Skip to main content

LENR and Muon Catalyzed Fusion

Reading about low energy nuclear reactions, (LENR), I came across several theoretical references to protons capturing heavy electrons and then participating in nuclear reactions as a result.  The heavy electron, because it sits in a much tighter orbit around a proton, serves to shield the proton's positive charge from other unsuspecting nuclei until the proton has crept in close enough to fuse with them via the strong force. In modern day LENR parlance, it is speculated that these sufficiently heavy electrons exist in materials, (condensed matter), as a result of the periodic potential due to crystal lattice sites, and the wave nature of the electron, (more on this later), leading to a higher effective electron mass.

While the previous paragraph describes theories of how LENR might occur in present day experiments, it's based on a set of actual observations made in the 1940s and 50s, (picture 1)[6]. In 1958, Luis Alvarez in a report to the Unitied Nations[8 open access] on high energy physics announced that his team had observed several muon catalyzed fusion events.  A muon is a naturally occurring particle that is a member of the same family of particles,(leptons), as the electron.  The muon has the same charge as an electron, but it is about 200 times more massive.  As a consequence of this extra mass, the hypothesis described above for heavy electrons actually takes place.  Interestingly, it was reported in the proceedings of a liquid scintillation conference[5] that as far back as 1958, the term cold fusion was being reported by the press and even then creating a fair bit of mayhem.

You may have heard how Canadian uranium stocks fell several months ago when a newspaper carried the announcement that uranium was now unnecessary because of the discovery of 'cold fusion'.
Jackson, of Jackson EM book fame, did an analysis of the process in 1957 and writing in the +American Physical Society's Physical Review[3] determined that in all likelihood, without a much cheaper source of muons, it would be impossible to derive any useful power,(picture 2).  For more detail on Jackson's involvement  and a rather complete explanation of the subject in general, check out Wikipedia[7].

Alvarez and Jackson both mention that similar observations had been made as early as 1947[1][2].


1.  Frank on hypothetical muon fusion

FRANK F.C. (1947). Hypothetical Alternative Energy Sources for the ‘Second Meson’ Events, Nature, 160 (4068) 525-527. DOI:

2.  Experimental observation I
LATTES C.M.G., OCCHIALINI G.P.S. & POWELL C.F. (1947). Observations on the Tracks of Slow Mesons in Photographic Emulsions, Nature, 160 (4066) 453-456. DOI:

3.  Jackon on Muon Fusion with speculations on useful energy release
Jackson J. (1957). Catalysis of Nuclear Reactions between Hydrogen Isotopes by μ- Mesons, Physical Review, 106 (2) 330-339. DOI:

4.  Wheeler on muon fusion
Wheeler J. (1949). Some Consequences of the Electromagnetic Interaction between μ--Mesons and Nuclei, Reviews of Modern Physics, 21 (1) 133-143. DOI:

5.  Cold fusion report circa 1958 (open access)

6.  Alvarez in Physical Review on Muon Fusion
Alvarez L., Bradner H., Crawford F., Crawford J., Falk-Vairant P., Good M., Gow J., Rosenfeld A., Solmitz F. & Stevenson M. & (1957). Catalysis of Nuclear Reactions by μ Mesons, Physical Review, 105 (3) 1127-1128. DOI:

7.  Very handy Wikipedia article on muon catalyzed fusion

8.  Alvarez to the United Nations (open access)


Popular posts from this blog

Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems, there seem to be fewer explanations of the procedure for deriving the conversion, so here goes!

What do we actually want?

To convert the Cartesian nabla

to the nabla for another coordinate system, say… cylindrical coordinates.

What we’ll need:

1. The Cartesian Nabla:

2. A set of equations relating the Cartesian coordinates to cylindrical coordinates:

3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system:

How to do it:

Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables.

The chain rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1.  While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero.  This is typically explained in the following way.  While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare.  That doesn't stop us from looking for them though!

Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2].  Cabrera was utilizing a loop type of magnetic monopole detector.  Its operation is in concept very simpl…

Kids R Kapable

Just a little note to concerned ‘grownups’ everywhere.  If you look at a kid—and I mean really look—I don’t mean notice a person shorter than you, I mean make eye contact, notice their facial expression and observe their body language—If you look at a kid, don’t assume they need your help unless they’re obviously distressed, or ask for it.  You might think this is difficult call to make.  You might think, not having kids of your own, that you’re unable to make this determination.  You are.  You do in fact, already have the skills even if you’ve never been around kids  It’s a remarkably simple call to make, just use the exact same criteria you would for determining if an adult was in distress.  Because, guess what, kids and adults are in fact the same species of animal and communicate in the same way.  Honest.  If someone—adult or child—doesn’t need your help, feel free to say hello, give a wave, give a smile, but don’t—do not—try to force help on anyone that doesn’t want or need it.