Thermonuclear reaction rate ($r_{12}=n_1{n}_2⟨\sigma v⟩/(1+{\delta }_{12})$)

A thermal distribution of relative velocities weights a nuclear cross-section to determine the reaction rate per volume. Identical reactants require the denominator two to avoid counting each pair twice. Specific deposited power is $r_{12}{Q}_{\mathrm{deposited}}/\rho$. Charged-particle quantum tunnelling through a Coulomb barrier produces a Gamow peak, while resonances and plasma screening can alter the rate.

For a nonresonant charged-particle thermonuclear reaction rate, the thermal high-energy tail favors low $E$ while the Coulomb barrier penetration factor favors high $E$. Their product peaks in an intermediate energy window. Resonant reactions such as the Triple-alpha process require an additional resonance treatment.