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

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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.)

This claim is important because they are trying to explain cold fusion experiments in which neutron detectors register very few if any neutrons. So any theory involving neutron production would seem to be ruled out. However, Widom and Larsen say that a super-slow-moving neutron would be very likely captured by a nucleus within a very short distance, so it would have negligibly probability of reaching a neutron detector a few centimeters away. Thus, the theory is not ruled out by the experiments after all!

(Incidentally, I am deeply skeptical that slow neutrons would actually solve this problem. Even if the neutron is ultra-slow, the relative velocity between the neutron and a nucleus is not ultra-slow, because the other nucleus is shaking around randomly at room temperature. And if the ultra-slow neutron is elastically scattered from a moving nucleus, it would stop being ultra-slow! But that’s a story for another day. For this post I want to investigate whether there are slow neutrons in the first place.)

At first you may wonder: Isn’t the final neutron momentum determined by energy-momentum conservation?? If the electrons have up to 10.5MeV of energy, as stated in the papers, then the final neutron momentum would be typically huge, not super-low.  This seems like an obvious question, and I have no idea how Widom and Larsen would answer it. Maybe there is a distribution of electron energies, and only the electrons with just the right energy do this reaction? But that would be a negligible fraction. The energy window is way too narrow. You could argue that there’s something like the Mössbauer effect (this would be recoil-less neutrino emission, whereas the Mössbauer effect is recoil-less photon emission). But the neutron isn’t bound into a lattice, like nuclei are, so I don’t think it works.

I am strongly inclined to believe that this already proves that Widom and Larsen cannot be right about the neutron momentum. But anyway, I’ll leave that point aside and press on. Let’s assume for the sake of argument that energy and momentum conservation is not an issue. It happens magically! I want to look at the papers and figure out why Widom and Larsen think that the neutrons are very likely to be created with an extremely low momentum. Then I can decide whether the argument is any good.

Here is the big picture of their argument:

  • Step 1: Surface plasma wave has long wavelength
  • Step 2: ???
  • Step 3: Neutron has long wavelength

(Remember that long wavelength corresponds to low momentum, by the de Broglie wave equation.)

The big problem is step 2, which (I will argue) does not and cannot work. I think I know what they were trying to get at, so as background I’ll present…

An example where this kind of argument actually works: A photon is absorbed by an electron in a semiconductor. The important part is that when this process really happens, the electronic excitation wave lines up perfectly with the photon wave! They have the same wavelength and direction, the same peaks and troughs! (In an introductory semiconductor physics course, they would describe this fact in a way that sounds different, but is actually the same: \mathbf{k}_{\text{photon}} = \mathbf{k}_{\text{electron}} - \mathbf{k}_{\text{hole}}.)

Why do the waves match up? The way to think of it is: The electron-photon interaction can happen at any location. When the waves match up, the quantum transition processes all act coherently (“in phase”). The process “the photon interacts with the electron over here” adds coherently (in phase) with the process “the photon interacts with the electron over there”. Therefore the total transition probability is dramatically higher when the waves match up.

Widom-Larsen is trying to make a similar argument. When the plasmon wave matches up with the neutron wave, then the quantum transition processes all act coherently (according to this argument). The process “Electron capture occurs over here” would be coherent with the process “Electron capture occurs over there”. So the transition probability would be dramatically higher when the waves match up.

But it doesn’t work. Those transition processes cannot add coherently because they have different final states.

If proton A is converted to a neutron, then there is no more proton where proton A used to be. If proton B is converted to a neutron, then there is no more proton where proton B used to be. You cannot have quantum interference between two processes unless the final states are identical.

Widom and Larsen are arguing that the final neutron state can be identical in both of these processes, if the neutron is delocalized. OK, sure, that’s possible. But that doesn’t help, because the proton configuration is different!

Another way to say the same thing is in terms of the isotopic spin (a.k.a. isospin) waves described in WL2007:

The wavelength of the isotopic spin wave has no relation to the wavelength of the final neutron.

The isotopic spin wave is:

\sum_{\mathbf{r}} |\text{the proton at }\mathbf{r} \text{ has become a neutron} \rangle e^{i\mathbf{k} \cdot \mathbf{r}}

(Bra-ket notation.) The k here is the wavevector of the isotopic spin wave. But it’s unrelated to the wavevector of the neutron, which I actually left out above. Here:

\sum_{\mathbf{r}} |\text{the proton at }\mathbf{r} \text{ has become a neutron with wavevector }\mathbf{k'} \rangle e^{i\mathbf{k} \cdot \mathbf{r}}

Nothing special happens when \mathbf{k}' = \pm \mathbf{k}. Those two parameters are unrelated. It is only k, not k‘, which is related to the surface plasmon wavevector.

Summary: Even if everything else in Widom-Larsen is true, i.e. there is really electron capture producing neutrons, I think that Widom and Larsen are wrong to say that those neutrons would have an unusually low momentum.

(Or am I misunderstanding something?)

7 thoughts on “Widom-Larsen 5: Would the neutrons actually be slow?”

  1. Ron Maimon

    Another fatal flaw in Widom-Larsen is that even if you make neutrons magically, neutrons would not explain the effects in the experiments even in wild speculation. Neutrons absorbed by nuclei don’t conspiratorially go to the same nucleus multiple times to get +2 transmutations, so they can’t explain He4 production or any other +2 transmutation. They can only explain tritium generation, but tritium generation is not the main event, the tritium is not commensurate with the heat, it is an occasional trace product which is distinguished by it’s ease of detection, not because it is the main event. The decay of tritium to He3 is slow and understood, so you need more magic to hide the tritium. The He detection in the second generation cold-fusion work detected He4 not He3, and the He4 was roughly commensurate with the heat. So it looks like actual fusion, not Widon Larsen nonsense.

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    1. Doug Yuill

      You said: “Or am I misunderstanding something?”

      That’s something you only hear “good” scientists asking! Your postings about the W-L theory are among the few examples I’ve seen of someone trying to reason their way through the reaction mechanism on first principals, while keeping their doubts in check long enough to make some constructive progress.

      It seems to me that in the case of W-L, electron capture by a hydrogen proton *must* be an inelastic reaction. For this to be true, the transfer of charge required to increase the apparent mass must equal exactly 782 keV, which is the rest mass deficit needed to form a ULM (Ultra Low Momentum) neutron.

      This implies that initially, the SPP (Surface Plasmon Polariton) forms a topological insulator that can’t conduct until a 782 keV charge accumulates. Note: I don’t (yet) understand exactly why it has to be this value for a phase change from an insulating to a conducting state to occur. But it could it be that the electrons that form the SPP need to become “heavy” enough to enter the conduction band of the lattice?
      The proper explanation likely involves the interdependent formation of a resonate cavity which inhibits spontaneous emission, which I hope my deepening appreciation of QED (Quantum Electro-Dynamics) will eventually elucidate!

      You also said: “Even if the neutron is ultra-slow, the relative velocity between the neutron and a nucleus is not ultra-slow, because the other nucleus is shaking around randomly at room temperature.”

      Strictly speaking, if I understand your statement correctly, I don’t think this is true.
      i.e.: The other nuclei are NOT “shaking around randomly at room temperature”.

      Larsen refers to the participating atoms as being “quantum mechanically entangled”.
      I understand this to mean that “special conditions” are required to form the NAE (Nuclear Activation Environment) or as W-L refer to it, a “region of nuclear abundance”.

      If there’s a “reveal” to be discovered by understanding the W-L theory it’s this:

      The contiguous area of otherwise monotonic hydrogen physisorbed (physically adsorbed) on the surface of metallic hydrides that the SPP is formed out of, is being held in place on the surface because it’s at the same temperature, or proton resonance frequency, as the hydrogen that’s been loaded into the lattice (in the case of palladium) at a ratio of over 900:1. I think the “emergent properties” of such systems are a consequence of this one to many relationship.

      Continuing with my explanation, the absorption of hydrogen by palladium is an exothermic process, so in this sense, even though the hydrogen on the surface hasn’t been absorbed, for it to be physisorbed, it has to have been cooled to the same temperature, or proton resonance frequency, as the hydrogen that’s been loaded into the bulk of the lattice. An SPP formed under such conditions can absorb IR photons via the photo-electric effect, which is how the SPP can gather charge. Note: It’s been reported that prosaic dressing of an active LENR cathode using an IR laser pointer, can noticeably increase the rate of anomalous heat production.

      In summary:

      – The protons within this “nursery” of “special conditions” are oscillating coherently
      – When an electron within this nursery gains 782-keV of charge, its apparent mass
      allows it to be captured by a proton
      – Because the reaction is inelastic, there is no recoil energy to dissipate
      – It’s because the ULM neutron is generated from an already coherently oscillating proton within
      the nursery, that it can’t be captured by any nuclei that are “shaking around randomly at room
      temperature”; ie: By definition, the protons involved are all oscillating coherently

      Please let me know if this makes sense as I welcome constructive feedback on my contribution to the understanding of the W-L theory. It’s reassuring to see it finally getting some intellectually honest consideration, please keep up the good work!

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    2. Abd ul-Rahman Lomax

      Yeah, I’ve made the same argument. Tritium would be a major product if ULM neutrons were formed in a heavy water environment.

      It looks like “actual fusion”, all right, as long as we don’t insist that this means d+d. If a process other than d+d converts deuterium to helium, it would generate that commensurate heat. “Fusion” as a description of a result, rather than of a specific example process.

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  2. steve Post author

    Dear Doug,

    First of all, thanks for your kind comments!

    It’s hard for me to follow what you’re saying. I think you’re using some words in a weird way. For example, when you say “SPP forms a topological insulator that can’t conduct until a 782 keV charge accumulates” — I can’t make sense of any part of that sentence. SPPs are a type of electromagnetic wave, topological insulators are a type of solid, 782 keV is an amount of energy (not charge). Then you are comparing temperatures to frequencies in a weird way … If a photon excited an SPP you wouldn’t call it “photo-electric effect” … Etc. etc.

    I mentioned “Maybe there is a distribution of electron energies, and only the electrons with just the right energy do this reaction? But that would be a negligible fraction. The energy window is way too narrow.” Here is more detail about what I mean. if you’re saying that the electrons can participate in the reaction only if they have an energy between 782000 and 782000.000000001 eV, then that’s automatically hard to believe. It means you need to have probably hundreds of trillions of electrons with every other condition more-or-less just right, before you find one electron that also has the right energy. (“Hundreds of trillions of electrons” may not sound like THAT many electrons, but most electrons are not at the surface monolayer etc.)

    Another thing: The word “Coherent” is not a synonym of “Abracadabra!” You can use the word as part of an argument, but it doesn’t make magic happen. 😛 Same for “quantum mechanically entangled” etc. The problem is (1) These terms are vague, until you actually specify the entangled wavefunction or what degree of freedom is coherent with what, and what is their relative phase factor; (2) You need to explain what specific process has made things coherent or entangled in that way (it usually doesn’t just happen on its own), and why this overcomes the competing tendency for complex systems to decohere.

    This post is an example: If a “coherent” wave creates a neutron, I am arguing that you cannot automatically assume that the neutron has any “coherent” relation to the wave that created it.

    I remember reading something written by Larsen, and the impression I got was: He said everything is coherent with everything, and everything is entangled with everything, and therefore any magical process can happen. I came away with a really bad impression, largely he didn’t explain anything. Do you know of any writings where there is more detail on how these things are supposed to work? Maybe I was just reading the wrong paper.

    Finally, in more detail: In Widom-Larsen theory, the neutrons are supposed to react with lithium nuclei and with helium nuclei. I understand that the protons are supposed to be all oscillating as part of a temporally-coherent (i.e. monochromatic) and spatially-coherent (i.e. oriented) wave. (I don’t believe that these oscillations really exist, but let’s move on.) What about the lithium and helium nuclei? The way I see it, there are only two remotely-plausible options. Either they are oscillating too, as part of the same wave, or they are shaking around randomly at room temperature. Either way, their velocity is constantly changing. So even if the neutrons have exactly the same velocity as the Li and He nuclei when they’re created (and the point of this post is that they don’t), they certainly won’t have the same velocity a moment later, because the Li and He will have changed speed! 😀

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  3. Robert Godes

    If you look at Neutron diffraction studies of Palladium, the hydrogen is confined to an area of 0.1 or 0.2 angstroms depending on the angle of interrogation. This is not on the surface, this is in the bulk of the material. This is roughly only one order of magnitude away from the confinement scale necessary for the proton energy to hit 782 KeV, the mass energy required for an electron capture event to take place. If you have a grain structure which focuses photonic energy to specific locations where there are protons in the lattice, this would spontaneously cause electron capture events resulting in ultra-low momentum neutrons. Under these conditions the neutrons would likely be in the peeko eV range. Formation of the neutron removes the coulomb barrier and allows another hydrogen ion to Tunnel into the location where the neutron just formed. Your thoughts?

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    1. steve Post author

      Dear Mr. Godes, I’m having trouble following your logic. Can you help me by clarifying? (1) I’m not familiar with neutron diffraction studies of palladium. Can you suggest a reference? (2) I cannot reproduce your claim about “only one order of magnitude away…”. I initially guessed that you were using the Quantum Mechanics 101 formula for a particle-in-a-box (a.k.a. infinite square well), and plugging in the mass of a proton. But when I tried that, I wound up with <1keV energy even for a 0.01 angstrom cubic box. So maybe you're calculating something else? Can you show the calculation that the "only one order of magnitude" sentence is based on? (3) When you say "photonic energy" what kinds of photons are you talking about (Visible? RF? X-ray?) and where did those photons come from? (4) Why would the electron capture events result in pico-eV ultra-low-momentum neutrons, as opposed to higher-momentum neutrons? Why did you say pico-eV, as opposed to milli-eV or zepto-eV or whatever? (Does pico-eV come from a calculation, and if so, what's the calculation?)

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