Illustrating_theoryThis piece realized by the physicist Alessandro Cavalieri is about the Gullström’s theory, an interesting attempt to explain how the E-Cat works. It shows that Sweden believes in LENR and that Swedish graduate students are studying it and writing papers on it:

To produce an isotopic shift in an E-Cat reactor we need an “ad hoc” mechanism, i.e. a good theory taking account the detailed experimental results obtained by Rossi and his team, because for many reasons it is not plausible that the fuel burning in the reactor is due to the thermal neutrons. As we do not have yet much totally reliable information about the fuel and the ash, this is not an easy task.

This is the reason for which Rossi considers interesting the theory developed by Carl Oscar Gullström – a doctoral student in the Department of Physics and Astronomy at Uppsala University, Sweden, where also prof. Bo Höistad works – and described in the paper “Low radiation fusion through bound neutron tunneling”, released on October 25, 2014.

Uppsala universitet Foto. Mikael WallerstedtThe Uppsala University, founded in 1477, is the oldest in Sweden and in the Nordic countries.

It tries to explain the isotopic shifts resulting from the analysis performed on fuel and ash powders after the Lugano test and published in the second Third Party Report (TPR-2). So, the different tunneling probabilities are calculated, in the so-called “WKB approximation”, for interaction between nickel (Ni), lithium (Li) and protons (H).

The expression “bound neutron tunneling” in the title of the paper simply means that a neutron which is bound to a nucleus (e.g. Li-7) moves to another nucleus (e.g. Ni-60). Being neutrons particles with no charge, there is no a Coulomb barrier, but instead a strong interaction potential barrier which tries to keep the neutron attached to its original nucleus.

But what is the meaning of the word “tunneling” in physics?

Everyday experience teaches us that surmounting a hill implies climbing up it (see picture). Quantum physics knows another way. Objects can get to the other side of the hill without climbing: they penetrate the hill horizontally. This phenomenon, dubbed tunnelling, has been understood in terms of the wave-like nature of matter.

tunnel el_3A very simple explanation of the “tunneling” in physics.

For macroscopic objects its probability is very low, that’s why we have never observed it. By sharp contrast, in the microcosm particles may – with significant probability – “tunnel” through regions of space where they could not be according to the laws of classical physics (e.g. in the bowels of the hill in the figure above).

Due to the tunneling effect, quantum mechanically described particles are able to overcome potential barriers without having sufficient energy to do so – they hence “tunnel” through the barrier. In contrast, as we’ve seen for particles described by classical mechanics only a “climbing over the barrier” is allowed.

The tunneling effect occurs in various different processes in nature. These are, for instance, nuclear fusion, nuclear fission, and alpha decay in nuclear physics as well as ionization processes, photo-association and photo-dissociation in biology and chemistry.

These processes almost exclusively take place in systems that are open and consist of many particles interacting with each other. The tunneling process of single particles has been well-understood in quantum mechanics since decades – yet almost nothing is known on the tunneling process of many particles interacting with each other.

The question to which extent the interactions between the particles cause the occurrence of cooperative phenomena is of particular interest in the context of Low Energy Nuclear Reactions (LENR), where such conditions may occur.

many_body_2Illustration of one-body tunneling (left) and the many-body tunneling process (right).

Well, the idea behind Gullström’s paper is that “bound neutron tunneling between 2 potential wells created by two nucleons should be considerable larger than Coulomb barrier tunneling. Bound neutron tunneling should give rise to a ground-state to ground-state interaction if the neutron energy level is close in the two considered nuclei”.

In his work, Gullström analyses a particular class of reactions theoretically allowed, in which the neutrons are stripped from one nucleus and captured by a second nucleus. So, they do not have to be generated, as in Widom-Larsen theory, where they result from electron capture by a proton (i.e. from an inverse beta decay).

Gullström’s theory is derived from basic quantum mechanical tunneling principles, whereas a detailed calculation should be done with advanced quantum mechanical process including spin-orbit and 3D properties for tunneling probabilities. Moreover, he does not explain why such reactions do not occur in ordinary lump of matter.

Finally, the scientists have shown that the many-body tunneling process cannot be described as the tunneling process of a single effective particle, because such a description neglects the occurrence of the collective phenomena and the build-up of correlations. The scientists found with the aid of exact numerical simulations that collective phenomena show up in the many-body process even for weak interactions.

However, this theory received some positive attention from Bo Höistad, one of the authors of the Lugano report, who told Mats Lewan: “It is very interesting. It fits like a glove with our results, both the isotopic changes and the absence of radiation. It is the first time that I see a scenario that could explain the results: it has not existed before!”.

In another paper published on November 18, 2014, tiArticolo_3tled “Collective Neutron Reduction Model for Neutron Transfer Reaction”, Gullström refines his neutron transfer theory. Again, the paper was not released through the normal scientific channels and there is not mention of a peer review, perhaps advisable on sensitive topics like these.

Here’s his comment: “I have improved the neutron transfer theory. In my first attempt the radiation was still a bit high but it is solved now. The trick is to not have high energy protons to drag out the neutrons but instead neutrons that are so low in energy that they can’t enter the nucleon but at the same time they could drag out more neutrons”.

The problem is whether “bound neutron tunneling” is something real or not. Experimental work in such direction would be necessary. Moreover, we don’t know if Nickel and Lithium are the only participants in the heat generating process, because it’s sure that the old E-Cat used a secret catalyst (which could not be Lithium, probably introduced only for the storage of hydrogen in a tablet) and LENR are probably a multi-stage process.

Indeed, on October 31, 2014, Rossi wrote on his JoNP: “As a matter of fact I think a (our) theory is ready, but it is strictly bound to particulars of the reactor that cannot be disclosed so far. I am working on this issue in collaboration with nuclear physicists”.

So, we must be patient: the answer is in the future!

ALESSANDRO CAVALIERI is a physicist who teaches Mathematics and Physics in a secondary school, in Northern Italy. His cultural interests goes from Chaos Theory to the Mind-Matter connections. He loves to read books on the history of Physics.

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  1. Perhaps Mesrrs. Rossi, Gullström, and Cavalieri might pose some further explanation as to how this theory might account for the strange emissions, the Mischugenon’s of cold fusion, that are characteristically produced that I studied with the help of my dearly departed friend and mentor Edward Teller.

  2. Interesting article of Prof Alessandro Cavalieri.
    Warm Regards,
    Andrea Rossi

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