gamow_energy
plain-language theorem explainer
Gamow energy supplies the peak energy for nuclear fusion reactions in stellar cores as the expression 1.22 Z₁Z₂² μ (T/10⁷)^{2/3} in keV. Stellar astrophysicists cite it when building main-sequence luminosity-mass relations from nuclear burning equilibrium in Recognition Science. The definition is a direct algebraic encoding of the standard Gamow peak scaling with no lemmas or reductions applied.
Claim. $E_G(T, Z_1Z_2, μ) = 1.22 (Z_1Z_2)^2 μ (T/10^7)^{2/3}$ keV, where $T$ is temperature in K, $Z_1Z_2$ the product of nuclear charges, and $μ$ the reduced mass.
background
The StellarEvolution module derives main-sequence relations L ∝ M^{3.9} from Recognition Science by combining the Gamow factor for nuclear burning with radiative transport and hydrostatic equilibrium. Upstream results include the dimensionless bridge ratio K = ϕ^{1/2} from Constants and the triangular number T(n) = n(n+1)/2 from Gap45.SyncMinimization, though gamow_energy itself uses a fixed numerical prefactor. The local setting is the paper RS_Stellar_Evolution_HR_Diagram.tex, where the pp chain dominates at solar core temperatures near 10^7 K.
proof idea
This is a direct definition that encodes the Gamow peak formula as a one-line algebraic expression. No lemmas from the depends_on list are invoked; the body simply multiplies the squared charge product, reduced mass, and the temperature ratio raised to the two-thirds power.
why it matters
The definition feeds the downstream theorem gamow_energy_increases_with_T that proves the T^{2/3} scaling. It supplies the nuclear energy scale required for the RS Gamow factor in the stellar evolution framework, supporting the main-sequence lifetime and luminosity relations derived from the phi-ladder and eight-tick octave structures.
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