| # Photon-momentum partition in direct strong-field ionization |
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| ## Physical setting |
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| Consider fixed-nucleus hydrogen exposed to a finite, right-handed circularly |
| polarized plane-wave pulse that propagates along the laboratory $z$ direction. |
| Use atomic units unless stated otherwise. Work to leading observable order in |
| $1/c$ within a direct, length-gauge nondipole strong-field approximation. |
| Rescattering and spin dynamics are outside the required scope. |
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| For the state-dependent study, use a carrier wavelength of $1400\ \mathrm{nm}$ |
| and compare the $1s$, $2s$, $2p_{m=0}$, and $2p_{m=\pm1}$ initial states. For |
| the photon-order study, use the $1s$ state at a peak intensity of |
| $10^{14}\ \mathrm{W\,cm^{-2}}$ and vary the carrier frequency over a justified |
| sequence that extends from few-photon to substantially larger absorbed-photon |
| orders. Choose a smooth finite pulse envelope and duration that resolve the |
| claims you make, and state the convention used. |
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| The primary observable is the normalized mean photoelectron momentum along |
| the propagation direction. Overall ionization yield is not a grading target. |
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| ## Research problem |
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| Determine how photon linear momentum is partitioned into longitudinal |
| photoelectron momentum during direct strong-field ionization, including its |
| dependence on the initial orbital and its evolution from finite to large |
| absorbed-photon order. Decide from moments calculated within the same physical |
| branch whether a well-defined asymptotic partition law is established. |
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| Your report must distinguish a relation established by computed observables |
| from one assumed or inserted analytically. Explain the physical origin and |
| scope of the state dependence and of any asymptotic law you infer. Limit every |
| conclusion to the direct circular-polarization branch actually studied. |
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| The task-specific derivation, numerical representation, integration strategy, |
| frequency and intensity sampling, evidence design, reliability assessment, |
| plotting choices, and report organization are for you to decide. Your evidence |
| must make the physical states, pulse |
| convention, observable definitions, and case-to-data mapping auditable. No |
| particular number, order, or layout of figures is prescribed. |
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| ## Submission and resources |
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| Submit one self-contained scientific report and an auditable offline |
| calculation package. Include the task-specific derivation, code, numerical data |
| underlying all material claims, a provenance note listing every offline source or software document actually consulted and the method basis for items supplied from general knowledge, and concise run and |
| environment information. No fixed file tree, filename scheme, numerical grid, |
| solver, window, plot range, or complete exploration history is required. |
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| Resource limits are supplied exclusively by the accompanying |
| `resource_limits.json`. Its fixed CPU allocation, candidate-active |
| wall time, network boundary are binding. No separate aggregate CPU-hour limit applies. Greater computational expense |
| receives no additional credit. |
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| ## Reference and integrity policy |
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| This examination is conducted without network access or live literature |
| retrieval. You may rely on your existing general scientific knowledge and, if any are |
| explicitly supplied with the examination, on those offline materials or |
| software documentation. Record every such source actually consulted. For formulas, |
| methods, constants, or conventions used from general knowledge rather than a |
| consulted source, state enough of the method basis, definition, value, units, |
| and convention to make the calculation auditable; do not invent a citation. |
| You are not required to identify or prove a publication date or to retrieve |
| literature during the examination. |
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| The hidden target article and its identifying metadata, figures or captions, |
| supplementary material, author code or data, target-specific reproduction |
| code, solution or scoring material, online solutions, and worked |
| reproductions of this case must not be used. All submitted scientific figures |
| and numerical data must be generated by your own implementation of the stated |
| problem. |
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| See [submission requirements](../../submission_requirements.md) for the common submission entry points. |
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