Branching ratio, collective effects, and special relativity

When you read cold fusion theories you hear a lot about collective effects, ways that atoms in a solid work together to do things individual atoms cannot. One iron atom cannot be a permanent magnet, but a trillion of them together can be.

Widom-Larsen 5: Would the neutrons actually be slow?

In Widom-Larsen theory, they say that the surface of a metal hydride has very energetic (“heavy”) electrons that can undergo electron capture $e^- + p^+ \rightarrow n + \nu_e$ (electron plus proton turns into neutron plus electron neutrino).

A central claim in the theory is that the electron capture process creates extremely slow neutrons. And I mean extremely slow! The neutron kinetic energy is supposed to be as low as $10^{-9}$ electron-volts, or even less! (Room-temperature thermal neutrons have millions of times higher kinetic energy. Even “ultracold neutrons” are fast by comparison.)

Widom-Larsen 4: The protons’ magical restoring force

As explained best in the 2008 paper, Widom-Larsen theory envisions a weird sort of surface plasma oscillation. Now, normal plasma oscillations (in solid-state physics) refer to a collective electron motion. But they’re talking about proton motion (the protons or deuterons embedded in the hydrated palladium). There is a vague suggestion that the electrons also move. But they certainly emphasize the proton motion by itself, and describe it in an explicit way here:

Widom-Larsen 3: Ponderomotive (quiver) energy

In Widom-Larsen theory, it is argued that there is a region at the surface of a metal-hydrogen (or -deuterium) system where electrons have an insanely high mass, as much as 10.5MeV/c², because of the electromagnetic environment they are in.

In the the previous post, I argued that you should understand that “insanely high mass” implies (or maybe is equivalent to) “insanely high energy”. In this post I will explain what exactly this energy is, according to Widom-Larsen theory. It’s simpler than you might think!

Widom-Larsen 2: The meaning of enhanced mass

As described in the last post, Widom-Larsen theory states that the electron-capture process $e^- + p^+ \rightarrow n + \nu_e$ (electron plus proton turns into neutron plus electron neutrino) can and does happen on the palladium hydride surface. (Discussed in Sections 1-3 of the paper.)

Now, if you compare the energy of the two sides in $e^- + p^+ \rightarrow n + \nu_e$, you’ll see that this would work if the electron mass is at least 1.3 MeV/c², rather than the usual 0.51 MeV/c². Well, that’s exactly what Larsen and Widom are arguing! They say that the environment at the surface of a metal hydride has properties which dramatically increases the electron mass.

Widom-Larsen part 1: Overview

The Widom-Larson theory of cold fusion started with this paper:

“Ultra Low Momentum Neutron Catalyzed Nuclear Reactions on Metallic Hydride Surfaces” by A. Widom, L. Larsen, 2005.

A follow-up paper with more mathematical details is here, while a follow-up with slightly more qualitative discussion is here.

This is apparently the most popular theoretical explanation of cold fusion. For example, it was the theoretical justification supporting NASA’s cold-fusion program. Apparently, lots of reasonable people are convinced by it.