40) A Cold Fusion Essay

Ludwik Kowalski (January, 22, 2003)
Montclair State University
Upper Montclair, NJ 07043

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1)What follows is a lecture outline for the second semester of General Physics. My goal is to focus on conceptual aspects of CF rather than on its historical and social aspects. I think that trying to avoid the phrase “cold fusion” is like trying not to use the noun “heat.” Cold fusion is not the best name for the phenomenon of LENR (low energy nuclear reactions) but it is the name under which it was introduced, and under which it is remembered by most people. Some prefer CANR (chemically activated nuclear reactions), others prefer AEP (anomalous energy) phenomenon. These are more descriptive names but CF is likely to be used most frequently.

2) The term fusion will be introduced as an act of a perfectly inelastic collision between two atomic nuclei moving toward each other. The nuclei will be visualized as uniformly charged spheres. This is a mental picture, and a mathematical model, responsible for naming the phenomenon CF. What is necessary to make two positively charged nuclei fuse like two drops of water? They repel each other with Coulomb force and that force must be overcome by the cohesive nuclear force. The nuclear force is known to be negligibly small (with respect to repulsion) when the gap between the spheres is about 2 F (2*10-15 m) but it becomes dominant at shorter distances.

3) After discussing nuclear fusion in terms of forces I will start describing it in terms of energies. To facilitate the transition I will refer to a familiar example of a frictionless cart pushed along a horizontal road toward a hill, as illustrated in Figure 1. Yes, the size of the cart is exaggerated. Will the cart go over the hill (this represents fusion) or will it start rolling back, after reaching some elevation? Students know that the answer depends on the initial kinetic energy of the cart, KEi. The car will go over the hill when KEi>PEt, where PEt=m*g*h is the potential energy at the top of the hill. Otherwise it will roll back without reaching the top. The energy diagram to discuss nuclear fusion is shown in Figure 2.

The horizontal axis of that figure, r, is for distances between the centers of the spheres; the vertical axis. E, is for energies, both potential and kinetic. The line with a maximum shows how the potential energy, PE, depends on the distance r. By convention, potential energy associated with repulsive (electric) forces is positive while the PE associated with attractive (nuclear) forces is negative. Repulsion is dominant at r>r1 while nuclear forces are dominant when r<r2. The maximum potential energy occurs between r1 and r2. The lines labeled KEi1 and KEi2 show how kinetic energies change with r, in two different cases. In one case the initial kinetic energy is smaller than the maximum potential energy; in another it is larger. The total energy PE+KE must remain constant at any r>r2 (before fusion), as for the cart in Figure 1. This explains why fission is energetically forbidden unless KEi>PEt.

The maximum potential energy, PEt is often referred to as the Coulomb barrier. It turns out that for two deuterons the PEt is slightly lower than 1 MeV (1.6*10-13 J) while r2 and r1 are about 1 F and 2 F, respectively. The non-sphericity of deuterons, and the centrifugal potential energies, can be ignored in a preliminary, semi-qualitative, description.

4) After introducing the energy diagram I will digress toward two ways of increasing the initial kinetic energies (to satisfy the KEi>PEt condition). The first way is to increase the gas temperature and the second is to accelerate ions, for example, by using an electrostatic generator. Referring to kinetic theory of gasses, and assuming that the absolute temperature is ten billion K, I will show that only a very small fraction of particles has enough kinetic energy to exceed 1 MeV. Electric accelerators will be mentioned because they are often used to study probabilities of fusion at different kinetic energies. These experiments showed that fusion occasionally occurs even when KEi is less than the Coulomb barrier, PEt. This is schematically illustrated in Figure 3.

The thick line, in that figure, corresponds to predictions of classical theory while the thin line corresponds to experimental data. Our classical theory predicts that the probability of fusion, p, changes suddenly from zero to one at KEi=PEt. The experimental data, on the other hand, show that the transition is gradual (the energy scale strongly expanded in Figure 3).

5) I will tell students that in physics, unlike in mathematics, theories are validated by experimental data. The data show that the familiar classical model, highly reliable in macroscopic physics, is no longer a good description of what actually happens in a submicroscopic process. This observation led, in the 1920’s, to the development of a new theory known as quantum mechanics, QM. That theory is in good agreement with experimental data for kinetic energies above 10,000 eV. For any given KEi the theory can be used to calculate the probability of fusion, p. The value p=0.1, for example, would indicate that, on the average, only one out of ten collisions result in fusion while the rest result in rebounding (scattering).

Referring back to Figure 1 I will ask: “what is needed to allow the cart to pass to the other side of the hill when KEi is smaller than PEt?” And I will wait till the word “tunnel” is mentioned. The QM under-barrier fusion is often referred to as a tunneling effect. The new theory can be naively interpreted by saying that p is a probability of “finding a tunnel.” Detailed calculations show that p decreases very rapidly when D=PEt-KEi becomes larger and larger. The consequence of this is that fusion at ordinary temperatures should be extremely rare, p is much smaller than 10-50. In other words, according to the tunneling theory, fusion at room temperature should be practically impossible. That is why most physicists were skeptical when a claim was made, in 1989, that experimental data contradict this prediction. The controversy, as far as numbers are concerned, has to do with the probability of fusion. Is it smaller than 10-50 or is the order of magnitude closer to 10-20? Note that p=10-20 still means that only one out of 1020 collisions results in a nuclear fusion event. But considering how many atoms move toward each other at any given moment, and the amount of energy released (for example 10 MeV per event), the p=10-20 is large enough to produce detectable heat.

Criticizing cold fusion experiments was easy in the first two or three years after its premature announcement because the phenomenon turned out to be more complex than anticipated. The numerous factors influencing outcomes of experiments, such as the role of impurities, were not known and “failures to confirm” were not rare. But the situation changed and experimental data are said to be much more reproducible today. The consensus of scientists working in the field of cold fusion is that nuclear processes do occur with measurable probabilities. They claim that the QM tunneling theory is no longer applicable at very low kinetic energies and when ions are oscillating about their equilibrium on metallic surfaces. On the other hand, a generally accepted theory of cold fusion does not exist.

It is important to emphasize that the tunneling theory has not been developed to deal with kinetic energies as low as 0.05 eV (room temperatures). An attempt to verify the tunneling theory, at very low kinetic energies, was made in 1998 (Kasagi et al.). By using beams of accelerated particles the authors showed that theoretical predictions agree with experimental data at KEi>10,000 eV but not below that limit. At 2,500 eV, for example, the experimentally measured p was found to be over fifty times higher than what was predicted. The main argument against the idea of cold fusion was based on the assumption that the tunneling theory, and its parameters, are valid down to kinetic energies as small as 0.05 eV?

What should scientists do when experimental data seem to disagree with a model in an area in which the model has never been tested? The first thing to do is to make sure that data are reproducible, the second is to agree on the interpretation of data. For example, if excess heat is confirmed then what evidence do we have that it is due to nuclear reactions? If alpha particles, or tritium, are observed then we must be sure that this is not due to a contamination. And the third thing to do is to reanalyze and to improve the theory. A theory which disagrees with confirmed and reconfirmed facts should be declared to inapplicable.

6) The overall (scientific and social) picture of the situation in the field of cold fusion can be summarized as follows.

a) The scientific community is divided into supporters and skeptics.

b) Skeptics, representing mainstream science, claim that supporters are not true scientists. The skeptics refuse to conduct cold fusion experiments.

c) Supporters continue experimenting and discussing significance of their findings. Evidence backing reality of nuclear processes influenced by changes in chemical (atomic) arrangements is mounting. But most of that evidence is not described in mainstream journals.

d) Conducting research in the area of cold fusion is a “risky business” for young scientists. This is caused by practically non-existing financial support, for example, from NSF or DOE, and by unjustified accusations that anything connected with cold fusion is “pathological science”. Most scientists conducting cold fusion research are at least sixty years old.

e) In my opinion, the time is ripe to conduct an objective evaluation of what has been accomplished in the last ten years, and to either confirm or deny that the area is unscientific. If the interdisciplinary cold fusion field is found to be scientific then research in it should be encouraged, as in any other area.

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