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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.26126 |
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| _version_ | 1866914608343678976 |
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| author | Boumali, Abdelmalek |
| author_facet | Boumali, Abdelmalek |
| contents | We generalize Tweed's seminal Born~I formalism for the electron-impact double ionization of two-electron atomic systems ($\text{H}^-$, $\text{He}$, $\text{Li}^+$) to non-extensive plasma environments described by Tsallis $q$-statistics. The bare Coulomb interaction is replaced by a $q$-deformed screened potential, which introduces a unique form factor envelope into the momentum-transfer integrations. We rederive the differential, partial, and total cross sections, demonstrating that this screening regularizes the classical high-energy Bethe logarithm and, in the $q < 1$ regime, induces diffraction-like oscillations in the angular cross sections. The model is calibrated against digitized historical experimental data to quantify how non-extensive screening deforms the vacuum baseline. Finally, coupling these cross sections to a $q$-Maxwellian distribution yields the macroscopic rate coefficients and reveals a novel subextensive critical-temperature threshold below which ionization is energetically forbidden. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26126 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Extensive Generalization of Double Ionization by Electron Impact: Calculations of Both Cross Sections and Rate Coefficients for $\text{H}^-$, $\text{He}$, and $\text{Li}^+$ Boumali, Abdelmalek General Physics We generalize Tweed's seminal Born~I formalism for the electron-impact double ionization of two-electron atomic systems ($\text{H}^-$, $\text{He}$, $\text{Li}^+$) to non-extensive plasma environments described by Tsallis $q$-statistics. The bare Coulomb interaction is replaced by a $q$-deformed screened potential, which introduces a unique form factor envelope into the momentum-transfer integrations. We rederive the differential, partial, and total cross sections, demonstrating that this screening regularizes the classical high-energy Bethe logarithm and, in the $q < 1$ regime, induces diffraction-like oscillations in the angular cross sections. The model is calibrated against digitized historical experimental data to quantify how non-extensive screening deforms the vacuum baseline. Finally, coupling these cross sections to a $q$-Maxwellian distribution yields the macroscopic rate coefficients and reveals a novel subextensive critical-temperature threshold below which ionization is energetically forbidden. |
| title | Non-Extensive Generalization of Double Ionization by Electron Impact: Calculations of Both Cross Sections and Rate Coefficients for $\text{H}^-$, $\text{He}$, and $\text{Li}^+$ |
| topic | General Physics |
| url | https://arxiv.org/abs/2605.26126 |