Some thoughts about muon-catalyzed fusion as it relates to cold fusion:

Background: What is muon-catalyzed fusion?

A muon is an elementary particle which has the same negative charge as an electron, but a heavier mass (200× heavier than an electron, but still 10× lighter than a proton). It is unstable, living an average of just 2 microseconds (or longer if they are moving fast, thanks to relativistic time dilation). Muons rain down on us from above: They are created when cosmic rays (fast-moving particles from outer space) slam into air molecules at the top of the atmosphere. At sea level there is about 1 muon per cm2 per minute coming down from the sky.

Being negatively charged, muons are attracted to protons and other nuclei. As we all know from playing Bond Breaker, muons settle into very very close orbits to the nuclei, much closer than electrons can get. The reason is purely because of their larger mass, which allows them to get close to the nucleus (large momentum) without having an excessively large kinetic energy ( = p2/(2m)).

That brings us to muon-catalyzed fusion. If you have some deuterium gas, each molecule is normally two deuterons and two electrons. If a muon approaches, it displaces one of the electrons, and then the equilibrium bond distance between the two deuterons goes way down. Then they are close enough to quantum-tunnel through the remaining Coulomb barrier and undergo nuclear fusion. Pretty cool!!

Unfortunately, we cannot build a muon-catalyzed fusion power plant with today’s technology, because nobody knows how to get enough energy out of each muon to make up for the considerable amount of energy that it takes to create the muon in the first place.

Confusingly, muon-catalyzed fusion is sometimes called “cold fusion”. I will not use that terminology for obvious reasons. When I say “cold fusion” in this blog I am talking only about Fleischmann-Pons and related experiments.

Unlike cold fusion, every physicist agrees that muon-catalyzed fusion is a real phenomenon.

Is cold fusion actually muon-catalyzed fusion?

Obvious question: If muons are always raining down from the sky, and muons can catalyze nuclear fusion, isn’t it possible that cold fusion is actually a kind of muon-catalyzed fusion?

Intriguingly, Fleischmann and Pons were working in Salt Lake City, at a high enough altitude that you expect about 100× more muons than at sea level (ref). Edmund Storms, a prominent cold fusion experimenter, works at Los Alamos which has even higher elevation! …Unfortunately for this theory, there seems to be plenty of near-sea-level cold fusion experiments too :-/

There is a much bigger problem: Even if we ignore the low-altitude experiments and use the high-altitude figure of 100 muons/cm2/min, and plug in a 1cm2 electrode size and 1W of power generation, then we need each muon to catalyze a whopping 1013 reactions of D+D→Helium-4 before decaying! That’s crazy. To get 1013 reactions in the muon’s lifetime, we need 5000 reactions per femtosecond (in the muon’s rest frame). Any muon-catalysis process you could possibly imagine will be much much much slower than that. The deuterons can barely move in that amount of time! Moreover, each time the muon is free there is a reasonable chance that it will get stuck in palladium or another large atom. It can also wind up outside the electrode in the fluid, etc.

Oh, and that assumes that all those muons come to a stop in our cold-fusion electrode. In reality, almost all of them will fly right through it. So the real figure is even higher than 1013.

So, for these very good reasons, nobody believes that cold fusion is catalyzed by cosmic-ray muons.

Does muon-catalyzed fusion have the same branching ratio as hot fusion? Is there a new muon-spectator branch?

Conventional (“hot”) D+D fusion (in plasma and accelerated beams) has the following branching ratio:

  • D+D → neutron + helium-3 (~50% of the time),
  • D+D → proton + tritium (~50% of the time),
  • D+D → helium-4 + a gamma-ray (0.0001% of the time)

Is the same true in muon-catalyzed fusion? In particular, there is a new possibility here:

  • D+D+muon → helium-4 + muon

where the muon is a spectator which enables energy and momentum to be conserved. (This is similar to internal conversion.) The probability for this to occur is almost definitely larger than zero, but how large is it? Maybe it’s very very low because muons don’t feel the strong force. Maybe it’s pretty high. I don’t know enough nuclear physics to make a theoretical guess. Experimentally, there are tons of muon-catalyzed fusion experiments, but in my (cursory) search I have not found any papers that took the appropriate data to figure out whether or not this branch actually happens. If any readers know something about this, please comment!

I’m interested in this question because, notwithstanding my previous post about why spectators are implausible in cold fusion, it seems that everything else I read about cold fusion theory these days is even more implausible. So spectators are something I still think about. Therefore it would be very interesting to know whether the muons can be spectators in this more familiar kind of nuclear fusion.

12 thoughts on “Muons

    1. Abd ul-Rahman Lomax

      This was a reference to the work of Andrea Rossi. There is a lot of information now available because of the lawsuit Rossi filed against his investors, Rossi v. Darden. Simple summary. The “independent verification” was not independent, Rossi ran the show, and the technique used for measuring temperature didn’t work, they used the wrong value for alumina at the operating temperature. There were no decent control experiments, etc. It is entirely possible and even likely from the evidence that Rossi never had anything, it was all error and fraud. Fraud, I’ll say, because he was claiming a successful megawatt reactor. It’s really hard to pretend you are generating a megawatt in a warehouse with no special cooling facilities, unless people just look at numbers on instruments and don’t notice that they are not dying from the heat. Rossi seems to manage to hypnotise even scientists (such as Hanno Essen, who had been a leader of the Swedish Skeptics Society), into not noticing the obvious. In the next iteration of that test, the Lugano test, they measured the temperature of the reactor *exterior* at 1400 C, using a thermal camera. Never mind that inside, this would melt the materials and the control thermocouple, there are photographs of the device in operation, that show a dull red glow, indicating a temperature consistent with the input power of 900 W. They did not run a control at that same input power, giving a total BS reason probably fed to them by Rossi. At 1400 C., the reactor would have been white-hot, glowing so brightly that it would have been painful to look at. It wasn’t.


  1. steve Post author

    Chris, I understand that particle accelerators can produce muons, but the E-CAT apparatus is not a particle accelerator, and I don’t see any way that it could be producing muons.

    You said they “claim they have lots of neutron radiation”, but I don’t think that’s true. The arxiv paper does not mention neutrons. The press release mentions neutrons but only in the context of summarizing Widom-Larsen theory (i.e., as background) –


  2. steve Post author

    Chris – the whole point of this post is that muons are definitely not the “unknown additive”. A better (more technical) link for that E-CAT HT thing is . But I don’t have any particular plans to read the paper or comment on it, it’s not really in the scope of this blog or my interests right now.


  3. Chris

    My was that the muons were being seeded in the process, I know in the accelerator physics world, muon beams are possible, so seeding the reaction in real time is possible. It is an interesting topic. Also, those folks are using accelerators, but would not say why. That is what made me believe that they are seeding the reaction with muons in real time.


  4. Axil

    Check out the work of Leif Holmlid who produces overunity energy (COP =2) from muons generated chemically from iron oxide catalyst. His work is peer reviewed by the AIP.


  5. Dan steinberg

    Muon catalyzed fusion occurs because of charge screening.

    I believe Cold fusion also occurs because of charge screening. But with cold fusion, its the electrons of the host metal that do the screening.

    Charge screening has an enormous impact on the fusion reaction rate. Rate can be increased by 50-70 orders of magnitude, even with very low impact energy.

    charge screening can facilitate fusion from thermal impact energies, or perhaps no impact energy at all. There is no need for the deuterons to acquire 10kev or even 10ev or 1ev of energy.


  6. Dr Richard Shiells

    Why not turn the problem around and propose that under some conditions ordinary electrons can behave like muons? Not so far-fetched if RF high voltage/terahertz laser techniques are being used to stimulate LENR in transition metals saturated with protons/deuterons and heated up to form plasmas. In such plasmas electrons could approach a relativistic mass 100X their stationary mass at 0.995c ie just below light speed, so have about half the probability of inducing fusion by the 207X electron mass of the muon! Thus a very simple explanation for cold fusion and also how difficult it is to replicate/commercialise.


    1. steve Post author

      The reason that there is muon-catalyzed D2 fusion but not electron-catalyzed D2 fusion is basically the Heisenberg uncertainty principle. See section 2-4 for a closely related back-of-the-envelope example. When you have a very massive particle, even a weak attractive force can pull it into a very small space. Lighter particles are not as easily confined. In other words, if you try to squeeze a particle into a small box, the lighter the particle, the more energy is required to squeeze it inside.

      As the two Ds move closer together, there is an electrical attractive force that pulls negatively-charged particles into the smaller and smaller space between the two Ds. At some point, the attractive force is not strong enough to provide the energy necessary to confine the negative particle into that increasingly small space. Then the D’s start repelling each other and cannot move any closer. For muons, that equilibrium position is much closer than for electrons, because of the heavier mass as described above.

      Yes you can add a lot of energy to an electron by shaking it back and forth so violently that it approaches the speed of light. You can call that a “heavy electron” if you want, though I find that terminology to be far more misleading than helpful (see my post on that here). Instead of calling it “an electron with mass 50MeV/c²”, I suggest that we should call it what it really is, “an electron with mass 0.5MeV/c² and with 49.5MeV of ponderomotive energy”. Whatever you want to call it, we can ask the question, does this extra 49.5MeV reduce the amount of energy required to confine the electron to a small space? No, quite the contrary, it makes it impossible to confine the electron to a small space! Think about it: If the electron is moving back and forth a distance of amplitude d, then it is certainly not sitting in a space much smaller than d. I encourage you to do this back-of-the-envelope calculation; you’ll find that the quiver amplitude d is orders of magnitude too large for the electron to be effectively screening two nearby D’s from each other in the way that a muon can.


  7. Rick Cordasco

    So happy to see this blog. I suggest Nate Hoffman’s book to start with. He was commissioned by EPRI to research and provide facts, post Pons and Flieschman. Very detailed scientific analysis on many other Cold Fusion experiments world wide of palladium deuterium data, post fusion, helium, and other byproduct analysis. Short on theoretical analysis. Mind you the original Electro-chemistry magazine article was only a page and a half. A few sentences on possible unexplained over heating. I was at Georgia Tech taking a SCADA class. At that time March 1989. I happen to meet an engineer that was from Salem Nuclear plant in NJ. A primary step up transformer, a few million watts, was ripped apart from a Coronal Mass Ejection, (a very high increase in muon flux). The iron veins in the Appalachia, and through the Delaware basin. had very extreme, Van Allen belt, Delta and Y current imbalance from the CME coupling to Cosmic Rays.

    Cold Fusion from muon’s is a fact, Lewis Thomas Alverez. Noble Laureate. Break even is not viable with normal muon flux. CME is another story. I didn’t put this together until much later on. I have designs that collect normally occurring muon fluxes, at ground level that can be used to cause muon relativistic mass to energy conversion.



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