Scientific Sources — Case30
References
A. W. Bray, S. Eckart, and A. S. Kheifets, Keldysh-Rutherford Model for the Attoclock, Physical Review Letters 121, 123201 (2018).
Scattering-angle identities, weak-field assumptions, equal-binding screened potentials, screening-dependent response, and the limits of the classical interpretation. Quantum and CTMC results provide context; they are not required candidate calculations or pointwise targets.
Relevant locations
pp. 123201-1–2, Eqs. (1)–(6), Fig. 1
p. 123201-3, Eq. (9), Fig. 3
pp. 123201-3–4, Fig. 4 and adjacent screening/applicability discussion
pp. 123201-4–5, Fig. 5 and conclusion; quantum/real-atom context only
Criterion-to-source crosswalk
| Criteria | Source locations, scientific use and limits |
|---|---|
| F1 | Bray, Eckart and Kheifets (2018), pp. 123201-1–2, Eqs. (1), (2), (4)–(6), Fig. 1; intensity convention on p. 123201-3, Eq. (9). |
| F2 | Bray et al. (2018), pp. 123201-2–4, Eqs. (2)–(6), (9), Figs. 3–4. Reconstructible submission and branch-separation requirements follow the stated examination task, not a source-specific file convention. |
| F3 | Bray et al. (2018), pp. 123201-3–4, Fig. 4 discussion: each screened target retains hydrogen binding energy $I_p=0.5$. |
| F4 | Bray et al. (2018), pp. 123201-1–2, Eqs. (1), (3) and physical-root discussion; omitted correction acknowledged adjacent to Eq. (3). |
| O1 | Bray et al. (2018), pp. 123201-2–3, Eqs. (2), (4)–(6), Fig. 3 (classical branches only). |
| O2 | Bray et al. (2018), pp. 123201-3–4, Fig. 4 and adjacent equal-binding/range-response discussion (robust structure, not pointwise matching). |
| O3 | Bray et al. (2018), p. 123201-4, Fig. 4 comparison and classical-applicability discussion. |
| I1 | Bray et al. (2018), pp. 123201-2–3, Eqs. (5)–(6), Fig. 3 and intensity-scaling discussion. |
| I2 | Bray et al. (2018), p. 123201-4, Fig. 4 and adjacent tunnel-width versus screening-length explanation. |
| I3 | Bray et al. (2018), p. 123201-4, Fig. 4 discussion of wavelength/range competition; p. 123201-2, Eq. (4) and weak-field assumptions. Equivalent scale arguments are accepted by the examination criteria. |
| M1 | Bray et al. (2018), p. 123201-2, Eqs. (2), (4)–(6) and kinetic/potential scale explanation. |
| M2 | Bray et al. (2018), pp. 123201-2, 123201-4, Eq. (3), Fig. 4 and exit-width/range competition. |
| M3 | Bray et al. (2018), p. 123201-4, Fig. 4 and conclusion: smooth transition across screening, not a universal inference from $\lambda=1$. |
| M4 | Bray et al. (2018), p. 123201-4, Fig. 4 classical-versus-quantum applicability discussion; p. 123201-2, Eq. (4) assumptions. Functionally equivalent validity arguments are examination acceptance routes. |
| M5 | Bray et al. (2018), p. 123201-4, Fig. 4 range dependence and conclusion. |
| M6 | Bray et al. (2018), pp. 123201-1–2 and 123201-4–5, model assumptions, Fig. 4 discussion and conclusion. |
| M7 | Bray et al. (2018), p. 123201-1 abstract and pp. 123201-4–5 conclusion; Fig. 5 is context for target-specific testing, not required CTMC reproduction. |
| V1 | Bray et al. (2018), pp. 123201-1–2, Eqs. (1)–(4), and p. 123201-4, Fig. 4; risk-triggered award and N/A treatment are examination scoring rules, not claims made by the article. |
| V2 | Bray et al. (2018), p. 123201-2, Eq. (4), barrier-suppression and weak-field assumptions; p. 123201-4, Fig. 4 quantum-applicability discussion, Fig. 5 and conclusion. Risk-triggered scoring is an examination rule. |
| V3 | Bray et al. (2018), pp. 123201-3–5, TDSE/iSURF description, Figs. 4–5 and conclusion; examination task explicitly excludes regenerating TDSE/iSURF and CTMC. |
Formula and convention notes
The commissioned observable is the outgoing half-deflection of post-release central-potential scattering. For an attractive potential, $\theta=2\int_{r_0}^{\infty}\frac{\rho/r^2}{\sqrt{1-(\rho/r)^2-2V(r)/v_\infty^2}},dr-\pi$, with r0 the physical closest-approach root; $\theta_A=\theta/2$, with a declared consistent sign convention.
For Coulomb scattering $\tan(\theta/2)=Z/(v_\infty^2\rho)$, $v_\infty=A_0=E_0/\omega$, and $\theta_A=\arctan[Z/(A_0^2\rho)]$. The full deflection is not the attoclock offset. $\omega=0.057$, $I_p=0.5$ and $I=2E_0^2$ are the stated atomic-unit conventions.
With $\rho\approx I_p/E_0$ and the small-angle approximation, $\theta_A\approx\omega^2Z/(E_0 I_p)$, hence $I^{-1/2}$. The kinetic scale $v_\infty^2/2$ grows as I; the Coulomb potential scale $Z/\rho$ grows as $I^{1/2}$, yielding the linked scaling. Finite-angle or exact-exit departures must be distinguished from a false observable.
The exact Coulomb outer exit solves $Z/r+E_0r=I_p$: $r_{\mathrm{out}}=I_p/(2E_0)+\sqrt{I_p^2/(4E_0^2)-Z/E_0}$. The double-root barrier threshold is $E_{\mathrm{BSI}}=I_p^2/(4Z)$, equal to 0.0625 for the Coulomb reference. Low gamma alone does not establish the separate sub-barrier or weak-field condition; this Coulomb threshold is not a universal screened-target threshold.
For the leading screened approximation, $\tan(\theta/2)=Z_\lambda e^{-1/z_0}/(v_\infty^2\rho)$, with z0 the physical root of $1-(\rho/\lambda)^2z^2-(d/\lambda)z e^{-1/z}=0$ and $d=2Z_\lambda/v_\infty^2$. This approximation is an accepted route, not the only allowed implementation; direct classical integration is also accepted.
The required family includes the Coulomb limit, $\lambda=1$ and enough candidate-chosen intermediate lengths to test transfer. No fixed intermediate list, charge table, intensity grid, radial discretization, solver, tolerance, figure count, panel order, plotting range or source curve style is prescribed.
Scope of the source anchors
Scattering-angle identities, weak-field assumptions, equal-binding screened potentials, screening-dependent response, and the limits of the classical interpretation. Quantum and CTMC results provide context; they are not required candidate calculations or pointwise targets.