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Coulomb Barrier

The electrostatic energy barrier created by the mutual repulsion of two positively charged atomic nuclei, which must be overcome or tunneled through for nuclear fusion to occur.

Reviewed Last reviewed: 9 Aug 2026 · Category: Concepts & Physics

Electrostatic Repulsion

Atomic nuclei carry positive charge (Ze). The Coulomb barrier is the maximum potential energy that must be surmounted to reach the ~10−15 m distances where the attractive nuclear strong force takes over and fusion can occur.[1]

Barrier height:
EC = Z1 Z2 e2 / (4πε0 R)

For D–T: EC ≈ 0.4 MeV. For p–11B: EC ≈ 2.7 MeV.

Quantum-Mechanical Tunneling

Classically, 0.4 MeV corresponds to ~5 × 109 K — far higher than the ~1.5 × 108 K where D–T fusion actually occurs. The resolution is quantum-mechanical tunneling, first described by George Gamow in 1928.[3]

The Gamow Peak

In a thermal plasma, the fusion reaction rate is determined by the product of tunneling probability (increasing with energy) and the Maxwellian distribution (decreasing above thermal energy). This produces the Gamow peak near 20–30 keV for D–T at 15 keV.[2]

Barrier Heights for Key Fuels

D–T: ~0.40 MeV (Z=1, lowest barrier, leading fuel choice). D–3He: ~0.67 MeV (Z=2). p–11B: ~2.7 MeV (Z=5, extremely difficult; bremsstrahlung losses dominate).[4]

Implications for Reactor Temperatures

The Coulomb barrier, modulated by quantum tunneling, determines the minimum operating temperature for a fusion reactor. It is the single most important factor in determining which fusion reactions are energetically accessible under terrestrial conditions.[4]

Sources

  1. G. Gamow, "Zur Quantentheorie des Atomkernes," Zeitschrift fur Physik 51, 204–212 (1928).
  2. S. Atzeni & J. Meyer-ter-Vehn, The Physics of Inertial Fusion, Oxford University Press (2004).
  3. D.D. Clayton, Principles of Stellar Evolution and Nucleosynthesis, University of Chicago Press (1983).
  4. J.P. Freidberg, Plasma Physics and Fusion Energy, Cambridge University Press (2007).

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