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.