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249) An interesting theory of Akito Takahashi

Ludwik Kowalski (6/18/05)
Department of Mathematical Sciences
Montclair State University, Upper Montclair, NJ, 07043

As mentioned in another unit, I belong to the International Society of Condense Matter Nuclear Science (ISCMNS). That society has a restricted discussion list, called CMNS, for its members. A recently published theoretical paper of a well known Japanese researcher is now available for downloading at

That is what was announced on that list yesterday. After reading this paper I posted this message:

Thanks for making this paper of A. Takahashi available to all. I sense that it is an important contribution. But my background is not sufficient to understand the theory. What I would like to achieve is a simplified (intuitively appealing) description of basis assumptions and essential conclusions. I am probably not the only one who would appreciate help from somebody who already grasped the main idea. Let me try to write down what comes to my mind as I read the paper. Please correct where I am wrong.

a) The so cold "hot fusion" involves collisions between two D ions. The coulomb barrier is high because the nearest electrons are too far away to help lowering the barrier.

b) And what about two neutral D atoms forming a neutral covalent molecule? Here the average distance between positive nuclei is 0.07 nm. Thermal fluctuations around this internuclear distance do not lead to fusion because orbitals in which electrons reside are too far away. In other words, the coulomb barrier is still too high to make cold fusion observable.

c) Takahashi invents a neutral quaziparticle TSC (Tetrahedral Symmetric Condensate). It is a squeezed quazi-molecule made from two neutral molecules in tetrahedral configuration. One way to visualize this configuration is to take two identical tooth picks and imagine four positive deuterons at their four ends. Make a symmetrical cross (two sticks on top of each other) and pull one stick away from another. The distance between the sticks should be such that distances between any pair of deuterons is the same. In Figure 5 (on page 7 of A.T. paper) the four deuterons are blue sphere. Each deuteron has an electron associated with it; electrons are represented by yellow spheres.

d) I do not know what causes such system of eight charged particles to collapse. And I believe the author that orbitals in which electrons reside are such that the coulomb barrier is lowered very significantly. The main point is that fusion of four deuterons into 8 Be is much more probable than fusion of two deuterons into 4H (from a neutral molecule). Once formed, the 8Be nucleus at once breaks into two alpha particle. instability of 8Be with respect to fission into two helium nuclei is a well known process.

e) Another important point is that the TSC, approaching another nucleus (such Al, Ni, Pd or U) acts as a nearly neutral particle. This happens because negative electrons reside very close to positive deuterons. (Do not ask me why.) For that reason fusion of TSC is no longer inhibited by coulomb barrier. The probability of fusion with heavier nuclei, in this model, depends essentially on the probability of formation of TSC in condensed matter. The same is true for the probability of producing helium from TSC.

5) Is this a fair description of the main idea? Numerical conclusions are summarized in Figure 6. I see an obvious font substitution error here; what is labeled Rambda should probably be lambda. Is lambda the usual decay constant in sec^-1? I have other questions about that essential figure. But this can wait.

Please comment, please correct, please add. Please share your own attempt to understand. Thanks in advance.

That was about 24 hours ago. Nobody answered so far. Actually it is wrong; I did receive an interesting essay from Russia but I do not think it explains Takahashi’s theory. Today I downloaded -- from the library at -- the paper that A. Takahashi presented at the last International Conference of Cold Fusion (ICCF11). It is also about tiny clusters of more than two hydrogen atoms. The author states that a TSC does not have to be a DDDD. In a mixture of heavy and light water a TSC can also be a DDDH, DHDH, DHHH or HHHH. Pure DDDD produces 8Be that decays into 4He +4He liberating 47.6 Mev of nuclear energy. The DDDH, on the other hand, produces 7Be which decays into 3He+4He liberating 29.3 MeV of energy. Likewise DHDH produced 6Be which decays into 3He+3He. Both 4He and 3He are expected when an electrolyte contains a mixture of heavy and ordinary water. Instead of fissioning a TSC quaziparticle, created near the surface of a large nucleus, can fuse with that nucleus.

In other words, the variety of output reaction channels is much larger than it would be if all TSCs were DDDD. Takahashi performed an experimentally verifiable (in principle) relation between the percentage of light water in heavy water and the expected 4 He / 3He ratios. I like when theoretical results are presented in terms of relations between measurable quantities. But I still have a bunch of questions. What leads to formation of TSC clusters? Why are these clusters so small? I hope that someone will answer such questions. I guess the answers are hidden somewhere in earlier theoretical publications of Takahashi.

Small clusters make me think about DD molecules, made from two hydrinos. They are also said to be tiny. Occasional cold fusion of two hydrinos residing in a DD molecule would produce 4He while 3He can be produced from fusion of hydrinos in the HD molecules. Likewise, very small DD and HD clusters, approaching heavier nuclei, would produce compound nuclei because coulomb barriers are nearly eliminated. In other words, cold fusion (CF) and cold transmutation (CT) can be explained either by hydrinos (introduced by Mills) or by larger clusters (introduced by Takahashi). What is not clear is why such clusters formed in the first place. Was their existence postulated to explain experimental data or was it derived from preexisting theories?


Appended later on 8/17/05:
I was composing a reply to Kozima when the follwing message from Takahashi arrived.

Thank you for your comments to my models. I think, you are hitting the essence of my models. Could you please read my two papers and see ppt slides available at SIENA2005 of site, which treats some details, together with my paper for ASTI5 at the same site.

I have now no time to respond your questions to write detail explanation, but I hope you kindly read my older papers for ICCF9, 10, 11 and JCF4, 5, which have treated elaboration of  EQPET/TSC models. For fission products distribution for A<200 nuclei, please read my paper Jpn. J. Appl. Phys., 41(2001)7031-7046.

To improve my models, I need great helps from other researchers to formulate for example TSC formation rate at some sites (we need modeling) at/near fractal surface, and for other key issues.

PS: In the last 6 days, I was busy due to the funeral of my father who died with 95 years old.

Appended later on 8/18/05:
1) The following comment was posted by Hideo Kozima, a theoretically inclined CMNS researcher.

It is necessary to understand clearly what is a theory, what is a model and what is an assumption. There are too many assumptions pretending [to be] theories. Generally speaking, following definitions will be applicable. A theory is based on principles commonly accepted in scientific world. A model is a system of assumptions based on facts but not deduced from principles trying to explain various phases of facts. An assumption is individual explanation of facts not forming a system of explanation for facts.  We have to distinguish them especially in research of the cold fusion phenomenon. P.S. In my opinion, "Akito's theory" is an assumption to explain "Iwamura's data" and some others.

My reply, composed last night, was essentially "philosophy" of science not science itself. It looked childish today and I am glad it was not posted on the list. Let me replace what I wrote with what Frank Wilczek wrote recently, in Physics Today.

“A popular class of problems specifies a force and asks about the motion, or vice versa. These problems look like physics, but they are exercises in differential equations and geometry, thinly disguised. To make contact with physical reality, we have to make assertions about the forces that actually occur in the world. All kinds of assumptions get snuck in, often tacitly.”

I see nothing wrong with making reasonable assumptions in attempts to match limited sets of experimental data. After being successful one can go further and make theoretical predictions. Such predictions are either confirmed of contradicted by experimental data. . . . Everybody knows how basic laws of nature were discovered. But experiments must be reproducible to rely on that kind methodology. Experimental scientists are blind without theories and theoretical scientists are paralyzed without reproducible data. That is our tragedy in CMNS.

Added on 8/19/05:
Yes assumptions must be reasonable. Some assumptions are not reasonable. Such assumptions can be called wishes . For example, I can assume that, under certain unspecified conditions, an electron can enter a duteron an remain in its center. A deuteron containing an electron (De) is not repelled by another hydrogen nucleus and fusion can take place at low temperatures. The De clusters are also not repelled by heavier nuclei. Thus they can lead to all sort of cold transmutations. Why are cold fusion (CF) and cold transmutations (CT) so rare? Because the probability of capturing an electron by a deuteron is very low. And why are CF and CT not reproducible? Because we still do not know how to control conditions under which De clusters are formed. My assumption is not reasanable; it cannot be justified in terms of what I know about nuclear forces (either strong or weak).

I suppose that Akito’s assumption about neutral DDDD clusters, named TSCs, is not wishful thinking. But I do not know how it can be justified in terms of what is known about distributions of electrons in quazi-molecules. A DDDD is essentially a neutral precursor of 8Be.

Last night a teoretically inclined colleague made an interesting comment about theoretical assumptions that are not reasonable. He said that an assumption should not be rejected on the basis of absence of reasonabliness. The only valid reason for rejecting an assumption should a discrepancy between logical (mathematical) consequences of using it and experimental data. The well known assumptions on Niels Bohr were that (a) electrons do not radiate electromarnetic waves due to centripetal acceleration, and (b) only certain orbits are allowed. These two ad hoc assumpions were in conflict with laws of macroscopic physics. They were certainly not based on anything known before 1912. His hypothetical theory became valid after its true predictions (facts that were not known in advance) were confirmed.

One true prediction, in Takahashi’s paper presented at ICCF11, is a graph showing how the isotopic 3He/4He ratio should depend on the percentage of light water in the D2O + H2O electrolyte. Will experimenta data confirm this graph? This remains to be seen. The unreasonable assumptions, when they lead to accepted theories are said to be beginnings of new paradigms. In the periods of normal development (between scientific revolutions) assumptions should not conflict with accepted theories. To what extent are Takahashi’s assumptions reasonable and to what extent are they ad hoc?

= = = = = =

Responding to:

> I liked your comment:  "Let the perfect not be the enemy of
> the good". This is a simple explanation of what Dr. Talbot
> Chubb has been saying to the Cold Fusion community for
> years.  "If a quantum mechanical explaination is a useful
> model of cold fusion, then use it to predict your experiments". 
> (Even if it is not perfect in some peoples view)  It could
> be quite GOOD!

I just posted this reply :

Two deuterium atoms, separated by a distance 0.07 nm, form a covalently bound molecule. What kind of bounding keeps four deterium atoms together in a neutral TSC quazi-molecule?

Hopefully somebody familiar with quantum mechanics, and who followed the evolution of the Takahashi’s model, will explain what the DDDD clusters are. Meanwhile I drew this schematic picture of a TSC.

Large black dots are atomic nuclei of four deuterium atoms while crosses represent centers of orbitals where electrons reside. If necessary, individual dots and individual crosses can be indentified by the edges at which they are located, for example, the deuteron BC. Note that only 8 edges are occupied. And I am ignoring that this TSC cluster is surrounded by other atoms. These other atoms are probably playing an important role. But this is only a guess. In my mind EFGH is one unusually small molecule and ABCD is another. They are orthogonal with respect of each other. But I have no idea why the molecules are much samller than common molecules and what keeps them together.

Added on 8/20/05:
A theoretical physicist XX posted an interesting summary of a paper that was submitted, but not accepted at a conference this year. But that was not what I expected. An hour later I received a very brief private message from Takahashi. He is going to address the issue at the ICCF12 (next International Conference on Cold Fusion, starting on November 28, 2005). Then he wrote ” Please look my ppt slides for IMFP2005 (International Meeting on Frontiers of Physics), especially #58-62 slides, according to transient electron bonding for TSC.” The CC of Akito’s message was sent to XX.

Slides that were shown at IMFP2005 (Malaysia, July 2005) can be downloaded by going to:

and scrolling to “Saturday 14 May.” The third item contains two links, one to Akito’s slides and another to his talk in Siena. The slides show that the issue of formation of TSC has been addressed. One slide, for example, has this title: “Orthogonal coupling of two molecules makes a Miracle!” Another slide has long equations describing wave functions; presumably indicating where components of the “miracle” (four deuterons and four electrons in a TSC) are located. Unfortunately, my familiarity with QM is very limited; I never had a chance to go beyond what I learned about 40 years ago. For example, I accepted reality of attractive covalent forces (as between two hydrogen atoms in common H2 molecules) without studying QM machinery. What people like me need are popular versions of serious papers. Theoretically inclined physicists often overestimate their audience.

In the Siena paper I see a section about formation of TSC. Here an interesting quote: “We know surface of metal is complex and fractal with ad-atoms, dimers and corner-holes, for example, as illustrated in Fig.2. Somewhere, for instance in corner holes, incident D2 molecules are trapped by dangling bonds. Free D2 molecule has freedom of rotation and vibration. Trapped D2 would lose freedom of rotation, but can vibrate for changing distance between pairing two deuterons, and waiting for incoming D2 molecule. When incoming D2 molecule meets near to trapped D2, incoming D2 rotates with 90 degrees maximum against waiting D2 molecule to neutralize charge (minimize Coulomb repulsion energy) and form an orthogonally coupled two D2 molecules when there meets coherence in vibration modes and electron-spins are anti-parallel for counter part electrons. In this way, TSC may be formed on surface. Since the scenario is still very speculative, we need further substantiating studies.”

What is missing, as far as I am concerned, is an explanation of causes of such behavior of two molecules, for example, during the electrolysis, or when hydrogen diffuses through palladium.

Appended on 8/21/05:
1) Here is the message I posted yesterday: “The slides show that the issue of formation of TSC has been addressed. One slide, for example, has this title: “Orthogonal coupling of two molecules makes a Miracle!” Another slide has long equations describing wave functions; presumably indicating where components of the “miracle” (four deuterons and four electrons) are located. Unfortunately, my familiarity with QM is very limited; I never had a chance to go beyond what I learned about 40 years ago. For example, I accepted reality of attractive covalent forces (as between two hydrogen atoms in a common H2 molecule) without studying QM machinery. People like me need popular versions of serious papers. A set of assumptions and a set of conclusions is usually sufficient. Theoretically inclined physicists often overestimate their audience. “

2) Why am I writing all this? To dramatize situations that are probably more common than theoretically sophisticated people believe. What is the best possible way to guide experimental researchers? I do not know. Experimentalists must try to learn the vocabulary, if not the language, of those who guide them. But theoretically inclined leaders should try not to overwhelm experimentalists with details. Likewise, experimental people should not overwhelm theoreticians with practical details. What is essential for one group is not essential for another.

3) Takahashi sent me the most recent version of his slide show; it should already be downloadable from the library at <>. The beginning of formation of TSC is shown on slide 27. All four electrons, represented by crosses at my illustration above, are simultaneously pushed toward the center. The center is called site T and the process is referred to as squeezing. Squeezing forces are represented by red arrows; they originate from four Pd ions. These ions also form a tetrahedron; they are situated further away from the center than electrons. I suppose that squeezing forces are electrostatic; what else can they be? I am puzzled by directions of these forces on slide 27. Positive Pd ions should attract and not repel electrons.

4) Slide 28 introduced new notation “Quadruplet e*(4,4).” On slide 29 I see that e*(4,4) is called a single particle at site T. The size of that site (~0.01nm) is seven times smaller that the average distance between D and D in an ordinary molecule. The lifetime of that particle is calculated as 2.3 fs. Then, if I understand this correctly, it becomes TSC, whose lifetime is 60 fs. Should I assume that the TCC, in the slide title, is a typing error (it should be TSC)? Slide 31 is not clear because I do not know, for, example, what probability = 10% refers to. I also do not know the difference between dde* and dde*e*. Unfamiliar notation is the most frequent inhibitor, as far as i am concerned. Slide 32 is a reminder that the probability to penetrate a coulomb barrier depends not only on the height of the barrier but on its width as well.

5) Should I assume that 60 fs (on slide 29) is the expected time for the cold fusion to occur? If so then this time determines the outcome of competition between cold fusion (CF) and cold transmutation (CT). The probability of CT would increase if that time interval were longer.

Appended on 8/22/05:
Last night I received a private message from Dr. Takahashi; he started addressing questions and comments that were appended yesterday morning (see above). I am glad that XX, who is a theoretical physicist, also received that private message. He will certainly understand Akito’s papers much better that I can. My suggestion is that he cooperates with Takahashi and that together they develop a tutorial. In my opinion a popularized version of Takahashi’s model is going to help many physicists, both inside and outside the CMNS community. To trigger this potentially desirable project I am going to send this paragraph to both XX and Takahashi. I am nearly certain that XX would not object if his identity were revealed. I will do this next time, unless he prefers to remain known as XX.

2) Water at low temperatures is a crystal. At higher temperatures it becomes a liquid and than a vapor. In a liquid molecules often cluster into attached groups. Clustering is possible because water molecules are polar and because they are close to each other. Hydrogen molecules, such as DD, are not polar. Therefore the existence of a tetrahedral cluster (see the drawing above) must be explained by something else that electric attraction. Likewise, something else than electric force must explain the squeezing of a DD-DD cluster into a TSC. According to Takahashi phonon excitations are responsible for processes leading to formation of TSC. I guess I must learn something about phonons to understand this.


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