Geiger-Nuttall Law — Alpha Decay Half-Lives

WKB Gamow tunneling: log₁₀(t₁/₂) is linear in the exact Gamow factor γ — 24 orders of magnitude from one equation

Geiger-Nuttall: log₁₀(t₁/₂) vs WKB Gamow factor γ
Click any nucleus to inspect. RED line = best-fit. Color = element. Gamow axis collapses all Z onto one universal line; 1/√E axis shows Z-dependent scatter.
Sensitivity Sliders
ΔE_α (MeV) 0.00 MeV
Shifts selected nucleus energy ±2 MeV — see half-life change
R₀ scale (fm) 1.20 fm
Nuclear radius R_nuc = R₀·A^(1/3). Shifts Gamow γ (intercept shifts, slope unchanged).
Physics Checks
P1 (Gamow-axis R² > 0.99): —
P2 (R₀ ±20% → slope unchanged <5%): —
P3 (Po-212 vs U-238 range): —
Selected Nucleus
Click a nucleus on the plot
Coulomb Barrier Profile
Shaded = classically forbidden region (Gamow tunneling zone). R_nuc = nuclear radius; R_turn = classical turning point.
Fit: log₁₀(t₁/₂) = A·γ + B
A = —
B = —
R² = —
γ = exact WKB Gamow integral:
γ = (2Z_dZ_αα/β)[arccos(√u) − √(u(1−u))]
where u = R_nuc/R_turn, β = v_α/c

Decay rate λ ∝ exp(−2γ) → log(t₁/₂) ∝ γ ✓
Gamow γ absorbs the Z-dependence → universal linear fit