Science in Society Archive

Widom-Larsen Theory Explains Low Energy Nuclear Reactions & Why They Are Safe and Green

All down to collective effects and weak interactions Lewis Larsen

Widom-Larsen theory of LENRs predicts ultra low momentum neutrons created by collective weak interactions

The Widom-Larsen (W-L) theory explains low energy nuclear reactions (LENRs) in terms of the production of neutral subatomic particles called “neutrons” at ordinary temperatures and pressures. Unlike conventional neutron-triggered fission and hot fusion reactions (that involve random collision of individual particles and require extremely high temperatures and pressures), the W-L theory proposes that collective processes involving many particles acting in concert to generate neutrons with negligible kinetic energies, i.e., they have ‘ultra low momentum’ (ULM) [1] (Transmutation, The Alchemist Dream Come True, SiS 36).

Such neutrons are created within collectively oscillating patches of protons or deuterons (found on surfaces of hydrogen-loaded metallic hydrides) that can react directly with heavy-mass electrons created by the huge local nanoscale electric fields that also occur on the hydrogen-coated metallic surfaces. In such nanoscale surface environments, neutrons are created collectively in a weak interaction process directly from electrons (e-) and the nuclei of hydrogen, i.e., protons (p+) and/or deuterium, deuterons (d+), as follows [2]:

  e- + p+ -> neutron + neutrino                                                              (1)

  e- + d+ -> 2 neutrons + neutrino                                                          (2)

This type of neutron production due to weak interactions in very high surface electric fields is well-described by the generally accepted electroweak theory [3] on which the W-L theory of LENRs is based.

An isolated ‘normal’ thermal neutron outside a nucleus travelling through a solid has a quantum mechanical wavelength of about 0.2 nanometre (1 nanometre is 10-9m) and a speed of about 2 200 metres per second, which is faster than a rifle bullet. Interestingly, the ‘size’ of a neutron confined inside an atomic nucleus is even smaller, at several femtometres (10-12 m).

By contrast, an ULM neutron formed on a metallic hydride surface in a LENR is more-or-less standing still. Being formed collectively, ULM neutrons have almost no kinetic energy at the instant of their creation, effectively zero. This gives them huge quantum mechanical wavelengths compared to ‘normal’ neutrons. ULM quantum mechanical wavelengths (conceptually, effective ‘size’) increase dramatically [2]. Note that ULM neutrons have much smaller energies (and correspondingly larger quantum mechanical wavelengths) than even the ‘ultracold’ neutrons [4] produced so far in certain experiments.

The ‘size’ of ULM neutrons is typically extremely large in comparison to thermal neutrons. It is directly determined by the spatial dimensions of the surface ‘patch’ of protons or deuterons in which they were created. In particular, their wave function must span the entire patch. Therefore, on the surfaces of condensed matter (e.g., a metallic hydride), the wave functions of ULM neutrons can easily reach 20 – 30 microns, i.e., 10 000 to 15 000 times that of thermal neutrons; and roughly the size of a large bacterium or a cell. Surfaces of hydrogen-loaded metallic hydrides are one of the few environments in the Universe where subatomic neutrons become almost microscopic.

Capture of ultra-low momentum neutron results in a variety of transmutations to non-radioactive elements 

At a ‘size’ of 0.2 nanometre, a thermal neutron is only able to interact with just a few atoms at any given instant; and it is also moving fast. In contrast, the gigantic ULM neutrons can interact collectively with literally thousands of nearby ‘target’ atoms all at once. This unique property increases the probability of their being absorbed by those nearby atoms to nearly 100 percent. A nuclear physicist would say ULM neutrons have phenomenally high “absorption cross-sections.”

ULM neutrons’ huge size is exactly why biologically dangerous energetic (‘hot’) neutrons are not released by LENR systems. ULM neutrons are extraordinarily ‘cold’ to begin with; and virtually all are absorbed locally; they never get a chance to escape and go anywhere. It is the first reason why LENRs are safe and environmentally friendly in comparison with heavy element neutron-triggered fission and light element hot fusion.

After being created, ULM neutrons are efficiently absorbed by nearby target atoms, resulting in nuclear transmutations into different elements or isotopes [5]. Unstable transmutation products undergo subsequent weak interaction beta decays [6] that, depending upon exactly which nearby target elements were used as ‘fuel,’ can then release large amounts of nuclear binding energy [7].

Another reason why LENRs are green (environmentally friendly) is that extremely neutron-rich, very unstable intermediate transmutation products turn into stable, non-radioactive elements very quickly via cascades of rapid beta decays. Such neutron-rich intermediate nuclear products have short half-lives, of milliseconds, seconds, minutes, or at most hours; and typically not even days or months, let alone years. That is why LENR systems do not produce large quantities of long-lived hot radioactive isotopes like today’s commercial fission reactors. As a result, there are no known nuclear waste disposal issues with LENR systems. Long-lived, highly radioactive isotopes (gamma emitters like cobalt-60) are not produced in detectable quantities; this has been verified in many LENR experiments.

Hard gammas and X-rays are absorbed and converted into soft radiation or heat

The W-L theory also explains why hard gamma and X-rays are not released during LENR system operation [8]. This arises from unique heavy-mass electrons created by the very strong nanoscale electric fields that occur in regions above localized patches of collectively oscillating protons and deuterons where neutron production and absorption are taking place. Unlike isolated normal-mass electrons situated in a vacuum or a hot plasma, heavy-mass electrons created in condensed matter LENR systems can directly absorb a hard gamma or X-ray photon, “ring like a bell” for an infinitesimal fraction of a second, then (according to conservation of energy) reradiate a much larger number of much less energetic photons (mostly in the infrared region, with a much smaller ‘tail’ of soft X-ray photons).

In operating LENR systems, therefore, hard gamma ray photons in an energy range between 0.5 MeV and 10.0 MeV (often created during absorption of ULM neutrons by some, but not all, atoms/isotopes) are locally absorbed by heavy-mass electrons before they can escape [8]. Those electrons then convert the absorbed gammas directly into raw heat in the form of benign infrared photons that are also locally absorbed. LENR systems have what amounts to built-in gamma shielding during operation, a remarkable property by any standard.

A gamma-absorbing ‘patch layer’ of heavy-mass electrons in an LENR system has the ability to stop a very dangerous (~5 MeV) gamma ray in less than two nanometres. Whereas it would take ~10 cm of lead, ~25 cm of steel, or ~1 metre of very heavy concrete to accomplish the same degree of protection against ‘hard’ gamma radiation [9].

LENR-based power generation much safer and affordable than fission or hot fusion

Unlike the deadly energetic neutrons and X-ray/gamma radiation produced by nuclear fission or hot fusion reactions, the charged-particle products produced by LENRs (beta and alpha particles) cannot penetrate a piece of paper or the human skin [10]; they could not escape through the outer casing of an LENR system in the first place.

Future commercial versions of Lattice’s purely weak interaction, LENR-based systems would not require expensive, bulky shielding or radiation confinement structures. Neither would they have any costly end-of-life nuclear waste disposal issues, as LENRs do not in the end produce biologically significant quantities of long-lived hot radioactive isotopes. That being the case, it would seem unlikely that government regulation of LENRs would be anywhere near as onerous as it is for existing fission and the hoped-for fusion technologies. Altogether, it seems reasonable to assume that power generation based on LENRs would be much less expensive as well as safe from accidents or intentional sabotage.

A revolution in power generation

Prior to W-L theory, weak interactions were thought to be useless for power generation.

In contrast to hot fission and fusion associated with the controversy over nuclear weapons and the potential of a nuclear war in the aftermath of WWII, Enrico Fermi’s beloved weak interactions became somewhat neglected. It was looked upon more as a scientific curiosity of theoretical interest with no practical applications. After all, every physicist and chemist ‘knows’ that radioactive beta decay rates are mainly low-energy and, being random, cannot be controlled; and hence useless for power generation applications. Also, no one considered the possibility of creating neutrons directly via the weak interaction; there just didn’t seem to be any reasonable way to get weak interaction rates high enough to be useful. The Widom-Larsen theory of LENRs and hundreds of credible experiments have demonstrated otherwise.

Weak interactions are not weak energetically

Contrary to common belief, weak interaction LENRs are not necessarily weak in terms of the total amount of energy released. Widom and Larsen’s 2006 European Physical Journal C paper [2] shows the following net result of a series of LENR reactions starting with lithium

Lithium-6 + 2 neutrons -> 2 helium-4 + beta particle + neutrino + 26.9 MeV                (3)

This particular series can release about the same amount of energy as fusion reactions without creating any energetic neutrons, hard gamma radiation, or hot radioactive isotopes. While some of the 26.9 MeV in excess nuclear binding energy released is certainly lost to the neutrino, much of it remains in the kinetic energy of the two helium atoms (alpha particles) and beta particle. Local solid matter is heated-up by the impacts of the alpha and beta particles; and heavy-mass electrons also convert any locally produced hard gamma or X-rays directly into infrared heat.

The details of nuclear reactions that comprise a condensed matter LENR lithium cycle are as follows (n = ultra low momentum neutron; beta particle = e; neutrino = n):

Li-6 + n -> Li-7 + n -> Li-8 -> Be-8 + e+ n   {neutron absorption, then beta decay} (4)

Be-8 -> He-4 + He-4 {perfectly symmetric, ‘green’ fission of a beryllium-8 nucleus} (5) 

He-4 + n -> He-5 + n -> He-6       {neutron absorption, making neutron-rich helium} (6)

He-6 -> Li-6 + e+ n        {final beta decay of helium- 6 that regenerates lithium-6} (7)

The above series of nuclear reactions comprise a ‘reaction cycle’ in that lithium-6 is regenerated as the final reaction product [2]. Lattice has also uncovered other LENR reaction cycles that release varying amounts of energy.

Although LENRs occur in condensed matter at comparatively low temperatures and pressures, weak interaction LENR reaction cycles are conceptually analogous to the ‘CNO cycle’ [11, 12] of stars in which the carbon-12 nucleus, at which the CNO cycle starts, is regenerated at the very end. While this stellar nuclear reaction cycle also releases ~27 MeV, it differs from the LENR lithium cycle shown in Eqs.(4)–(7) above in that the CNO cycle involves primarily high-temperature strong interaction fusion reactions rather than a combination of neutron absorption and weak interactions.

Theoretical astrophysicists believe that the CNO cycle is responsible for most of the energy production in stars that are larger and hotter than our sun. Interestingly, the LENR lithium cycle releases roughly as much energy as the stellar CNO cycle, but without using energetic neutrons or emitting gamma rays and, amazingly, can be initiated in ‘tabletop’ experimental systems.    

By comparison, each fission reaction in a commercial power reactor releases roughly 190 MeV per fission of a uranium-235 atom. Depending on the specific reactions, known individual fusion reactions involving charged nuclei (which includes protons and deuterons) and high coulomb barriers can produce energy releases that range from ~0.6 MeV all the way up to ~23 MeV.

Why would anyone want to build the gigantic International Thermonuclear Experimental Reaction (ITER) [13] that has been proposed for the expensive deuterium-tritium (D-T) fusion if LENRs could be used to achieve about the same level of energy release with markedly greener, near-infinitely scalable power generation systems at a small fraction of the cost? For those interested in learning more about the long quest for controllable fusion, its history and the many foibles of some of the scientists searching for this ‘Holy Grail’,  please see Charles Seife’s new book, Sun in a Bottle [14].  

LENRs produce enormous heat in tiny hot spots on metallic hydride surfaces

Lithium LENRs can produce huge amounts of heat in tiny hot spots located on the surfaces of metallic hydride substrates. There is direct experimental evidence for the existence of such hot spots in before-and-after scanning electron microscope (SEM) images of the surfaces of experimental LENR devices, some of which have lithium in or around them. In post-experiment SEM images [15], a host of new, weird looking micron-scale structures are observed scattered randomly across the metallic surfaces. Various researchers have described these unusual structural features as resembling “craters”, “volcanoes”, flash melted and cooled “puddles,” “gas holes”, “ejecta from craters”, etc. Based on their appearance, they appear to be the result of some sort of “flash” melting of the surface in small sites at many locations. A US Navy group actually imaged an operating cathode with an IR camera: hot spots in infrared looked like fireflies in a field at night [16, 17] (see From Cold Fusion to Condensed Matter Nuclear Science, SiS 36).

In their paper, Widom and Larsen calculated LENR reaction rates based on their theory and found they matched the experimental results [18]. They also estimated the ‘noise temperature’ for such ‘hot spots’ to be 4 000 – 6 000 degrees Kelvin, comparable to the temperature on the surface of the sun and above the boiling point of any metal. This is entirely consistent with many experimental observations.

LENR devices produce vastly higher energy densities than chemical power sources

Being nuclear, LENRs have intrinsically huge, orders-of-magnitude advantages over any chemical power generation technologies with regard to energy density. Chemical reactions can release stored electronic energy on the order of several electron-Volts (eVs). By contrast, nuclear reactions can release stored nuclear binding energy on the order of Mega electron-Volts (MeVs), which is more than a million times larger than typical chemical energies. This creates a potential commercial opportunity to develop cost-effective LENR portable power sources that have unprecedented performance in terms of system energy density and longevity.

It must be noted that 100 percent of the theoretical difference in energy density shown in Table 1 below will not be realized in real-world LENR devices; heat dissipation and thermal management issues will prevent that from happening. Nonetheless, realizable energy densities with LENRs would still be vastly larger than those of chemical technologies. In fact, Lattice and others have occasionally observed experimental LENR devices that had larger measured power densities than fuel rods in operating U-235 fission reactors.

Table 1. Comparative Energy Densities of LENRs versus Chemical Energy Sources

Energy Source

Specific Effective Energy Density
(Watt hours/kg = Wh/kg)

Alkaline Battery


Lithium-Ion Battery


Zinc-Air Battery


Direct Methanol Fuel Cell
(Efficiency = 35%)

1 680

Gasoline Burning Microgenerator
(Efficiency = 20%)

2 300

Combustion of Pure Methanol
(Efficiency = 100%)

5 930

Combustion of Pure Gasoline
(Efficiency = 100%)

11 500

LENRs – Lattice estimate (based on a conservative assumption of ~0.5 MeV per nuclear reaction)

 57 000 000   (Maximum potential)

Note that LENRs at energies of just 0.5 MeV will have an intrinsic energy density that is nearly 5 000 times that from a 100 percent efficient combustion of pure gasoline. Importantly, there are many types of practical LENR fuel cycles based on certain beta decays that could theoretically generate substantially more energy than 0.5 MeV, such as the lithium LENR reaction series summarized in Eq.(3) that releases ~ 27 MeV [2].

Longevity in terms of the total duration of power output from a given power source is also directly related its effective energy density.

The author declares his commercial interest as President and CEO of Lattice Energy LLC.

Article first published 04/12/08


  1. Ho MW. Transmutation, the alchemist dream come true. Science in Society 36, 36-38, 2007
  2. Widom A and Larsen L. Ultra low momentum neutron catalyzed nuclear reactions on metallic hydride surfaces, European Physical Journal CParticles and Fields 46 107 2006 (arXiv version released 2 May 2005),  
  3. Electroweak interaction, Wikipedia, 25 October 2008,
  4. Ultracold neutrons, Wikipedia, 25 October 2008,
  5. Nuclear transmutation, Wikipedia, 25 October 2008,
  6. Beta decay, Wikipedia, 24 October 2008,
  7. International patent application No.  PCT/US2006/016379 filed by Larsen L and Widom A. 28 April 2006 titled (WO/2006/119080) APPARATUS AND METHOD FOR GENERATION OF ULTRA LOW MOMENTUM NEUTRONS
  8. Widom A and Larsen L. Absorption of Nuclear Gamma Radiation by Heavy Electrons on Metallic Hydride Surfaces (September 2005),
  10. Ionizing radiation, Wikipedia, 24 October 2008,
  11. CNO cycle, Wikipedia, 1 November 2008,
  12. Carbon fusion cycle, HyperPhysics, 1 November 2008, Website maintained by Prof. R. Nave of Georgia State University, Atlanta, GA USA
  13. ITER, Wikipedia, 25 October 2008,
  14. Seife C. Sun in a bottle – The strange history of fusion and the science of wishful thinking, Viking 2008, Reviewed on 24 October 2008 by Davide Castelvecchi for Science News    
  15. Szpak, S,  Mosier-Boss P, Young C, and Gordon F. Evidence of Nuclear Reactions in the Pd Lattice, Naturwissenschaften 92 394 2005,
  16. Special Collections – U.S. Navy Cold Fusion Research – provided courtesy of (follow the links to video clips and images),
  17. Ho MW. From cold fusion to condensed matter nuclear science.  Science in Society 36, 32-35, 2007.
  18. Widom A and Larsen L. Theoretical Standard Model Rates of Proton to Neutron Conversions Near Metallic Hydride Surfaces (September 2007),

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