Tunneling

Some scattering experiments of the early twentieth century paved the way for tunneling. Ernest Rutherford, the pioneer of the scattering method, came across a paradox in a series of uranium experiments in 1910. Scattering involves the probing of a microscopic object by bombarding it with other particles and then keenly observing how the particles are, literally, scattered by the object in question. Specifically, Rutherford tried to pinpoint where the bombarding particles were scattered and how fast they were moving.

An example using tennis balls gives one a simple and accurate picture of a scattering experiment. Say a statue exists in a dark courtyard and we want information about the statue without being able to see it. Mainly, we want to know what its shape is (e.g., a horse or a person) and from what materials it is made (e.g., granite or clay). To learn more about the statue, we stand at the edge of the courtyard and toss tennis balls into the dark area, hoping to hit the statue. After many thousands of tennis balls, we've learned a lot. If only a few of the tennis balls have hit anything, we know the statue is probably quite small. Also, the directions that tennis balls were scattered are important. If most of them come straight back to us, we can ascertain that the statue has a large, flat front like a wall. Moreover, by observing the speed of the scattered tennis balls, we can get an idea of how hard the statue is. Atomic scattering set a similar scene for Rutherford, but he was interested in the nuclei of atoms and he preferred alpha particles to tennis balls.

Through a series of remarkable scattering experiments, Rutherford, working in conjunction with his students Hans Geiger and Ernest Marsden, had accurately mapped the insides, or nucleus, of the uranium atom. Uranium was of great interest at the time because of its radioactive properties. The summation of Rutherford's results for Uranium came in the form of a potential diagram. Potential refers to electric potential energy, so his diagram mapped out an energy barrier. Any particle that escaped the nucleus (i.e., any particle of nuclear radiation) would have to overcome this energy obstacle before it left. Rutherford estimated the top of this barrier to be at least about nine units of energy high. However, when observing the occasional radiated alpha particle (see radiation), he found that it had only four units of energy. The paradox was born. How could a particle with so little energy overcome a barrier of such height? Such a problem can be compared to a man walking next to a huge baseball stadium and suddenly seeing a baseball floating toward him, as if gently tossed. Surely any ball hit out of the stadium would have been moving fast enough to at least sting his palm.

The question lingered for 18 years until George Gamow, assisted by his colleagues Edward Uhler Condon and Ronald Gurney, proposed a solution. In 1928, quantum mechanics was gaining credibility, and the Figure 1. A particle before and after tunneling. It approaches from the left with far less energy than it would need to pass over the energy barrier. Illustration by Hans & Cassidy. Courtesy of Gale Group. three physicists performed a relatively simple calculation, treating the alpha particle as a quantum mechanical wave function. In essence, they analyzed the problem from the viewpoint that an alpha particle was not located precisely at any given spot, but rather that its existence was spread out, like a wave. Their explanation proposed that the alpha particles tunneled out of uranium's energy barrier, and it fit Rutherford's observations perfectly. The acceptance and practical application of tunneling theory had begun.