Coulomb Barriers and Gamow Window

The first scene of this movie illustrates the potential energy function of a nucleus, a combination of the strong nuclear interaction between all the particles in the nucleus and the Coulomb potential due to the positively charged protons. A beam of particles (e.g., from an accelerator) incident on a target nucleus sees this potential. Classically, if the energy of the beam particles is less than the height of the Coulomb barrier, the beam particles cannot penetrate the barrier: they are repelled by the electrical force of the nuclear protons. (The beam particles are generally positive ions that have been formed by having one or more of their electrons stripped away.) But quantum mechanically, a small (but finite) number of beam particles can pass through the barrier to reach the target nucleus.

The probability for barrier penetration depends exponentially on the energy of the beam particles; the probability goes down rapidly with decreasing energy. This is illustrated schematically by the green curve in the second scene of the movie. On the other hand, 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 in this scene). The product of these two factors implies that there is a narrow range of energies for which nuclear reactions can be induced. This product is illustrated by the gray curve and is called the Gamow peak, or the Gamow window. Usage: Keep clicking the "Play" button to view the movie. When the "Home" button appears, click it to review the movie.