Scientific sources - Case46
References
Noslen Suárez, Alexis Chacón, Marcelo F. Ciappina, Jens Biegert, and Maciej Lewenstein. 2015. Above-threshold ionization and photoelectron spectra in atomic systems driven by strong laser fields. Physical Review A, 92, 063421. Source.
Fixed-parameter short-range SFA complex b0/b1 engine shared by longitudinal CEP and polarization-plane components. Source manuscript page numbers are used explicitly; task-visible B/g/parameter corrections govern, and TDSE/Coulomb quantitative comparisons are excluded.
Criterion-to-source crosswalk
| Criteria | Source locations, scientific use and limits |
|---|---|
| F1 | Suárez et al. (2015), author manuscript pp. 5, 8–9, Eqs. (1), (11)–(13) and endpoint/envelope paragraph. Electric-field CEP identity and integrated vector potential. The waveform is E, not A; a direction convention fixes the asymmetry sign. |
| F2 | Author manuscript pp. 8–15, Eqs. (12)–(18), (26), (28), (31)–(37). Complex direct/single-rescattered engine, action, saddle, dipole and continuum element. The visible task fixes the source ambiguities: negative B, 2 Gamma-squared numerators and independent Gamma/gamma inputs; source Eq. (25) does not override them. |
| F3 | Author manuscript p. 10, Eq. (15); p. 19, Eq. (38); p. 23, Fig. 6(a–d). Signed amplitude interference, common-normalization total and longitudinal left/right definition; reconstructible component reporting is task-defined. |
| O1, I1 | Author manuscript pp. 19–21, Eq. (38), Fig. 3 and Fig. 4(a,b). CEP-dependent directional asymmetry and high-energy sign under the stated left/right convention, not source pixels or a mandatory phase grid. |
| O2, I2 | Author manuscript pp. 16–17, Fig. 1(a,b); p. 21, Fig. 4(a,b); Eq. (15), p. 10. Direct-low/rescattered-high hierarchy and coherent contribution. Classical 2 Up/10 Up scales are broad anchors, not exact numerical cutoff thresholds. |
| O3 | Author manuscript pp. 23–24, Fig. 6(a,b) and component interpretation paragraph. Central direct ATI and outer rescattering support in the polarization plane; these are SFA components, not the TDSE panel in Fig. 5(b). |
| O4, I3 | Author manuscript pp. 23–24, Fig. 6(c,d), Eq. (15), p. 10. Signed texture and coherent total preserve transverse reflection and CEP-compatible longitudinal imbalance. The task explicitly requires both interference signs; the source logarithmic display cannot erase this identity. |
| M1, M3, M4 | Author manuscript pp. 20–21, Fig. 3, Fig. 4(a,b), waveform/phase and birth-return paragraphs; Eqs. (12)–(17), pp. 8–11. Waveform CEP alters event timing and phases, leading to directional coherent response; source vector-potential phase mislabelling is not an equivalent explanation. |
| M2 | Author manuscript pp. 8–15, Eqs. (12), (14), (17), (28), (37); pp. 16–17, Fig. 1(a,b). Bound-free and continuum-continuum weighting of direct/return pathways and their energy-domain support. |
| M5, M6 | Author manuscript pp. 23–24, Fig. 6(a–d), same-engine component paragraphs; Eq. (15), p. 10. One engine assembles the 2D total; signed/common-scale relations distinguish it from incoherent or independently normalized panels. |
| M7, M8 | Author manuscript pp. 19–24, Figs. 3, 4(a,b), 6(a–d); action/amplitude chain Eqs. (12)–(18). Task-defined cross-domain compatibility and bounded causal synthesis, not proof of exact Coulomb or TDSE behavior. |
| V1 | Author manuscript p. 5, low-ionization SFA paragraph; pp. 22–24, potential/low-energy limitations and conclusion. Fixed short-range first-rescattering SFA scope; source Fig. 5(b) TDSE comparison is excluded and no target inversion is established. |
| V2 | Author manuscript pp. 8–15, Eqs. (12)–(18), (28), (33), (37); p. 19, Eq. (38). Task-defined conditional phase, matrix-element, aliasing, denominator-mask and normalization risks; no unique mesh or preferred check is required. |
Formula and convention notes
$\mathbf E(t)=E_0\sin^2[\omega t/(2N_c)]\sin(\omega t+\phi)\hat{\mathbf z}$, $\mathbf A(t)=-\int_0^t\mathbf E(s)ds$ and $U_p=E_0^2/(4\omega^2)$ (source Eq. (1) and pulse paragraph; stated $N_c=4$). $A(0)=A(t_f)=0$ binds the canonical/final kinetic momentum. Directly substituting the supplied E waveform as A changes the physical CEP case.
$S(\mathbf p,t,t\prime)=\int_{t\prime}^t[(\mathbf p+\mathbf A(s))^2/2+I_p]ds$, $\mathbf p_s=-(t\prime-t\prime\prime)^{-1}\int_{t\prime\prime}^{t\prime}\mathbf A(s)ds$ (Eqs. (13), (16)); $b_0=i\int_0^{t_f}dt\prime,\mathbf E(t\prime)\cdot\mathbf d[\mathbf p+\mathbf A(t\prime)]e^{-iS(\mathbf p,t_f,t\prime)}$. The source single-return Eq. (17) retains both excursion actions, the matrix element $\mathbf g$ and complex diffusion factor $[\pi/(\varepsilon+i(t\prime-t\prime\prime)/2)]^{3/2}$; omitting their relative phase is not equivalent.
The visible benchmark resolves the printed source branches by $B(\mathbf q)=-2\gamma(q^2+\Gamma^2)^{-1/2}[1-4\pi^2i\gamma/(|\mathbf q|+i\Gamma)]^{-1}$ and the stated $2\Gamma^2$ numerators of $\mathbf g$, with $\Gamma=1$, $\gamma=38$, $\epsilon=0.2$ independent fixed inputs. These are task-defined formula identities, not a demand to reproduce the conflicting signs/powers in source Eqs. (25), (33), (37).
The bound-free identity is $\mathbf d(\mathbf q)=i\mathcal N\mathbf q[(q^2+\Gamma^2)+(q^2/2+I_p)]/[(q^2+\Gamma^2)^{3/2}(q^2/2+I_p)^2]$, $\mathcal N^2=\sqrt{2I_p}(\Gamma+\sqrt{2I_p})^2/(4\pi^2)$ (Eqs. (26), (28)). The fixed continuum element is $\mathbf g_{12}=iB_2\mathbf q_1(3q_1^2-q_2^2+2\Gamma^2+i\epsilon)/[(q_1^2+\Gamma^2)^{3/2}(q_2^2-q_1^2-i\epsilon)^2]-iB_1^*\mathbf q_2(3q_2^2-q_1^2+2\Gamma^2-i\epsilon)/[(q_2^2+\Gamma^2)^{3/2}(q_1^2-q_2^2+i\epsilon)^2]$, $B_j=B(\mathbf q_j)$ (task-fixed reading of Eq. (37)). Here $\Gamma$ is the potential shape scale, $\gamma$ its independent coupling input and $\epsilon$ the declared pole regularization; none is the Keldysh parameter.
$P_{\rm tot}=|b_0+b_1|^2=|b_0|^2+|b_1|^2+2\operatorname{Re}(b_0b_1^*)$ and $\mathcal A=(P_--P_+)/(P_-+P_+)$ (Eqs. (15), (38)), where minus/plus mean negative/positive longitudinal momentum at the same energy. The cross term is signed; its absolute value or independently normalized components are different objects. At a vanishing denominator the asymmetry is undefined, requiring a declared claim-adequate domain rather than artificial extreme values.
Scope of the source anchors
Source examples verify physical identity and robust structure; their numerical samples, plotting conventions and panel layout are not compulsory candidate deliverables. Reporting, reconstructibility, evidence attribution, conditional validation and Research Closure are examination-defined obligations, not additional results asserted by the article. A derivation or physical entailment is identified as such rather than presented as a directly printed source formula.