{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"53770519122858ce6eed8fbeca587a64041abba9eeeb9da84f8ab90dcbb0578e","created":"2026-10-03T07:17:56Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"b43a1ad45221596b0c4b93224476b1ece9e10e2fe27ef55ef7e2dcd16394eb82","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"beams.beam-brightness.quantum-degenerate-beams","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Even in the best beams, far fewer than one electron occupies each smallest quantum cell of position and momentum; reaching about one per cell would allow quantum-optics experiments with free electrons.","posed_since":"","precise":"The degeneracy $\\delta$ is the mean number of electrons per phase-space cell of volume $h^{3}$ (per spin state), proportional to the 6D normalized brightness. Determine whether any free-electron source (cold field emitter, laser-triggered nanotip, cryogenic photocathode) can reach $\\delta \\ge 0.1$ over a pulse, and identify what limits it (Coulomb heating, Boersch energy broadening, emitter temperature).","problem_ref":null,"references":"","settled_by":"A measured 6D phase-space density of a pulsed source giving $\\delta \\ge 0.1$, or a bound from Coulomb heating that excludes it.","status_note":"","title":"Free-electron beams with quantum degeneracy approaching one","topic_ref":"3311684a3644100d5c4072cc7fb5698b312b296ec8b7139e230fbc39301d2361"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"e40ec95f47779b0b4257f77cd05430d7eed11f712ec815fed72ec3bc38919ed2","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"c3b83db537a8c38e74d4a5f50af5dd44a2b857752d6790ec74f604b07138c970","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"mBkWspv5o_qUdD_QZZZ14Tt5xCP7SRIm5lBqrFO3szqhq8XQMw4Rtjy22HGh8BVnkQwZ72kGgvj_JKyTqvF_BA"},"schema":"pubphys.envelope/1"},"record_hash":"e40ec95f47779b0b4257f77cd05430d7eed11f712ec815fed72ec3bc38919ed2","leaf_index":647}