Gamow factor

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The Gamow Factor or Gamow-Sommerfeld Factor,[1] named after its discoverer George Gamow, is a probability factor for two nuclear particles' chance of overcoming the Coulomb barrier in order to undergo nuclear reactions, for example in nuclear fusion. By classical physics, there is almost no possibility for protons to fuse by crossing each other's Coulomb barrier, but when George Gamow instead applied quantum mechanics to the problem, he found that there was a significant chance for the fusion due to tunneling.

The probability of two nuclear particles overcoming their electrostatic barriers is given by the following equation,


Where is the Gamow Energy.

Here, is the reduced mass of the two particles.

The constant is the fine structure constant, and the constants and are the respective atomic numbers of each particle.

The probability of overcoming the barrier increases rapidly with increasing particle energy, but at a given temperature the probability of a particle having a high energy falls off rapidly, following the Maxwell–Boltzmann distribution. Gamow found that, taken together, these effects mean that for any given temperature, the particles that actually fuse are mostly in a temperature-dependent narrow range of energies known as the Gamow window.[3]


  1. ^ Yoon, Jin-Hee; Wong, Cheuk-Yin (February 9, 2008). "Relativistic Modification of the Gamow Factor". arXiv:nucl-th/9908079free to read. 
  2. ^ "Nuclear reactions in stars" (PDF). Dept. Physics & Astronomy University College London. 
  3. ^ "Temperature and Pressure in Stars". Dept. Physics & Astronomy, University of Tennessee.