{"product_id":"gamowyn-the-narrow-window-physics-t-shirt","title":"Gamowyn – The Narrow Window Physics T-Shirt","description":"\u003cp\u003eGamowyn holds open a narrow, glowing door between two dark walls. Fusion in the Sun squeezes through it.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eIn a star's core, few nuclei have enough thermal energy to climb the Coulomb barrier, and the fast ones are exponentially rare. Quantum tunnelling helps: the chance of getting through rises steeply with energy. Multiply the falling Maxwell–Boltzmann tail by the rising tunnelling factor and you get a sharp peak, the Gamow peak, where almost all the fusion happens.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003erate ∝ e^(−E\/kT) × e^(−√(E_G\/E)),   E₀ = (E_G (kT)² \/ 4)^(1\/3),   E_G = 2μc² (π α Z₁ Z₂)²\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eE: kinetic energy of the colliding pair (keV)\u003c\/li\u003e\n\u003cli\u003ek: Boltzmann constant; T: temperature (K)\u003c\/li\u003e\n\u003cli\u003eE_G: Gamow energy (keV)\u003c\/li\u003e\n\u003cli\u003eE₀: energy of the Gamow peak (keV)\u003c\/li\u003e\n\u003cli\u003eμ: reduced mass of the pair (kg)\u003c\/li\u003e\n\u003cli\u003eα: fine-structure constant (dimensionless)\u003c\/li\u003e\n\u003cli\u003eZ₁, Z₂: charge numbers of the nuclei\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eFor p + p, E_G ≈ 493 keV. In the solar core, about 15.7 million K, kT ≈ 1.35 keV and the peak sits near 6 keV: several times kT, yet far below the barrier. The tunnelling theory behind it is George Gamow's, Z. Phys. 51, 204 (1928), written for alpha decay.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e Gamow's 1928 paper explained alpha decay; others applied tunnelling to fusion in stars. The 15.7 million K core temperature is a standard solar model value.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Gamowyn, the pixel-art character, with the title. Back: the two exponentials, the peak energy, the p + p Gamow energy and the solar-core numbers, with Gamow's 1928 paper. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50960834134119,"sku":"29014649163913096388","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50960834166887,"sku":"35069823904466359387","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50960834199655,"sku":"10295058772698570711","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50960834232423,"sku":"22658699047194113109","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50960834265191,"sku":"33624816453052428561","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50960834297959,"sku":"15016864150579712381","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50960834330727,"sku":"15166888521526081078","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50960834363495,"sku":"27588257112544075057","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50960834396263,"sku":"25426926509470501630","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50960834429031,"sku":"22444116226486112636","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50960834461799,"sku":"13540578833598331642","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50960834494567,"sku":"50447599692858071065","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50960834527335,"sku":"51497968397901396515","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50960834560103,"sku":"10951008760555928924","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50960834592871,"sku":"19881678476265240945","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50960834625639,"sku":"29878360987587279248","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/gamow-peak_front_01_white.png?v=1793628681","url":"https:\/\/pixelatedphysics.com\/sv\/products\/gamowyn-the-narrow-window-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}