10.3 Phenomenological Models in History of Physics

In the study of a complex phenomenon as the cold fusion, it will be advisable to recollect famous models which played important roles in the history of physics.

a) Bohr model of atoms

The most famous model in the atomic physics is "the Bohr model" of atoms proposed in 1913 by N. Bohr to explain paradox of their finite volume and atomic spectra difficult to understand by the classical electrodynamics: The old theory had told that (1) the electron in an atom accelerated by the nucleus lose energy emitting radiation and shrink to zero volume in contradiction with finite volume of the atoms well established by daily experience and (2) the emitted radiation has continuous spectrum corresponding to the frequency of its orbital motion but sharp line spectrum observed.

To explain these experimental facts, N. Bohr settled four postulates contradicting the classical electrodynamics. Following explanation is from Encyclopedia Britannica Vol. 2, p. 710 (1963):

"In these terms the postulates of Bohr's theory can be stated as follows:

1. Electrons can move in circular orbits around the atomic nucleus.

2. The only orbits possible are those for which the orbital angular momentum is an integral multiples of h/2п, where h is the Planck's constant.

3. Those orbits are "stationary" in the sense that so long as an electron remains in a given orbit it radiates no energy.

4. An electron may jump from one orbit to a second orbit, of lower (more negative) energy, closer to the nucleus; in this process the energy liberated is emitted as a single quantum of light.

The arbitrariness of these postulates was admitted, but their success was beyond dispute. Later the new atomic mechanics – called wave mechanics or quantum mechanics – led to the same results in a less forced manner. (A.P. French)"

b) Two-fluid model of liquid helium.

As one more example of effectiveness of a model, we take up "the two-fluid model of liquid helium" proposed by L. Landau.

A phase transition of liquid helium at 2.19 K (λ-point) was discovered by Keesom and Wolfke in 1927. P. Kapitza in Russia investigated the nature of the liquid helium below λ-point and discovered the superfluidity in 1938. Following sentences are from his explanatory recollection of his research written (perhaps) in 1943 and published in Kwant (Quantum) 1991, No. 1, pp. 7 ̴ 14 (in Russian).

"The explanation (two-fluid model) of this phenomenon given by L. Landau can be summarized as follows:

Liquid helium is a mixed state of two kinds of fluids. The two components of liquid helium are in two different quantum states. Therefore, it is possible that there exist counter streaming flows simultaneously in a liquid, one of which without viscosity is measured at the neck of the flask.

It would be very difficult to accept this model unless this assertion was completely verified by experimental facts.

The phenomenological theory by Landau could explain simultaneous co-existence of two different states below λ-point and also physical characteristics of these states.

(Furthermore,) this theory predicted several events. One of them, for instance, is an existence of {\it the second sound} in liquid helium which is not observed yet (in 1943). This theory cannot explain the critical velocity of superfluid observed in experiment, yet. However, I admit that this theory can explain the whole remarkable phenomenon of superfluidity fairly well and has made inevitable important contribution to the development of its investigation."

As is well known, the second sound predicted by the Landau's two-fluid model of liquid helium was discovered experimentally by V.P. Peshkov in 1944.