Educational · dimensionless

Gamow shape explorer

See where a Maxwellian energy distribution and the Coulomb-barrier factor overlap. The curve is normalized to its own maximum: it cannot produce an absolute cross section, reaction rate, power, Q, or net-energy result.

Boundary rule. If the largest displayed value lies at the edge, the result is a boundary maximum—not an optimum. Extend the energy range before interpreting the peak.

Shape inputs

Energy-unit temperature for the illustrative common-temperature Maxwellian.
Display range only; it does not change the analytic peak.

Equation

shape(E) ∝ exp[-E/(kT) - √(E_G/E)]
E_G = 22.589 MeV for p–¹¹B
E₀ = [E_G(kT)²/4]^(1/3)

Methodology and limitations →

Analytic shape peak E₀—not an engineering optimum
Range assessment——
Run specification—All displayed values are dimensionless except energy.