Lab 13 — Nuclear Physics
Nuclear Fusion & the Coulomb Barrier
Two light nuclei repel each other electrostatically long before the short-range strong force can bind them. The volcano-shaped curve on screen is that wall — the Coulomb barrier, V(r) = 1.44·Z₁Z₂/r MeV — and the two glowing nuclei climb it from either side. Classically they need kinetic energy above the summit to fuse. Quantum mechanically they don’t: exactly as on the tunneling page, the Gamow factor P = exp(−√(E_G/E)) lets a fraction sneak through well below the top. Pick a reaction and turn up the temperature (= kinetic energy) — watch rare tunneling successes give way to a routine climb over the summit.
Raise T — tunneling succeeds more often, then crosses the barrier classically (p–p crosses yet almost never fuses — the weak force is the bottleneck)
D–T fusion turns just 0.018884 u of mass — about 2% of a proton — into 17.59 MeV via E = Δm·c² = Δm × 931.494 MeV/u. Binding energy per nucleon peaks near ⁵⁶Fe / ⁶²Ni (~8.8 MeV per nucleon): light nuclei climb toward that peak by fusing, heavy nuclei by fissioning — fusion and fission are the same curve, read from opposite ends. The fuel (hydrogen isotopes, bred from seawater and lithium) is abundant and the ash is helium; there is none of fission’s long-lived high-level waste, though neutrons do activate the reactor walls. What makes fusion hard is the Coulomb barrier and confinement: tokamaks like ITER aim to run D–T at about 150 million kelvin, 10–20 keV. The Sun’s core is far cooler — 1.3 keV (1.5×10⁷ K) — so a proton there waits billions of years, on average, for its p–p turn. Tunneling alone wouldn’t make it that rare: the first step, p + p → d + e⁺ + ν, also needs the weak force, which slows it by many orders of magnitude (the p–p option on this page bundles the whole four-proton chain into one event). That is exactly why hydrogen bombs burn fast D–T instead — the Sun and the bomb both fuse hydrogen, but not via the same reaction.