{"paper":{"title":"The effect of energy amplification variance on the shock-acceleration","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Junichi Aoi, Kohta Murase, Shigehiro Nagataki","submitted_at":"2007-11-18T08:00:53Z","abstract_excerpt":"The shock-acceleration theory predicts a power-law energy spectrum in the test particle approximation, and there are two ways to calculate a power-law index, Peacock's approximation and Vietri's formulation. In Peacock's approximation, it is assumed that particles cross a shock front many times and energy-gains for each step are fully uncorrelated. On the other hand, correlation of the distribution of an energy-gain factor for a particle is considered in Vietri's formulation. We examine how Peacock's approximation differs from Vietri's formulation. It is useful to know when we can use Peacock'"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.2772","kind":"arxiv","version":1},"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"}