A Physicist’s Formula

tsyganov alghero 2012Update 01/2013 —Registration of Energy Discharge in D+D→4He* Reaction in Conducting Crystals (Simulation of Experiment) [.pdf] by Edward Tsyganov from Proceedings of Channeling 2012 Conference in Alghero, Sardinia, Italy.

Cube3x3x3In my point of view, series of the experiments in Gran Sasso Laboratory under leadership of Dr. Claus Rolfs and similar experiments in Berlin by Dr. K. Czerski and colleagues during 2002-2009 show unusually high electron screening potential in metallic crystals. These experimental facts give a good mechanism how the Coulomb barrier overcame with low energy (thermal) deuterons.

“The circumstances of hot fusion are not the circumstances of cold fusion”, wrote Julian Schwinger, co-Nobel-prize winner with Richard Feynmann and Shinichiro Tomonaga in 1965 for their work on quantum electro-dynamics (QED).

But there is no shortage of hot fusion analysis of cold fusion. Might some ideas be applicable?

Edward Tsyganov believes so.

Dr. Tsyganov is a professor at University of Texas Southwestern Medical Center who specializes in nuclear detectors, but in 1975, Tsyganov was part of an international group working on the Tevatron proton accelerator at Fermilab, just after successfully completing the first Russian-American scientific collaboration on the Serpukhov 70 GeV proton accelerator in Russia.

Muon catalysis had been discovered by Professor Luis Alvarez, whom he met at Lawrence Berkeley Lab in 1976. Although exciting, muon catalytic fusion did not look very promising to Tsyganov due to the short life time span of the muon.

Later, in December 1989, he was sitting in the audience of a seminar with Martin Fleischmann at CERN in Geneva, Switzerland, having participated in the DELPHI experiment at the Large Electron Positron collider. [visit] He was very excited with Fleischmann’s presentation but, at the time, he had just introduced bent crystals for beam deflection, now used in high-energy physics. The study of crystalline structures drew him away from cold fusion research, which he had heard was “a false observation” anyway.

Gran Sasso
Inspired by experimental work performed with the Gran Sasso Laboratory Underground Nuclear Physics (LUNA) facility in Italy, Tsyganov recently returned to the topic of cold fusion. [visit]

Scientists there have shown that when a deuterium atom is embedded in a metallic crystal, the cross section, which gives a measure of the probability that a fusion reaction will occur, increases in comparison with that of free atoms.

In the 2002-2008 series of international low-energy accelerator experiments, low-energy deuterium beams directed at embedded deuterium atoms showed that, in this environment, the screening potential for the orbital electrons of the embedded atoms is substantially increased. This means that in such conditions, any supplemental embedded nuclei in a single host crystal cell could sit much closer than they normally would due to the Coulomb repulsion.

Can this idea be applied to the low-energy nuclear reaction (LENR) in a solid?

The problem of overcoming the Coulomb barrier, the powerful force that keeps positively-charged protons away from each other, is the central issue for developing clean cold fusion energy. The force that holds nuclei together is called the strong nuclear force. Though it is an extremely powerful force, it only extends for a small distance. Unless nuclei can get close enough for the strong force to take effect, positively-charged nuclei remain too far away from each other to fuse. Elements other than hydrogen have an even bigger Coulomb barrier, since they have many more protons, and a stronger positive-charge. This is true for both free particles, and those housed in a solid metal.

JET Energy model of palladium metallic lattice infused with deuterium.
But inside a metallic lattice, the negatively-charged conducting electrons are free to move about, creating a negatively-charged screen. As a result, a positively-charged proton (or deuteron) inside the lattice sees mostly negative charges. But at some point, the bare nucleus could find itself suddenly close to another of its kind, the other’s positive-charge being “hidden”, or screened, by all the surrounding negative charges.

In this environment, deuterons or other nuclei may sit closer together in one host crystalline cell than they normally would. In a paper Cold Nuclear Fusion [1], Tsyganov cites data obtained by Francesco Raiola et al, for the screening Assenbaum potential for deuterium embedded in platinum as 675 +/- 50 eV, which is around 25 times larger than for free atoms of deuterium.

“The so-called screening Assenbaum potential is usually considered as an additional energy of interaction in a fusion process, and this effective energy should be used for calculations,” writes Tsyganov.

“This means that atoms of deuterium embedded in a metallic crystal do not feel the Coulomb repulsion down to distances of 25 times smaller than the size of the free deuterium atoms, increasing the probability of barrier penetration.”

“It was evident that in such conditions two deuteron atoms could approach each other to the distance of 1/10 – 1/20 of the size of an undistorted atom, without feeling the Coulomb repulsion.”

“Normally at very low energies for the deuterium molecule, the Coulomb barrier permeability for deuterium atoms is of the order of $10^{-84}$, including the Assenbaum screening potential (27 eV). However, in an environment of a single metallic crystalline cell this value jumps by $10^{50}$ – $10^{60}$ times! At the same time the real kinetic energy of the interacting deuterium atoms is still very low, some tiny fraction of an eV. All the enhancement of Coulomb barrier permeability is due to much shorter distance between the interacting deuterium nuclei.”

At low energies, the Coulomb barrier permeability is lowered and nuclei can position closer together.
“As one can see from the graph, in the region of low effective kinetic energies, as in the case of cold fusion, the dependence of the quantum mechanical probability of Coulomb barrier penetration vs energy is very sharp.”

For Tsyganov, this illustrates the difference between hot fusion and cold fusion.

“Hot fusion produces compound nuclei through multiple single encounters of the particles. In cold fusion, particles interact with the same partner through the quantum oscillations in a ‘closed box…'”, he writes. “This oscillation frequency is directly proportional to the screening potential, or box “size”, giving an additional boost to the process.”

Suppose that two deuterium atoms are trapped inside a single crystalline cell of palladium. The electrons associated with the deuterium will have an elongated shape in response to the cloud of conduction electrons, their orbits distorted by the catalytic effect. This is what allows the deuterium nuclei to situate themselves only a fraction of the distance they would normally tolerate.

Together, these two atoms make a “quasi-molecule” that oscillates at a particular frequency. While Tsyganov admits that calculating the particular oscillation frequency of a deuterium quasi-molecule in the midst of so many potential fields inside the crystal is difficult, he uses Planck’s relation as an approximation to give a frequency $\nu = E/h$, where $E$ is the experimentally measured screening potential and $h$ is Planck’s constant.

For deuterium embedded in a platinum metallic crystal, the screening potential was measured by Raiola as about 675 eV. This gives a vibrational frequency for the quasi-molecule as $1.67 \hspace{1 mm}\text{x}\hspace{1 mm} 10^{17}$ per second, and offers an estimate of the number of times the nuclei get close enough to fuse.

Multiplying this value for the oscillation frequency by the barrier permeability, a measure of the ability to overcome the Coulomb repulsion, of $2.52 \hspace{1 mm}\text{x}\hspace{1 mm} 10^{-17}$ yields a rate of 4.21 Deuterium-Dueterium fusion events per second.

Based on the calculation above, this table estimates DD fusion rates for crystals of palladium and platinum.

“I took this observation and applied these enlarged screening potential to the condition of McKubre experiments with deuterated palladium”, says Tsyganov.[1] “Heat release of Michael McKubre and the SRI team is well explained. In fact, this is the first confirmation of the cold fusion process using independent data from accelerators.”

Tsyganov believes experiments of Yoshiaki Arata and similar experiments of Mitchell Swartz could be also explained with this mechanism, if “quantitative data on deuterium contamination in palladium nano-crystals would be available.” He is convinced that the mechanism in McKubre’s experiments and that of Arata and Swartz’ are the same.

“Experiments of Francesco Piantelli and Andrea Rossi are well fitted in the above model. Higher heat release in the Rossi case is probably explainable by the use of platinum catalyst”, writes Tsyganov.
Professor S.B. Dabagov, Professor M.D. Bavizhev and I have tried to analyze the nuclear processes occurring in the Ecat installation and provide a possible explanation for the observed results, says Tsyganov. “In addition to the slowing of the nuclear decay processes of the intermediate compound nucleus formed during the cold fusion of elements [2], some modification of the decay process of the intermediate nucleus of the compound (H+Ni)* must be assumed to provide a plausible explanation of the Rossi results. We discuss such possibilities in this paper.”

Tsyganov’s idea pertains to how nuclei might become situated close enough inside a metal to overcome the Coulomb barrier and fuse, an idea derived from hot-fusion experiments. Still, he believes this model can be applied to the cold fusion environment too, claiming predictions agree well with heat energy measured by SRI and extend to the nickel-hydrogen systems as well.

I asked Dr. Tsyganov how his model might explain some other experimental data in cold fusion.

Dr. Tsyganov attended the 2011 LANR/CF Colloquia at MIT.

Q&A with Edward Tsyganov

CFN Supposing two deuterium can fuse in this way, how would the heat be dissipated through the lattice?

Tsyganov There is the traditional belief among nuclear scientists that nothing in a nucleus could depend on the outside world. It is very true for the fast processes in a nucleus (and these processes usually are very fast due to the very small size of a nucleus) because it is necessary that some time pass to reach the outside world. This time is about $10^{-19}$ seconds and is defined by the size of atom and speed of light.

However, according to the only hypothesis of mine, the intermediate compound nucleus 4He* created in cold DD fusion, as also in other cold fusion cases, presents an absolutely unique situation. After the penetration of main Coulomb barrier (about 200 keV high), deuterons save their identities for some time, due to the residual Coulomb mini-barrier, already inside the strong potential well. This mini-barrier very much reduced and smothered by the strong interaction forces (quark-gluon mechanism) and the finite sizes of the deuterons, but still prevents immediate nucleonic exchange between the two deuterons.

This figure represents the bottom of the potential well of strong interactions of two deuterons.
In my estimations, this mini-barrier is less than 2 keV high (~1% of the main Coulomb barrier), because at this kinetic energy usual nuclear decays of 4He* are still taking place. In fact, the Gran Sasso experiments, where this enhanced screening potential was discovered, used nuclear products to detect fusion processes. However, excitation (thermal) energy at cold fusion is still more than $10^{4}$ times less than 2 keV, or about 0.040 eV. Obviously, one can expect decreasing of nuclear decay rate of 4He* with decreasing of excitation energy.

I would highlight again that the decrease of nuclear decay rate at the very low excitation energy is the only hypothesis in all my consideration.

This situation could be treated as the experimental evidence. High electron screening potentials makes the cold fusion process the must. At the same time there are no neutrons and other nuclear products detected experimentally. An explanation must be provided. The only explanation (and the very reasonable one) that I could think of is the decrease of nuclear decay rate with decreasing of the energy of excitation.

If one adopts this hypothesis, further explanation does not presents real difficulties. Quantum electrodynamics provides the framework, through exchange by the virtual photons. Julian Swinger was very close to this solution but did not make the final step. Energy of discharge 4He* to the ground state 4He is released mostly by several hundreds of low energy electrons, with very short range in the crystal. About 400 60 keV electrons produce the heat.

CFN How might the production of tritium be explained with this process?

Tsyganov Production of tritium in McKubre’s experiments could be explained, if the nuclear decay rate of 4He* in cold fusion is reduced, but still non-negligible. This rate is at least two orders of magnitude less than expected for hot fusion. Perhaps, cracks and defects of the palladium sample could also contribute. I hope this question could soon be answered in future studies.

CFN Thank you Dr. Tsyganov.

Tsyganov My pleasure.

[1] Cold Nuclear Fusion by E.N. Tsyganov published Physics of Atomic Nuclei 2012, Vol. 75, No. 2, pp. 153–159 [.pdf]

[2] Cold Fusion Continues by E.N. Tsyganov, S.B. Dabagov, and M.D. Bavizhev, from the Proceedings of “Solid State Chemistry: Nano-materials and Nanotechnology” Conference, 22-27 April, 2012, Stavropol, Russia Report in Stavropol 4-24-2012 [.pdf]

[3] Cold Nuclear Fusion by E.N. Tsyganov on Journal of Nuclear Physics [visit]

17 Replies to “A Physicist’s Formula”

  1. Perhaps because I’m a chemist, I always think of what else is in my reaction vessel and what sort of unexpected side reactions might be taking place if I don’t get my expected product. The Coulomb barrier between deuterium and the nuclei of palladium (which also has a large cross section to fusion) would also be reduced. This is not taking place in a vacuum. Although the deuteron is being repelled by a palladium, there is an adjacent palladium that is preventing it from retreating to far from the other palladium nuclei (it’s being braced). The Coulomb barrier between deuterium and the nuclei of Cesium would also be reduced which may help explain the Mitsubishi transmutations. It may not necessarily be deuterium deuterium fusion. http://indico.cern.ch/getFile.py/access?resId=5&materialId=slides&confId=177379

    Cs(133) + 4D > Pr(141)

    1. Hey A, I emailed him, and this was his reply:

      “Alan proposed a fuse between Deuterium nucleus and Palladium nucleus of the lattice.

      A contaminant atom of deuterium is taking place in the center of the lattice, where repelling is minimized (just zero repelling, an equilibrium). Then the distance between palladium atom and deuterium atom is about of atomic distance (roughly, all atoms is about the same size, within factor of two). In this case Deuterium-Palladium distance is still of a size of the normal atom, and penetration through the barrier is very-very low.

      I have no data (no numerical formula) for Deuterium-Palladium Coulomb barrier permeability. I do not believe these data exist at all. I believe the permeability is negligible. I do not want to speculate.

      Palladium has charge 46, and only a part of outermost electrons are free to move.

      It is in fact very interesting topic. Piantelli recently got some measurable hit release in H+Ni reaction. In my view, it is possible when special dislocations in Ni crystals exist, namely, a single (extra) Ni atom is sitting in the center of normal cell of Ni crystalline. A parasite Ni atom in a normal Ni crystal cell. Then, electron shells in this parasite Ni atom are distorted (elongated). And then, later, a hydrogen atom arrives in that cell and H+Ni fusion happen.

      Rossi put both, Ni and H in platinum cell (attached). How he is doing this, it is his secret.”


      1. Thanks Ruby,

        I was just thinking that although palladium has a bigger charge than another deuteron its thermal neutron cross section is much larger. This may allow the deuteron to react with palladium by what may start out as an Oppenheimer-Phillips reaction where the neutron of the elongated deuterium nucleus penetrates the Coulomb barrier but instead of the proton popping off as it usually does, the whole deuteron gets sucked into the palladium nucleus to form silver (Ag) in an excited state. Then I start to think like a chemist again. Silver is a “soft acid” that will form a strong chemical bond with a “soft base” like deuteride (D-) This may allow it to undergo the set of nuclear reactions to form helium that I mentioned before. https://coldfusionnow.wordpress.com/2012/01/17/rumpelstiltskin-reaction/

          1. PS
            If the thermal neutron cross section is an indication of the size of the target a deuteron would see, it would be much easier for a deuteron to find a Pd nucleus rather than another tiny deuteron.

            Thermal Neutron Cross section (Barns)
            Pd-102 3.4+/-0.3

            Pd-104 0.6+/-0.3

            Pd-105 21.0+/-1.5

            Pd-106 0.315+/-0.029

            Pd-108 7.6+/-0.4

            Pd-110 0.227+/-0.032

            H-2 0.000519+/- 0.000007

        1. Hi JohnExactly. Once two-way laser/plasma beam bases are set up one can retire the fousin main engines and use fousin thrusters for manoeuvring. With enough focussing lenses and beam-power the maximum practical laser-pushed speed is Forward’s 0.5c from his two-way laser sail concept. That means a ship-time of 40 years gets you ~23 ly.I’m not over convinced that 0.7c is really feasible for a laser-sail, contra Avatar . Mass-beams might manage it. Of course the limiting speed depends on interstellar dust and the means available to mitigate the proton-storm as the gammas pile up. I think everything under ~0.999999c should be OK, which is enough to get to the Core in 40 years ship-time.

  2. Thanks for the clarification… I now know a lot more about nuclear reactive processes and the cold fusion nuclear reactive environment.

    Does excitation increase when more than one frequency is introduced to the lattice? Would harmonic waves bouncing back and forth through the container create standing waves and peaks where vibration energy is increased at points within the lattice?

    I’d assume that Dennis Bushnell and his team at NASA are following all cold fusion research, including Dr. Tsyganov’s work. (thanks Doc!) I wonder if they are, or plan to collaborate together to improve the devices “being engineered in real time” that Dennis Bushnell speaks of.

  3. I appreciate Dr. Tsyganov’s interest, but he is not describing cold fusion. The studies he cites bombarded materials with high energy deuterons and used the production of neutrons as a measure of the fusion rate, such as produced by the hot fusion process. The measured rate was then compared to the rate expected using typical plasma to show that the lattice produced a greater effect than would be expected in the absence of a lattice. This enhanced effect caused by the lattice is still 10 orders of magnitude below that possible using cold fusion.

    Neutrons are not produced by the cold fusion mechanism. Instead He4 is produced, which is not produced by the hot fusion process. Therefore, the studies apply to a mechanism typical of hot fusion. Dr Tsyganov is trying to describe an apple using the characteristics of an orange. We need to talk about the same reality before we can communicate.

    1. Hey Dr. Storms, Thank you for responding.

      What elements, if any, of hot fusion are common to both hot fusion and cold fusion.

      Is there any?

      Obvisously it’s the same particles, (or not?), but is there any process at all that is common to both hot fusion and cold fusion in spite of all the differences?

      1. Storms’ reply:

        “Hot fusion requires deuterium because hydrogen cannot fuse by the hot-fusion processes. The hot fusion process can occur in any material if the deuterons are given enough energy. Consequently, deuterons have been used to bombard various metals and compounds including liquid Li. The results have shown that the fusion rate can be increased slightly at low applied energy by the electron concentration in the target. However, the rate is very small compared to a typical CF process. Furthermore, hot fusion can not explain how energy can be obtained using H with the cold fusion conditions.”

      2. Adam,Biostasis is a deeper form of hitnerabion, yes? We still have large adult humans to accelerate to high speeds. So we need mastery of fusion and hence a large space-based infrastructure. We still have to deal with radiation issues. So you still think that this will be the first method of interstellar travel?As for uploading, there are two ways of looking at this. One is me being transported by radio broadcast in which we have the identity issues. And I agree with you re: me vs copy issues. But one could also spread humanity by broadcasting copies so that my identical twin is now in a robotic body on some exoplanet. In this case you don’t have to use massive amounts of energy to accelerate full-sized humans you just have to use large amounts of energy to accelerate fabricators.

    2. Dr. Tsyganov responds:


      I agree with Ed Storms: electron screening potentials in metallic palladium crystals were measured in Gran Sasso using hot fusion process and hot fusion products. I use these data as an “instrument” to understand what is really happening inside the crystal.

      However, these screening potentials characterize the shape of the target deuterium atom embedded in metallic crystal, as also the shape of the incoming deuterium atom moving in crystal. (To bombard the target deuterium atoms embedded in metallic crystals, physicists used accelerated ionized deuteron beams, not atoms, but at the very low energies of deuterons, in a solid state, deuterons esquire the orbital electron, if the speed of the deuteron nuclei is less than the Bohr velocity. It happen when incoming energy of deuterons is less than 50 keV).

      Yes, I suppose that two deuterium implanted atoms in the same crystalline cell, at the rest (i.e. at thermal energies) have the same elongated shape that was measured in Gran Sasso. It is definitely true for the target deuterium atom implanted in advance in palladium.

      How fast the bullet deuterium atom esquires elongated shape in the cell, is not known, but all the electronic processes in crystals are very fast and the speed of the bullet deuterium atom is low. If the bullet atom shape elongates not fast enough, cold screening potentials for cold fusion should be even larger.

      I recommend Ed to read my paper. Everything is explained there.

      I did not understand Ed’s statement:
      This enhanced effect caused by the lattice is still 10 orders of magnitude below that possible using cold fusion.



      [1] Cold Nuclear Fusion by E.N. Tsyganov published Physics of Atomic Nuclei 2012, Vol. 75, No. 2, pp. 153–159 [.pdf]

      1. Dr. Storms responds:

        A useful explanation must acknowledge that cold fusion and hot fusion are two separate process that have no relationship to each other. Without this understanding, we are not discussing the same reality. Dr. Tsyganov wants to apply the understanding that comes from studies of hot fusion. While this understanding is correct and accepted by physics, it simply can not be applied to cold fusion and still explain observed behavior.

        This effort to use hot-fusion to explain cold fusion was the source of the initial rejection and now has resulted in complete failure to explain the phenomenon. A successful explanation must be based on what has been observed. A very large amount of observation has been published. This information must be known, understood, and used in any theory. Dr. Tsyganov needs to master this knowledge before a discussion of his theory is worthwhile. This information can be obtained at http://www.LENR.org.

        As for the statement that a 10 orders of magnitude difference exists between CF and HF, CF is able to generate tens of watts of power at an energy equal to room temperature. Hot fusion requires energy 10 orders of magnitude greater to do the same thing.

        1. Edward Tsyganov replied:

          There is no doubt in my mind that quantum physics of Coulomb barrier penetration is the same for such different processes as hot fusion, muon catalysis or cold fusion. The only differences are arising with such “unimportant” circumstance as multiplicity of attempts. In hot fusion it is a single particle-to-particle interaction. “Yes” or “No” cases. In the case of “Yes” an intermediate excited nuclei is created. In the “No” case particles go away and (probably) never meet again. In muon catalysis attempts to penetrate Coulomb barrier are repeated again and again with frequency of about 10^17 per second, due to quantum oscillations in the “box”, until succeed. Similar story is with cold fusion, too. Remember quantum vibration of lattice atoms in a crystal at the absolute zero temperature. Therefore, hot fusion, muon catalysis and cold fusion are quite different processes, but with basically the same core physics.

  4. Looking at this mostly from a “hot” fusion perspective, I don’t see what the fuss is about. Any condition that increases the cross section of a particular reaction is worthy of note. The fact that such a condition is also similar to the conditions of “cold” fusion is suggestive. If what happens in “cold” fusion is actually fusion, I think work such as Tsyganov’s may help shed additional light on the conditions under which fusion in general may happen. In my opinion, Julian Schwinger’s words, though they may be true, are not terribly useful. They only serve as a stop-gap until a mechanism for cold fusion can be demonstrated, and the precise conditions required for such a reaction can be specified.

    Slightly off topic, I recently came across an abstract that looked interesting to me:


    Alas, I don’t have access to the full paper.

  5. Before any understanding of LENR is possible, a person has to acknowledge exactly what happens as a result of the process. Then a person has to explain how such behavior is possible using what is known in physics. When this is done, they will discover that the total behavior cannot be explained without making implausible assumptions or having logical conflicts with what is observed. A new insight is required. Simply concluding that the Coulomb barrier needs to be lowered by a process based on how hot fusion behaves is only a small part of the required mechanism. This lowering process must be much different from how the process operates during hot fusion to account for all behavior. I have obtained these conclusions and insights by reading all of the papers available on the subject, over 4000, and applying an understanding of hot fusion and chemical principles. If a person wants to make a useful contribution, they need to do at least this much study. Casual conclusions based on ignorance are not useful. LENR is a new phenomenon and needs to be viewed as such. So, please do your homework before you try to advance understanding. The required information is easily available.

  6. Dear Sirs,

    Do you know that in the program of coming Channeling 2012 meeting, 5th International Conference “Charged & Neutral Particles Channeling Phenomena” (Alghero, Italy, September 23-28, 2012 – http://www.lnf.infn.it/conference/channeling2012/) we have fixed a round table discussion based on the presentation of Prof. E. Tsyganov “Cold Fusion Now”. The discussion will take place in the meeting room of hotel Calabona (Alghero).
    It’s of my pleasure inviting you to take part in the discussion.
    For any details, please, do not hesitate to contact us directly via e-mail: channeling2012@lists.lnf.infn.it.

    Sincerely, Sultan Dabagov, chairman of the Channeling series

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