The Curious Story of the Muon-Catalyzed Fusion Reaction

Joshua Yoon
March 5, 2016

Submitted as coursework for PH241, Stanford University, Winter 2016


Fig. 1: Author's rendition of the muon-catalyzed fusion reaction.

Upon hearing the phrase "nuclear fusion," many of us are quick to associate the phrase with an immense explosion leaving behind a mushroom cloud or a loud, deafening blast it produces which nothing standing a chance. When it comes to anything nuclear of the sort, we already have this expectation that it must have a destructive effect, but surprisingly it turns out, there is an area of nuclear research which explores reactions that takes exception to this. After the end of World War II, a few nuclear researchers from all around the world began exploring a new process which would be known as muon-catalyzed fusion (μCF). It would take years before this nuclear fusion reaction took notice but when it did, a new field of nuclear research was born and has been the subject of much research ever since.

The Muon-Catalyzed Fusion, the Solution to Our Energy Needs ...

The μCF reaction all begins with a single muon, which holds the same charge as an electron but is 207 times more massive (Fig. 1). These fundamental particles get injected into a sea of liquid hydrogen heavy isotopes: (1) Deuterium, one proton and neutron, and (2) Tritium, one proton and two neutrons. Once the muon replaces an electron to form a Tμ atom, it may bind to a Deuterium nucleus to form a DTμ molecule with a muon orbiting both of them. A nuclear fusion event between Deuterium and Tritium then occurs and one α particle, one neutron, and one liberated muon. There are times during the cycle, however, where the muon will remain in the α particle. [1] It's a deceptively simple reaction that doesn't involve very heavy elements at all, but it had escaped nuclear scientists for many years.

The very notion of μCF had its first seeds planted by the theoretical work of Dr. Frederick Charles Frank in 1947 when he published a paper in Nature hypothesizing muon-catalyzed events that lead to energy production. [2] Two Russian scientists, Yakov Zel'dovich and Andrei Sakharov were also considering this same process a few years after, drawing the conclusion that an incoming muon could cause a mixture of Deuterium to fuse together. [3]

Then 1956 came when Luis Alvarez and his group published their work on μCF in the Physical Review in which they reported observing the formation of muonic atoms which subsequently catalyzed a nuclear fusion event in a liquid-hydrogen bubble chamber (Fig. 2). [4] The amazing thing is this discovery was a complete accident and was not what Alvarez was expecting at the time. He recalled his excitement during his 1968 Nobel Prize acceptance lecture:

"We had a short but exhilarating experience when we thought we had solved all of the fuel problems of mankind for the rest of time. A few hasty calculations indicated that in liquid HD (hydrogen deuterium) a single negative muon would catalyze enough fusion reactions before it decayed to supply the energy to operate an accelerator to produce more muons, with energy left over after making the liquid HD from sea water. While everyone else had been trying to solve this problem by heating hydrogen plasmas to millions of degrees, we had apparently stumbled on the solution, involving very low temperatures instead." [5]

A nuclear fusion reaction happening at low temperatures rather than at the usual millions of degrees was at the time something scientists had only dreamed about. But with mounting scientific evidence pointing towards a new energy source with limited waste and great feasibility, a new age of energy seemed to be upon the world.

... Or Is It?

Across the country, John David Jackson was on leave in 1956 visiting the Physics Department at Princeton University on a John Simon Guggenheim Memorial Fellowship. One of the nice things about living so close to New York was getting The New York Times every morning. As it would turn out, the one that he received the morning of December 29, 1956 would be the most important. A report was written regarding the discovery the Alvarez group made earlier regarding μCF and the speculation he made regarding energy production made Jackson very excited. [6] Putting himself into work, Jackson made a series of crucial calculations concerning (1) the sticking probabilities and (2) the amount of energy the nuclear fusion reaction creates. [3] The sticking probability here is defined by the average number of catalytic events a muon can induce, regardless of how rapidly the catalytic cycle occurs. Using simple quantum mechanics to make his calculations and taking into account the finite number of inelastic collisions with the atoms of the liquid hydrogen, he was able to calculate the following probabilities for the negative muon to stick to its positive reaction product:

ωs = 0.94% (DTμ → 4He + n + μ)
ωs = 15% (DDμ → 3He + n + μ)
ωs = 8% (DDμ → 4He + μ) and (DDμ → T + n + μ)

What's important from these numbers is that fact that on average a muon will not initiate more than 100 catalytic acts in a d-t mixture and not more than a dozen in pure liquid deuterium. Using this fact, with an estimated energy cost per muon at 10 GeV and only 1.7 GeV produced with 100 dt fusions, the amount of energy gained is a net negative. Jackson and Alvarez exchanged a series of letters discussing these results, which demonstrated that indeed a µCF reactor would not be able to be sustainable. Jackson shortly after published a paper that made clear the steps he took to make each calculation and ever since has been quite consistent with the experimental results. [7]


Although Jackson's paper and subsequent experiments demonstrated μCF as being a non-viable solution to our energy needs, it is by no means a dead field. Many groups have made great strides in understanding its hyperfine interactions, resonant processes, and under gaseous conditions. [8-10] However, there have been cases where scientists will take things just a bit too far for their own good and produce faulty results when attempting to do room temperature fusion reactions. [11] Martin Fleischmann and Stanley Pons from the University of Utah had claimed that they were able to observe (1) excess heat, (2) tritium production, and (3) a γ-ray spectrum without using muons. [12] Many groups were unable to reproduce their results, which put both scientists under a heavy storm of criticism. Despite all of this, μCF still stands as a scientifically sound process which has still yielded interesting results. Whether or not it will indeed turn out to be the "solution" Alvarez had hoped he had found many decades ago is yet to be determined, but at the very least we can continue searching for answers to our energy problems that can offer hope for our future.

© Joshua Yoon. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] L. I. Ponomarev, "Muon Catalyzed Fusion," Contemp. Phys. 31(4), 219 (1990).

[2] F. C. Frank, "Hypothetical Alternative Energy Sources for the 'Second Meson' Events," Nature 160, 525 (1947).

[3] J. D. Jackson, "A Personal Adventure in Muon-Catalyzed Fusion," Phys. Perspect. 12, 74 (2010).

[4] L. W. Alvarez et al., "Catalysis of Nuclear Reactions by μ Mesons," Phys. Rev. 105, 1127 (1957).

[5] L. Alvarez, "Recent Developments in Particle Physics," in Nobel Lectures, Physics 1963-1970 (Elsevier, 1970).

[6] "Atomic Energy Produced by New, Simpler Method," New York Times, 29 Dec 1956.

[7] J. D. Jackson, "Catalysis of Nuclear Reactions Between Hydrogen Isotopes by μ-Mesons," Phys. Rev. 106, 330 (1957).

[8] T. Case, et al., "Systematic Analysis of the PSI Experiment to Directly Measure the Sticking Probability ωs in DT Fusion," Hyperfine Interact. 82, 295 (1993).

[9] E. A. G. Armour, "Examination of a Key Resonant Process in the Muon-Catalyzed Fusion Cycle That Can Be Treated Theoretically in the Same Way as a Chemical Reaction," J. Chem. Soc. Faraday Trans. 93, 1011 (1997).

[10] D. V. Balin et al., "High Precision Study of Muon Catalyzed Fusion in D2 and HD Gas," Phys. Part. Nuclei 42 185 (2011).

[11] D. Chung, "Cold Fusion: a Study in Scientific Controversy," Physics 241, Stanford University, Fall 2015.

[12] M. Fleischmann and S. Pons, "Electrochemically Induced Nuclear Fusion of Deuterium," J. Electroanal. Chem. Interfac. Electrochem. 261, 301 (1989).