# Scientific Sources — Case15

## References

Zhao-Han Zhang and Feng He. 2021. *Photoionization of H₂⁺ beyond the dipole approximation with zeptosecond time resolution*. *Physical Review A*, 103, 033112. [Source](https://doi.org/10.1103/PhysRevA.103.033112)

Photoionization of H₂⁺ beyond the dipole approximation with zeptosecond time resolution

## 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 | Zhang and He (2021), article pp.033112-2-3, Eqs.(1),(4)-(9): light-cone nondipole amplitude, gerade initial molecular state and weak-field LCAO limit with field-free Ip matching. |
| F2 | Zhang and He (2021), article p.033112-2, Eqs.(2),(3) and 2D soft-core/energy-matching paragraphs: independent fixed-nuclei TDSE. Article p.033112-4 Fig.3 caption explicitly uses A0=1.0 for TDSE and 0.01 for NSFA. |
| F3 | Zhang and He (2021), article p.033112-3, longitudinal-marginal paragraphs and stationary central-peak definition; Eq.(9),(10) for angular branch. The central maximum is not generally a mean. |
| F4, M1, M3 | Zhang and He (2021), article pp.033112-2-3, Eqs.(4)-(12), and p.033112-4 bound-state phase paragraph: light-front interference phase includes photon momentum and Ip, with separated asymptote (Ek+Ip)/c. |
| O1, I1, M2 | Zhang and He (2021), article pp.033112-3-4, Fig.2(a,b), Eq.(9), compact-density/diffraction discussion: broad compact R=2 signal versus dense R=10 two-centre fringes and propagation-direction displacement. |
| O2, I2, M5 | Zhang and He (2021), article pp.033112-3-5, Eqs.(10)-(12), Fig.3 and compact/separated interpretation: stable central branch approaches omega/c at large separation; a hidden switch to another lobe does not establish timing. |
| O3, I3, M4 | Zhang and He (2021), article p.033112-5, Fig.5, caption and projected R*cos(beta) paragraph: orientation-dependent central angular signal at R=2 and 10. Orientation may use the weak-field branch; an off-axis TDSE must rotate the geometry consistently. |
| O4, M6 | Zhang and He (2021), article p.033112-4, Fig.3 caption and NSFA/TDSE comparison paragraph: distinct-amplitude models agree in structural single-photon central shift, not pointwise matched-intensity spectra. |
| M7, V1, V2 | Zhang and He (2021), article pp.033112-2-5, effective-dimensional fixed-nuclei model, compact/separated discussion and Sec.IV: relative timing remains molecular-state/branch dependent. Extraction alternatives and claim limits are task-defined; no universal absolute clock or source transition coordinate is compulsory. |

## Formula and convention notes

For F1/F4/M1/M3-M4, article pp.033112-2-3, Eqs.(4)-(9), the nondipole canonical momentum is
$$\mathbf q(\eta)=\mathbf p+\mathbf A(\eta)-\frac{p^2/2+I_p}{c}\mathbf n,\qquad \eta=t-\mathbf n\cdot\mathbf r/c.$$
The weak-field gerade interference factor contains $1+\cos[pR\cos\alpha-kR]$, $k=\omega/c$, with the full molecular envelope retained. Thus the separated central phase gives $p\cos\alpha_0\to\omega/c$, using $\omega=E_k+I_p$, not only $E_k/c$. At angle beta to propagation, the light-front geometric separation is $R\cos\beta$. A delay inferred from this phase must retain its energy and branch conventions; the envelope shifts a compact central maximum away from a pure interference maximum. Source Eq.(3) is attractive; the subsequently typeset soft-core model must retain negative attractive terms even where its prose formula omits signs.

## 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.