Scientific sources - Case45
References
Xu Zhang, Yueming Zhou, Yijie Liao, Yongkun Chen, Jintai Liang, Qinghua Ke, Min Li, András Csehi, and Peixiang Lu. 2022. Effect of nonresonant states in near-resonant two-photon ionization of hydrogen. Physical Review A, 106, 063114. Source.
Coherent reduced active-sector doublets and same-spectrum W/A across the given family, contribution discrimination by any physically equivalent design, and independently calculated bounded N=60 TDSE transfer. Full TDSE maps, long-duration TDSE, PAD and absolute yield are outside scope.
Criterion-to-source crosswalk
| Criteria | Source locations, scientific use and limits |
|---|---|
| F1 | Zhang et al. (2022), article pp. 063114-2–4, Eqs. (5)–(10). Adiabatic elimination, rotating-wave/local approximations, coherent active-sector amplitudes, detunings, all three Stark shifts and both losses. |
| F2 | Article pp. 063114-2, 063114-4–5, Eq. (3), Eq. (10), Fig. 2 caption and optimized-parameter paragraph after Fig. 3. Hydrogen pulse/intensity/cycle and energy-normalized continuum bindings, plus same-spectrum spacing/asymmetry. Source optimized coefficients, not separately rescaled example code, define the given reduced model. |
| F3 | Article p. 063114-2, Eqs. (1)–(4), TDSE continuum-extraction paragraphs. Independent hydrogen TDSE and PES mapping; gauge/basis/projection equivalents are accepted, without mandating FEDVR or the author mask. |
| O1 | Article p. 063114-5, Fig. 3(a,b) and caption; p. 063114-4, W/A definitions after Fig. 2. N=60/300 principal doublets, not dynamic subpeak pairing; both metrics come from the same declared spectrum. |
| O2, I1, I2 | Article p. 063114-4, Fig. 2(a–d); pp. 063114-5–6, Fig. 4(a–d) and captions. Spacing/asymmetry response across two intensities and pulse lengths, with a discriminating contrast. Source N=120 and complete TDSE maps are not compulsory task outputs. |
| O3, I4 | Article pp. 063114-4–5, Fig. 1(a), Fig. 3(a), captions and comparison discussion; TDSE Eqs. (1)–(4), p. 063114-2. Independent N=60 same-domain doublet/transfer evidence. Source Fig. 3(b) long-pulse TDSE is not required; no unique local-frequency scan is imposed. |
| I3, V1 | Article pp. 063114-5–6, Fig. 4(a–d), direct-path comparison and interpretation paragraphs. Candidate identification and physical validity of a contribution-discriminating intervention; the source direct-path-off switch is one optional route, not the criterion itself. |
| M1, M2 | Article pp. 063114-5–6, Eq. (11), Fig. 4(a,b), spacing-minimum and direct-path paragraphs. Initial/resonant Stark difference primarily controls spacing; direct-path spacing effect is comparatively weak in the studied family. |
| M3 | Article pp. 063114-5–6, Eqs. (12)–(14), Fig. 4(c,d) and symmetry discussion. Stark phases and coherent direct/resonant continuum competition explain asymmetry, not an incoherent probability sum. |
| M4, M5 | Article p. 063114-6, intensity-dependence and pulse-frequency-width paragraphs; Figs. 2(a–d), 4(a–d), pp. 063114-4–5. Intensity strengthens shift/path effects; pulse duration changes the finite-pulse response and asymmetry minimum, with mechanism links required rather than a list of numbers. |
| M6, M7 | Article pp. 063114-4–6, Figs. 1–4 and model/TDSE discussion. Task-defined bounded transfer judgment uses independent same-domain N=60 evidence; a central-doublet conclusion and a broader morphology/response conclusion remain separately judgeable. |
| V2 | Article p. 063114-2, TDSE continuum-extraction paragraph; pp. 063114-4–5, principal/dynamic-peak and normalization discussion. Task-defined triggered transfer risks from boundary/projection/continuum resolution or unsupported excluded-domain claims. No mandatory full TDSE scan, long-duration calculation or PAD test. |
| V3 | Article pp. 063114-2–4, method separation; Fig. 3(a), p. 063114-5. Positive identification of actual reduced-model and bounded N=60 TDSE domain, independent of broader transfer success; not a second charge for an overclaim owned by V2. |
Formula and convention notes
Let $f(t)=E_0g(t)/2$, $\Delta=\omega-(E_R-E_I)$, $\delta=E_R-E_\varepsilon+\omega$ and $\delta_I=E_I-E_\varepsilon+2\omega$. The active equations are $i\dot a_I=(S_I-i\Gamma_I/2)a_I+D_{IR}f e^{i\Delta t}a_R$, $i\dot a_R=D_{IR}f e^{-i\Delta t}a_I+(S_R-i\Gamma_R/2)a_R$, $i\dot a_\varepsilon=\widetilde M_{I\varepsilon}^\dagger f^2e^{-i\delta_It}a_I+D_{R\varepsilon}f e^{-i\delta t}a_R+S_\varepsilon a_\varepsilon$ (Eq. (9)). The two continuum sources add coherently before squaring.
$\Gamma_R=2\pi|D_{R\varepsilon}|^2 f^2$, $\Gamma_I=2\pi|\widetilde M_{I\varepsilon}|^2f^4$, $S_I=S_{I0}E_0^2g^2$, $S_R=S_{R0}E_0^2g^2$, $S_\varepsilon=U_p=E_0^2g^2/(4\omega^2)$ (Eq. (10)). $D$ are one-photon dipoles and $\widetilde M$ the effective nonresonant two-photon matrix element; $S$ are instantaneous energy shifts, not assigned causal conclusions. The task-supplied article coefficients remain binding.
For energy-normalized $P(\varepsilon)=|a_\varepsilon(t_f)|^2$ and the two principal peaks at $\varepsilon_L<\varepsilon_H$ with heights $S_L,S_H$, $W=\varepsilon_H-\varepsilon_L$ and source asymmetry $A=|S_L-S_H|/\max(S_L,S_H)$ (p. 063114-4). A declared invertible equivalent asymmetry is acceptable; metrics must not use a different pulse, separately rescaled spectrum or pair of dynamic subpeaks.
Under the source Stark-only analytic reduction, $\widetilde\Omega(t)\simeq\sqrt{[D_{IR}E_0g]^2+[\Delta+S_I-S_R-i\Gamma_R/2]^2}$ (Eq. (11)). It explains a mechanism domain, not an exact finite-pulse peak formula. Independent TDSE uses $i\partial_t\psi=[-\nabla^2/2-1/r-i\mathbf A(t)\cdot\nabla]\psi$ (Eq. (2)); a mapped length-gauge/continuum extraction is equally acceptable.
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.