{"product_id":"thomsonia-thomson-cross-section","title":"Thomsonia – Thomson Cross Section \/ σ = 8πr²\/3 Physics Sticker","description":"\u003cp\u003eThomsonia, an archery-target guardian of the early Universe in The SI Guard, turns photons aside with her shield and sends them off the same colour.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eWhen light meets a free electron at low energy, its electric field shakes the electron, which re-radiates at the same frequency. This elastic scattering has a fixed total cross section, the effective target area of one electron. It is J. J. Thomson's classical result, and it is the low-energy limit of quantum electrodynamics.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eσ\u003csub\u003eT\u003c\/sub\u003e = (8π\/3) r\u003csub\u003ee\u003c\/sub\u003e² = 6.652 458 7051(62) × 10⁻²⁹ m²\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eσ\u003csub\u003eT\u003c\/sub\u003e: Thomson cross section\u003c\/li\u003e\n\u003cli\u003er\u003csub\u003ee\u003c\/sub\u003e: classical electron radius, e²\/(4πε\u003csub\u003e0\u003c\/sub\u003em\u003csub\u003ee\u003c\/sub\u003ec²) = 2.817 940 3205(13) × 10⁻¹⁵ m\u003c\/li\u003e\n\u003cli\u003ee: elementary charge (exact)\u003c\/li\u003e\n\u003cli\u003eε\u003csub\u003e0\u003c\/sub\u003e: vacuum permittivity (measured)\u003c\/li\u003e\n\u003cli\u003em\u003csub\u003ee\u003c\/sub\u003e: electron mass (measured)\u003c\/li\u003e\n\u003cli\u003ec: speed of light (exact)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eValues: CODATA 2022 (NIST); both are measured, not exact. Thomson scattering kept light and matter locked together in the hot early Universe until hydrogen formed, about 380 000 years after the Big Bang; it also sets the Eddington luminosity of stars.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e r\u003csub\u003ee\u003c\/sub\u003e is not the electron's size. It is a length built from its charge and mass; experiments find no electron structure at all down to far smaller scales. The formula holds only for photon energies much less than m\u003csub\u003ee\u003c\/sub\u003ec² ≈ 511 keV; at higher energies the Klein–Nishina cross section takes over and the scattered photon loses energy (Compton scattering).\u003c\/p\u003e\u003ch3\u003eOn the sticker\u003c\/h3\u003e\u003cp\u003eThomsonia raises her shield, and a burst of cyan photon orbs scatters off it unchanged in colour. Printed text: \u003cstrong\u003eTHOMSONIA\u003c\/strong\u003e with the line \u003cstrong\u003eσ = 8πr²\/3\u003c\/strong\u003e. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"2\" × 2\" \/ White","offer_id":50963711033447,"sku":"25045484828281473170","price":4.99,"currency_code":"USD","in_stock":true},{"title":"3\" × 3\" \/ White","offer_id":50963711066215,"sku":"76605925886645497058","price":6.99,"currency_code":"USD","in_stock":true},{"title":"4\" × 4\" \/ White","offer_id":50963711098983,"sku":"14793227791942450747","price":8.99,"currency_code":"USD","in_stock":true},{"title":"6\" × 6\" \/ White","offer_id":50963711131751,"sku":"13083819459455622676","price":11.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/15979942760437137245_1200.jpg?v=1793665102","url":"https:\/\/pixelatedphysics.com\/pt\/products\/thomsonia-thomson-cross-section","provider":"Pixelated Physics","version":"1.0","type":"link"}