Nuclear Decay

In the nucleus of an atom, neutrons and protons are held by nuclear forces. Their total energy (ignoring the mc² contributions) is less than the barrier height potential energy. Yet some nuclear particles do escape. Any thoughts about the reason for an escape?

Answer

The wave function extends through the potential barrier to the outside world. Therefore the probability to be outside the nucleus is not zero. So why does the wave function itself extend into the barrier? All confinement problems, classical and quantum, have solutions with functions that extend into the barrier, usually decreasing exponentially to almost zero within a few wavelengths. Atomic particles have relatively long wavelengths compared to the barrier thickness. So why does the wave function itself not end in the barrier? Because the effective barrier height decreases with radial distance.

The probability to tunnel through the barrier is proportional to Exp , where E is the energy of the incident particle, U(r) is the barrier potential as a function of distance r, and A is a constant that includes Planck’s constant h. Some closely related problems to be treated as tunneling through a barrier are:

1. Bare copper wire is cut and the two ends are twisted together. In spite of the fact that the copper is coated with copper oxide, the twisted ends still conduct electricity readily.

2. Tunnel diode operation.

3. Scanning tunneling microscope.

For a discussion about how a nuclear decay rate may be influenced by its environment, see the Peres reference below.