Kinematics, cross-sections, and resonance structure of reactions among atomic nuclei — the bridge from nuclear structure to astrophysical nucleosynthesis and applied nuclear engineering. Core conservation laws: baryon number A, charge Z,…
nuclear-reactions
Q-value from mass defect: Q = (Σm_i − Σm_f)·c²
The Q-value of a nuclear reaction a + X → Y + b + … is the energy released (Q > 0) or required (Q < 0) in the transformation, equal to c²…
Breit-Wigner 1936 resonance: σ(E) Lorentzian with FWHM Γ
Breit-Wigner 1936 (Phys. Rev. 49:519) derived the energy-dependent cross-section for a reaction proceeding through an isolated…
Gamow 1928 Coulomb-barrier tunnelling → stellar-fusion peak
Gamow 1928 (Z. Physik 51:204) applied quantum tunnelling to the Coulomb barrier between two charged nuclei, deriving the penetration…
²²⁶Ra → ²²²Rn + α Q-value: 5.230·10⁻³ u·c² exact (sym. rational)
Closed-form Q-value computation for the α-decay ²²⁶Ra → ²²²Rn + α using tabulated atomic masses (AME2020; exact to 6 significant figures,…
Breit-Wigner FWHM = Γ exact (half-maximum solves to ±Γ/2)
Exact closed-form derivation of the full width at half maximum of the Breit-Wigner Lorentzian line shape. Lorentzian normalised peak:…
Gamow peak E_0 = (E_G·(k_BT)²/4)^{1/3} exact saddle point
Exact closed-form derivation of the stellar-fusion Gamow-peak energy. The integrand of the thermal reaction rate ∝ exp(−E/k_BT) ·…