathrm{.}\backslash widetilde\backslash Phi\_C=-\backslash sqrt\; b\backslash left[\backslash ln\; g+\backslash operatorname\{arsinh\}\backslash frac\{\backslash mathbf\; r\_f\backslash cdot\backslash mathbf\; v\_f\}\{g\backslash sqrt\; b\}\backslash right].$$ This is a supported standard closure, not required notation or permission to replace the task's own launch/action identity. A declared converged equivalent continuation remains accepted. For the no-Coulomb direct reference, Xiao et al. article p.053310-2, Eqs.(7),(8), uses $M_{\mathbf p}=i\int_{t_0}^{t_f}dt,e^{i\widetilde S_{\mathbf p}(t)}\langle\mathbf p+\mathbf A(t)|\mathbf r\cdot\mathbf E(t)|\psi_0\rangle$, with $\partial_t\widetilde S_{\mathbf p}=[\mathbf p+\mathbf A(t)]^2/2+I_p$ and one common finite endpoint convention.

Scope of the source anchors

The locators identify scientific objects and mechanisms, not compulsory figure layouts, solver settings, exact grids, pointwise tolerances or a fixed evidence package. Canonical examples may be replaced by functionally equivalent evidence subject to the rubric. Source readback verifies the candidate's science; it cannot supply missing candidate presentation, identification or inference. Reporting, applicability/N/A and descriptive Research Closure duties remain those stated in the rubric and task.