{"paper":{"title":"Leading Relativistic Corrections to the Kompaneets Equation","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["physics.plasm-ph"],"primary_cat":"astro-ph.CO","authors_text":"Dean L. Preston, Lowell S. Brown","submitted_at":"2012-01-26T19:03:06Z","abstract_excerpt":"We calculate the first relativistic corrections to the Kompaneets equation for the evolution of the photon frequency distribution brought about by Compton scattering. The Lorentz invariant Boltzmann equation for electron-photon scattering is first specialized to isotropic electron and photon distributions, the squared scattering amplitude and the energy-momentum conserving delta function are each expanded to order v^/c^4, averages over the directions of the electron and photon momenta are then carried out, and finally an integration over the photon energy yields our Fokker- Planck equation. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5606","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}