Displayed shape
shape(E) ∝ exp[−E/(kT) − √(E_G/E)]
The lesson uses E_G = 22.589 MeV for p–¹¹B and shows the analytic stationary point E₀ = [E_G(kT)²/4]^(1/3).
Gamow Shape · Methodology
A normalized teaching curve, not a reaction rate
The lesson multiplies an illustrative Maxwellian energy factor by a Coulomb-barrier penetration factor, then normalizes the sampled curve to its own maximum.
It does not include an absolute cross section, S-factor, resonance structure, density, composition, confinement time, screening correction, radiation loss, or device geometry. It cannot produce rate, power, gain, or net energy.
No edge optimum
If the largest sampled value occurs at the displayed energy limit, the interface reports a boundary maximum. The energy range must be extended before the peak is interpreted. A plotted edge is never relabelled as an optimum.
Reproduction steps
- Record the energy-unit ion temperature and displayed energy maximum.
- Generate the declared energy grid and evaluate the log-shape expression.
- Subtract the largest log value before exponentiation to avoid overflow/underflow.
- Normalize to the maximum sampled value and locate the analytic stationary point independently.
- Record whether the sampled maximum lies at the display boundary.
- Hash the canonical run specification; export inputs, constants, method version, and result.