Gamowyn

Gamowyn holds open a narrow, glowing door between two dark walls. Fusion in the Sun squeezes through it.

The Physics

In 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.

rate ∝ e^(−E/kT) × e^(−√(E_G/E)), E₀ = (E_G (kT)² / 4)^(1/3), E_G = 2μc² (π α Z₁ Z₂)²

• E: kinetic energy of the colliding pair (keV)
• k: Boltzmann constant; T: temperature (K)
• E_G: Gamow energy (keV)
• E₀: energy of the Gamow peak (keV)
• μ: reduced mass of the pair (kg)
• α: fine-structure constant (dimensionless)
• Z₁, Z₂: charge numbers of the nuclei

For 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.

Honest caveat: 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.

On the shirt

Front: 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.