{"paper":{"title":"Relativistic $<\\sigma v_\\text{rel}>$ in the calculation of relics abundances: a closer look","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP","nucl-th"],"primary_cat":"astro-ph.CO","authors_text":"M. Cannoni","submitted_at":"2013-11-18T19:33:42Z","abstract_excerpt":"In this paper we clarify the relation between the invariant relativistic relative velocity $V_\\text{r}$, the M\\o{}ller velocity $\\bar{v}$, and the non-relativistic relative velocity $v_r$. Adopting $V_{\\text{r}}$ as the true physical relative velocity for pair-collisions in a non-degenerate relativistic gas, we show that in the frame co-moving with the gas (i) the thermally averaged cross section times relative velocity $<\\sigma v_\\text{rel}>$ that appears in the density evolution equation for thermal relics is reformulated only in terms of $V_\\text{r}$ and $\\mathcal{P}(V_{\\text{r}})$ in a man"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4508","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"}