Nuclear Reactions

In the fusion of light elements to form heavier ones the nuclei (which carry positive electrical charge) must be forced close enough together to cause them to fuse into a single heavier nucleus.

The Coulomb Barrier

The electrical repulsion produces a barrier to this process called a Coulomb barrier, as illustrated in the following figure, which shows the potential energy of such a system as a function of the separation r between the nuclei.

Coulomb barrier for charged-particle reactions

This figure indicates that the force between nuclei is repulsive until a very small distance separates them, and then it rapidly becomes very attractive. Therefore, in order to surmount the Coulomb barrier and bring the nuclei close together where the strong attractive forces can be felt, the kinetic energy of the particles must be as high as the top of the Coulomb barrier.

Quantum Mechanical Tunneling

In reality, the situation is helped by effects associated with quantum mechanics. Because of what is termed the Heisenberg Uncertainty Principle, even if the particles do not have enough energy to pass over the barrier there is a very small probabability that the particles pass through the barrier. This is called barrier penetration or tunneling, and is the means by which many such reactions take place in stars. Nevertheless, because this process happens with very small probability, the Coulomb barrier represents a strong hindrance to nuclear reactions in stars.

Overcoming the Coulomb Barrier

The key to initiating a fusion reaction is for the nuclei that are to fuse to collide at very high velocities, thus driving them close enough together for the strong (but very short-ranged) nuclear forces to overcome the electrical repulsion between them. In stars, the probabability of this happening is governed by the temperature and the density at the center of the star.

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