The Energy Window for Nuclear Reactions

The Coulomb barrier for charged particle reactions and the distribution of velocities implied by the kinetic theory of gases dictate that there is a narrow range of energies (or equivalently temperatures) where nuclear reactions involving charged nuclei occur in stars. This energy window is illustrated schematically in the adjacent figure.

The Gamow Peak
The gray peak that defines the energy window is the product of the two curves decreasing in opposite directions: The probability for penetrating the Coulomb barrier goes down rapidly with decreasing energy (the green curve marked "Barrier Penetration"), but at a given temperature the possibility of having a particle of high energy and therefore high velocity decreases rapidly with increasing energy (the orange curve marked "Maxwell"); see the right panel. This peak is commonly called the Gamow peak, or the Gamow window in honor of Russian-American physicist George Gamow (1904-1968). He made important contributions to our understanding of radioactive decay and nuclear reactions in stars, and is also credited with proposing the basic idea of the big bang theory for the origin of the Universe.

The Energy Window
The product of these opposing effects produces an energy window for the nuclear reaction: only if the particles have energies approximately in this window (the region defined by the gray peak) can the reaction take place. The Gamow window may be thought of as defining the optimal energy for reactions at a given temperature in the star and places very strong constraints on the charged-particle reactions responsible for producing fusion energy in stars.

Animation: Coulomb Barriers and the Gamow Window