Scientific sources - Case41
References
Pei-Lun He, Michael Klaiber, Karen Z. Hatsagortsyan, and Christoph H. Keitel. 2022b. Nondipole Coulomb sub-barrier ionization dynamics and photon momentum sharing. Physical Review A, 105, L031102. Source.
Three-state launch weighting and two Ar-channel asymptotic comparison under the leading-order light-front model. Canonical topology plots are optional equivalents; source Fig. 4/TDSE average-slope claims are outside the quantitative grading scope.
Criterion-to-source crosswalk
| Criteria | Source locations, scientific use and limits |
|---|---|
| F1 | He et al. (2022), article p. L031102-2, Eqs. (2)–(4); SI p. 3, Eqs. (S21)–(S25). State-resolved Coulomb/PPT launch measure and spherical-harmonic weights; statewise constants may cancel in normalized moments but momentum-dependent factors may not. |
| F2 | Article p. L031102-2, exit statement after Eq. (6); SI pp. 1–5, Eqs. (S7), (S9), (S15), (S24)–(S25), (S37)–(S39). Saddle exit, launch momentum and probability weights; short-range launch removes sub-barrier Coulomb contributions, not the angular-state identity. |
| F3 | Article p. L031102-2, Eqs. (5)–(6); SI pp. 6–7, Eqs. (S54)–(S60) and Kepler-projection paragraph. Common launch for full/sub-barrier-only propagation, correct negative longitudinal quadratic term, field-off Kepler map and asymptotic momentum. |
| O1, I1 | Article pp. L031102-2–3, Fig. 1(a–f), Eqs. (7)–(8); SI p. 3, Eq. (S25). Three-state launch-policy response and angular-weighting signatures. Canonical one-/two-lobe marginals are not the only valid representation. |
| O2, I2, M4 | Article pp. L031102-3–4, Fig. 3(a), caption and continuum discussion; SI p. 7, Eqs. (S58)–(S65). Ar(3p,m=1) full/sub-barrier-only field response and retained/reshaped birth information; nonadiabatic additional curves are not compulsory. |
| O3, I3, M5 | Article pp. L031102-3–4, Fig. 3(b), caption and continuum discussion; SI p. 7, Eqs. (S58)–(S65). Distinct Ar(3p,m=0) channel and nonmonotonic structure; do not exchange the two magnetic channels or impose a capture-sensitive exact endpoint. |
| M1, M2, M3 | Article p. L031102-3, Fig. 2(a–c), ionization-window and bound-state-matching paragraphs; SI pp. 3–5, Eq. (S25), Sec. I A 7, Fig. S1. Nondipole window, Coulomb action and angular prefactor jointly reweight the launch ensemble. An attraction slogan or one mean without claim-relevant weighting evidence is insufficient. |
| M6, M7, M8 | Article pp. L031102-2–4, Figs. 1(a–f), 3(a,b), Eq. (6); SI p. 7, Eqs. (S58)–(S60). Task-defined causal synthesis distinguishes changing launch policy from changing post-exit propagation and establishes state-dependent continuum reshaping. |
| V1, V2 | SI p. 3, Eq. (S24); p. 7, Eq. (S58), field-off Kepler statement; article Fig. 3(a,b), p. L031102-4. Same-weight branch/sign/normalization and asymptotic-identity alternatives. V1 positive claim-relevant discrimination and V2 triggered risks remain distinct task roles; no unique check is prescribed. |
| V3 | Article p. L031102-2, leading-1/c validity paragraph; p. L031102-4, Fig. 3(c), Fig. 4 and conclusion. Leading-order direct-tunnelling scope. Fig. 4 slope/TDSE comparison is excluded as a quantitative endpoint; it cannot supply required closure. |
Formula and convention notes
$p_-=p_z-p^2/(2c)$, $\kappa=\sqrt{2I_p}$, $\nu=Z/\kappa$, $\widetilde\kappa^2=\kappa^2+v_\perp^2+\widetilde p_z^2$. The weighted launch measure is $d\mu=\Gamma_{nlm}d\eta,dv_\perp,d\widetilde p_z$ with $\Gamma_{nlm}=(\kappa/\widetilde\kappa)2^{2\nu+2}C_{\kappa l}^2\kappa^{6\nu}|Y_{lm}(\widetilde{\mathbf p}s)|^2[(1-\widetilde p_z/c)^{2\nu}E^{2\nu}]^{-1}\exp[-2\widetilde\kappa^3/{3E(1-\widetilde p_z/c)}]$ (SI Eq. (S24)). $E=|\mathbf E(\eta)|$ and $C{\kappa l}$ is the statewise asymptotic normalization. Constants cancel only within a state/policy normalization; angular and momentum weights do not.
The task saddle map is $\mathbf x_e=-\widetilde\kappa^2\mathbf E/[2(1-\widetilde p_z/c)E^2]$, $\mathbf p_\perp^e=\mathbf v_\perp-\mathbf A_\perp$, $p_-^e=\widetilde p_z+I_p/c$. Weighted final means use the same launch weights. Full and sub-barrier-only branches share this Coulomb-corrected ensemble; only the post-exit potential is changed to $V=0$ for sub-barrier-only. That branch is not the short-range-launch control.
Writing $q=p_-+V/c$ and $\boldsymbol\pi_\perp=\mathbf p_\perp+\mathbf A_\perp$, SI Eq. (S58) gives $dz/d\eta=[q+(-q^2+|\boldsymbol\pi_\perp|^2)/(2c)]/(1-q/c)^2$. The minus sign on $q^2$ is essential. After field-off, outgoing Coulomb trajectories require the asymptotic Kepler map; the instantaneous canonical momentum is not automatically the asymptotic mechanical momentum.
As leading quasistatic checks only, $\langle p_-\rangle_s=(I_p/c)[1/3+(2\nu-1)E_0/E_a]$ and $\langle p_-\rangle_{p,m=0}=(I_p/c)[-1+(6\nu-5)E_0/E_a]$, $E_a=\kappa^3$ (Eqs. (7)–(8)). They do not replace complete state/policy weighted evidence and do not prove exact relativistic or multielectron dynamics.
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.
Supplemental Material to the article: official supplement. Supplement locators above refer to its own numbered pages and equations.