Widom-Larsen Theory Papers, Tutorial, and Critiques
The Widom-Larsen Ultra-Low-Momentum Neutron Catalyzed Theory of Low-Energy Nuclear Reactions (LENRs) x

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Table of Contents
Summary of Theory
Highlights of Claims
Resolution to Huizenga's "Three Miracles of Cold Fusion"
Simple Explanation of Mechanics of Theory
Energy Release - Many Possible Low-Energy Nuclear Reaction Networks
Informal Articles by Larsen
Slides Presentations and Documents by Theorists
Source: New Energy Times
Scientific Papers and Published/Preprint Critiques
Issued Patents
Visual Examples of Data Correspondence
Positive Responses to Widom-Larsen Theory
Citations in Other Published Papers or Books
In the News Media
Testing Gamma Shielding, Per Widom-Larsen Theory


Summaries of Theory

By Krivit:
Source: New Energy Times
In 2005, Dr. Allan Widom, a condensed matter physicist with Northeastern. University, and Lewis Larsen, president and CEO of Lattice Energy LLC, began publishing papers that presented a new theory to explain the experimental anomalies observed in LENR experiments. Their theory claims these anomalies are due not to a fusion reaction, which would involve the strong force, but to other low energy nuclear reactions that involve weak interactions, namely neutron formation from electrons and protons/deuterons, followed by local neutron absorption and subsequent beta-decay processes. The following published papers and news items provide more details on the Widom-Larsen Ultra-Low-Momentum Neutron Catalyzed Theory of LENRs.

(1986 Reference on Surface Plasmons)

By Widom and Larsen:
Source: New Energy Times
Allan Widom and Lewis Larsen propose that, in condensed matter, local breakdown of the Born-Oppenheimer approximation occurs in homogeneous, many-body, collectively oscillating patches of protons, deuterons, or tritons found on surfaces of fully loaded metallic hydrides; Born-Oppenheimer breakdown enables a degree of electromagnetic coupling of surface proton/deuteron/triton oscillations with those of nearby surface plasmon polariton (SPP) electrons. Such coupling between collective oscillations creates local nuclear-strength electric fields in the vicinity of the patches.

SPP electrons bathed in such high fields increase their effective mass, thus becoming heavy electrons. Widom and Larsen propose that heavy SPP electrons can react directly with protons, deuterons, or tritons located in surface patches through an inverse beta decay process that results in simultaneous collective production of one, two, or three neutrons, respectively, and a neutrino. Collectively produced neutrons are created ultra-cold; that is, they have ultra-low momentum and extremely large quantum mechanical wavelengths and absorption cross-sections compared to “typical” neutrons at thermal energies.

Finally, Widom and Larsen propose that heavy SPP patch electrons are uniquely able to immediately convert almost any locally produced or incident gamma radiation directly into infrared heat energy, thus providing a form of built-in gamma shielding for LENR nuclear reactions.

By Anonymous Poster on Digg (link dead) (Feb. 1, 2010) Source: New Energy Times
It is looking more and more that "cold fusion" isn't fusion at all. The best theory out there that doesn't invoke any new physics is the Widom-Larsen theory (which has been published in a reputable peer reviewed journal). In a nutshell, it states what is going on is a multistep process. The plasmon modes in hydrated metals (think of them as surface electrons that all act together) get energized (many ways to do this) and get absorbed by protons. This produces a very low energy neutron (reverse neutron decay due to the weak nuclear force). Low-energy neutrons get absorbed quite easily by anything. This starts a cascade of creating unstable isotopes which beta decay. During the beta decay, gamma ray photons are released, but when they hit that metal plasmon they get shifted into mostly IR (heat) with a soft X-ray tail.

The challenge is that this phenomena requires very high energy densities (order of 10^11 V/m). So it more often will happen in small nano-crevices in materials.

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Highlights of Claims

Source: New Energy Times
- Not fusion or fission, but weak interactions—explains Huizenga's three miracles
- Explains most of the well-accepted experimental data in "cold fusion" field
- Miley-Larsen experimental transmutation correspondence
- Suggests an explanation for Iwamura transmutation effect
- Explains light and heavy hydrogen experiments
- Requires no "new physics"

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Resolution to Huizenga's "Three Miracles of Cold Fusion"

Source: New Energy Times
John Huizenga wrote a scathing book denouncing cold fusion research in 1993. He was a professor of chemistry and physics at the University of Rochester, a Department of Energy-funded hot fusion research laboratory. He was also chairman of the 1989 Department of Energy cold fusion evaluation panel that decided cold fusion research was not an area of science worthy of government funding. He mocked cold fusion by alluding to its unexplained characteristics as "miracles." Nevertheless, Huizenga's three miracles were scientifically valid demands. They were:
  • Miracle #1: the mystery of how the Coulomb barrier is penetrated
  • Miracle #2: the lack of strong neutron emissions
  • Miracle #3: the lack of strong emission of gamma or x-rays


Resolution to Miracle #1: There is no Coulomb barrier with neutrons
Resolution to Miracle #2: It is not a fusion reaction, so fusion-associated neutrons are not expected.
Resolution to Miracle #3: Converted to infra-red and shielded.

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Simple Explanation of Mechanics of Theory

See Full Article: "Widom-Larsen Theory Simplified"

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Energy Release - Many Possible Low-Energy Nuclear Reaction Networks

See Full Article: "Where Does the Energy Come From in LENR?"

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Informal Articles by Larsen

August 11, 2005, Letter to the editor of Make magazine
Source: New Energy Times
April 24, 2007 Larsen Letter in Chem Forums (HTML) (PDF)
Excerpt: Please note that there are short, "plain English" summaries of our four published papers down below. They will hopefully provide you with a high-level conceptual overview of what we are doing in each of our papers before having to delve into the details of the physics and mathematics.

Using the Widom-Larsen theory, we can now answer three important questions about anomalous LENR experimental results that previous "cold fusion" researchers have been unable to answer to the satisfaction of the mainstream physics community for the past 18 years.
Source: New Energy Times
Oct. 7, 2008, New Energy Times, "LENRs are Better Than Fusion"
"A revolutionary scientific paradigm shift has been brewing slowly over the past 19 years. The world of mainstream science is finally waking up to the possibility that previously neglected weak interactions might provide another new source of nuclear energy. In fact, given their unique characteristics, weak-interaction LENRs could prove to be a vastly cleaner, "greener," less expensive power generation technology than strong-interaction fission or fusion. In our 2006 European Physical Journal C paper, we showed an example of a LENR-based lithium reaction that generated roughly as much energy as fusion reactions, but without the release of any dangerous energetic neutrons or "hard" gamma radiation. LENRs are better than fusion. That is revolutionary. LENRs gore many long-standing sacred cows and threaten myriad vested scientific and commercial interests."
November 13, 2008, Institute of Science in Society #1
"Low Energy Nuclear Reactions for Green Energy - How weak interactions can provide sustainable nuclear energy and revolutionize the energy industry"
December 4, 2008, Institute of Science in Society #2
"Widom-Larsen Theory Explains Low Energy Nuclear Reactions & Why They Are Safe and Green - All down to collective effects and weak interactions"
December 10, 2008, Institute of Science in Society #3
"Portable and Distributed Power Generation from LENRs - Power output of LENR-based systems could be scaled up to address many different commercial applications"
December 11, 2008, Institute of Science in Society #4
"LENRs for Nuclear Waste Disposal - How weak interactions can transform radioactive isotopes into more benign elements"
January 26, 2009, Institute of Science in Society #5
"Safe, Less Costly Nuclear Reactor Decommissioning and More How weak interaction LENRs can take us out of the nuclear safety and economic black hole"
January 27, 2009, Institute of Science in Society #6
"LENRs Replacing Coal for Distributed Democratized Power Low energy nuclear reactions have the potential to provide distributed power generation with zero carbon emission and cheaper than coal"
Nov. 2009, Institute of Science in Society - Third World Network
Green Energies (Preview): 100% Renewables by 2050
(Larsen Blurb)

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Slides Presentations and Documents by Theorist (Larsen)

Slides Presentations by Theorist (Widom)

Feb. 10, 2010 - 34 slides
"Collective Nuclear Reactions in Condensed Matter," Prepared for but not presented, at Army Research Labs LENR Workshop (2010)
Slides Presentations by Theorist (Srivastava)
Dec. 10, 2005 - 20 slides
"Giuliano Preparata A Quintessential Physicist"
May 11, 2011 - 28 slides
"Low Energy Nuclear Reactions on the Cathode of a Chemical Cell," Coherence 2011 Conference
March 22, 2012 - 40c slides
"Overview of LENT Theory- Low Energy Nuclear Transmutations," CERN Colloquium Geneva, Switzerland

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Scientific Papers and Published/Preprints and Critiques

#1—Widom, Allan and Larsen, Lewis (March 9, 2006) "Ultra Low Momentum Neutron Catalyzed Nuclear Reactions on Metallic Hydride Surfaces," European Physical Journal C - Particles and Fields, 46(1), p.107-110

Preprint (pdf)
May 2, 2005
Published paper (pdf) Eur. Phys. J. C, March 9, 2006

Cited in S. Szpak, P.A. Mosier-Boss, and F.E. Gordon, “Erratum to Further Evidence of Nuclear Reactions in the Pd/D Lattice: Emission of Charged Particles,” Naturwissenschaften , 94 (2007) 511-514.

#2— Widom, Allan, Larsen, Lewis, "Absorption of Nuclear Gamma Radiation by Heavy Electrons on Metallic Hydride Surfaces"

Preprint (pdf)
September 10, 2005, http://arxiv.org/abs/cond-mat/0509269

#3—Widom, Allan, Larsen, Lewis, "Nuclear Abundances in Metallic Hydride Electrodes of Electrolytic Chemical Cells"

Preprint (pdf) February 20, 2006, http://arxiv.org/abs/cond-mat/0602472

#4— Widom, Allan and Larsen, Lewis (Sept. 25, 2007) "Theoretical Standard Model Rates of Proton to Neutron Conversions Near Metallic Hydride Surfaces"

Version 4.1 Preprint August 25, 2006
Version 4.2 Preprint September 25, 2007, http://arxiv.org/abs/nucl-th/0608059v2

#5—Widom, Allan, Larsen, Lewis, and Srivastava, Yogendra. N., "Energetic Electrons and Nuclear Transmutations in Exploding Wires"

Preprint (pdf) September 8, 2007, http://arxiv.org/abs/0709.1222
Related Wendt-Irion Papers (1922)

#6— Widom, Allan, Larsen, Lewis, and Srivastava, Yogendra. N.,"High Energy Particles in the Solar Corona"

Preprint (pdf) April 16, 2008, http://arxiv.org/abs/0804.2647
Related Cowley Paper (2004)
Related Fowler Paper (1965)
Related Goriely Paper (2007)

#7—Srivastava, Yogendra. N., Widom, Allan and Larsen, Lewis (Oct. 2010) "A Primer for Electro-Weak Induced Low Energy Nuclear Reactions," Pramana - Journal of Physics, 75(4) 617-637
Preprint (pdf) October 1, 2008

ACS Publication 2009
Pramana Publication 2010

Hagelstein and Chaudhary Critique

Hagelstein, Peter, and Chaudhary, Irfan (Jan. 24, 2008)" Electron Mass Shift in Nonthermal Systems," Journal of Physics B: Atomic, Molecular and Optical Physics, 41(12) (June 6, 2008)

Widom, Allan, Srivastava, Yogendra, N. and Larsen, Lewis (Feb. 5, 2008) "Errors in the Quantum Electrodynamic Mass Analysis of Hagelstein and Chaudhary," http://arxiv.org/abs/0802.0466

Widom Response to Hagelstein


Ciuchi et al. Critique

Ciuchi, S., Maiani, L., Polosa, AD, Riquer,V., Ruocco, G., Vignati, M. (Sept. 28, 2012) "Low Energy Neutron Production by Inverse beta decay in Metallic Hydride Surfaces," The European Physical Journal C, 72, p. 2193-6 (Oct. 26, 2012)

Widom, Allan, Srivastava, Yogendra. N., and Larsen, Lewis (Oct. 17, 2012)"Erroneous Wave Functions of Ciuchi et al. for Collective Modes in Neutron Production on Metallic Hydride Cathodes." http://arxiv.org/abs/1210.5212v1 (See also Larsen's Slide Presentation, Oct. 30, 2012)

Krivit comment: As Widom, Srivastava and Larsen explained in their paper and in Larsen's slide presentation, the Ciuchi group failed to understand, or take into account, the significance of collective effects in the LENR systems. As Larsen explained, the 0.78 MeV required to create the neutron in the Widom-Larsen theory does not come from a single proton and a single electron (as is typical with two-particle plasma physics), but from many protons and electrons that each contribute a small amount of their energy to only one electron.

Tennfors Critique

Einar Tennfors, "On the Idea of low-energy nuclear reactions in metallic lattices by producing neutrons from protons capturing 'heavy' electrons," European Physical Journal Plus, Feb. 15, 2013

Krivit comment:Tennfors made the same fundamental mistake in his analysis as did the Ciuchi group. The Widom-Larsen group elected to not write rebuttals to each and every scientist who made the same mistake.

Pourjafarabadi and Mojavezi Paper and Krivit Comment

E. Pourjafarabadi, A. Mojavezi, "Electron mass renormalization and absorption of hard photons". Eur. Phys. J. C 82, 752 (2022)

Krivit, S.B. Comment on “Electron mass renormalization and absorption of hard photons” by E. Pourjafarabadi and A. Mojavezi. Eur. Phys. J. C 84, 135 (2024). https://doi.org/10.1140/epjc/s10052-024-12508-z

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Source: New Energy Times
Issued Patents

US 7,893,414 - Feb. 22, 2011

“Apparatus and Method for Absorption of Incident Gamma Radiation and its Conversion to Outgoing Radiation at Less Penetrating, Lower Energies and Frequencies”
(Inventors: Lewis Larsen and Allan Widom)

This is a unique patent in that there is no prior art that is directly related. Only one prior patent is referenced, U.S. 5,887,042: "A cask for a radioactive material has a single gamma ray and neutron shielding layer disposed on the outside of a vessel body, and the shielding layer is formed of the compact of a mixture of lead and a metal hydride dispersed therein. This cask can exhibit an excellent shielding effect according to the balance of radiation source intensity between gamma rays and neutrons, and can be made more compact."

US 7,244,887 - July 17, 2007 (Inventor: George Miley)
"Electrical cells, components and methods"
US 6,921,469 - July 26, 2005 (Inventor: Lewis Larsen)
"Electrode constructs, and related cells and methods"

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Visual Examples of Data Correspondence

Source: New Energy Times
Widom-Larsen Optical Model

The Widom-Larsen optical model, depicted by the curve below, predicts a unique spectrum of elemental abundances as a function of the creation and capture of ultra-low-momentum neutrons. The dots represent transmutation product abundances from experimental work performed by George Miley from multiple experiments in the mid-1990s.

Qualitative predictions of the Widom-Larsen optical model:

- five-peak product-mass spectrum from A=1 to A=250
- peaks approximately at atomic mass numbers 12, 31, 62, 117 and 206
- position of each of the peaks in terms of mass number (A)
- increased spacing between successive peaks as A increases
- declining amplitude of peaks as A increases

Quantitative characteristics of the predicted product-mass spectrum compared with different data sets may vary based on differences in experimental configuration, deuterium versus normal hydrogen, (all things being equal, deuterium produces higher neutron fluxes), duration of experiment, and starting materials.

Widom and Larsen do not claim that the optical model would neccesarily have a quantitative high r*square coefficient of correlation between model output and any arbitrary collection of experimental data points. This is because significant amounts of statistical noise are randomly introduced in such limited amounts of data from complex LENR nucleosynthetic network processes operating in significantly different types experiments that are run over variable lengths of time.


Miley Spectrum of Elemental Abundances from LENR Transmutations
Four Peaks Visible (Z)

Graph, data and curve by Miley in 1996 from "Quantitative Observation of Transmutation Products Occurring in Thin-Film Coated Microspheres During Electrolysis," ICCF-6. Six runs are shown in this graph; all producing similar curves.


Miley Spectrum of Elemental Abundances from LENR Transmutations
Five Peaks Visible (A)

Source: New Energy Times
Lines drawn by George Miley in 1996. Source: "On the Reaction Product and Heat Correlation for LENRs. in 8th International Conference on Cold Fusion," which comes from G. H. Miley, “Possible Evidence of Anomalous Energy Effects in H/D-Loaded Solids—Low Energy Nuclear Reactions (LENRs),” Journal of New Energy, 2, No. 3-4, pp.6-13, (1997).

See related paper: Edward Anders and Nkolas Grevesse, "Abundances of the Elements: Meteoritic and Solar," Geochimica et Cosmochimica Acta (ISSN 0016-7037), vol. 53, p. 197-214, Jan. 1989

Mizuno Spectrum of Elemental Abundances from LENR Transmutations

Mizuno's data show a similar, but not identical multipeak pattern of atomic abundances. Miley's peak curve is based on data from multiple runs; Mizuno's data in this graph is based on the analysis of one run. The groupings are slightly different between Miley and Mizuno and this reflects the difference in starting seed-materials and neutron production.

Source: New Energy Times
Mizuno: "Count rates for Pd electrode electrolyzed in heavy water solution observed by SIMS measurement. Elements are mostly grouped in four ranges of mass number: lightest elements under mass 50, light elements from 50-80; middle elements from 100-140; and heavy elements from 180-208." Source: "Isotopic Distribution for the Elements Evolved in Palladium Cathode After Electrolysis in D2O Solution"

Mizuno: "EDX Spectra from the Pd rod before and after the electrolysis: 1.0 Mol LiOH-D2O, 378K, 0.2 A/cm^2 for 2.76x10^6s.
Source: "Isotopic Distribution for the Elements Evolved in Palladium Cathode After Electrolysis in D2O Solution"

Mizuno-Miley-Widom/Larsen Correspondance
Data points (in blue and red): Plotted by Mizuno
Miley data curve (in green): Drawn by Miley
Widom-Larsen theory curve (in purple): Drawn by Larsen

Source: New Energy Times
Where Mizuno identified a range for the peaks he observed[1], they equate to mass numbers 65, 120 194. Where Miley identified a range for the peaks he observed[2], they equate to mass numbers 25, 65, 120 and 200. Widom and Larsen calculated the transmutation peaks[3], based on their theoretical model, to occur around mass numbers 12, 31, 62, 117 and 206.

1. Mizuno, Tadahiko, Ohmori, Tadayoshi, Akimoto, Tadashi, Kurokawa, Kazuya, Kitaichi, Masatoshi, Inoda, Koichi , Azumi, Kazuhisa, Simokawa, Shigezo, and Enyo, Michio, "Isotopic Distribution for the Elements Evolved in Palladium Cathode After Electrolysis in D2O Solution," Proceedings of the Sixth International Conference on Cold Fusion: Progress in New Hydrogen Energy, Hokkaido, Japan, Oct. 13-18, 1996; Okamoto, M., Ed.; New Energy and Industrial Technology Development Organization: Tokyo, (1996). Also published in Denki Kagaku (Japanese Journal of Electro-Chemistry,) 64 (11), p. 1160-1165, (1996)
2. Miley, George H., "On the Reaction Product and Heat Correlation for LENRs," Proceedings of the 8th International Conference on Cold Fusion, Lerici (La Spezia), Italy, Italian Physical Society, Bologna, Italy (2000)
3. Widom, Allan and Larsen, Lewis, "Nuclear Abundances in Metallic Hydride Electrodes of Electrolytic Chemical Cells," Preprint, February 20, 2006

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Positive Responses to Widom-Larsen Theory

David Nagel: …may prove to be a viable mechanism” (May 6, 2005)
David Nagel: Nagel's Widom-Larsen Graphics (May 11, 2005)
David Nagel: University of Notre Dame Presentation (Sept. 16, 2005)
Lino Daddi (Italian Naval Academy): "Perhaps we have a theory that explains all the anomalous phenomena. The transmutation observed from Yasuhiro Iwamura [Mitsubishi Heavy Industries] are explained without the problematic multiple reactions of Takahashi." (May 11, 2005)
George Miley (University of Illinois) "This theory agrees with the distinctive multipeak reaction product data from my experiments amazingly well." (Feb. 26, 2006)
David Rees (Particle Physicist, SPAWAR) “…as far as I can tell correct” (Sept. 11, 2006)
Robert Park: "Low-energy nuclear reactions are real phenomena." (Dec. 12, 2006)
(Immediately following Widom and Larsen's presentations at DTRA)
SPAWAR LENR Research Group: "We find that Widom and Larsen have done a thorough mathematical treatment that describes one mechanism to create...low-energy neutrons." (Feb. 15, 2007)
Richard Garwin (IBM/JASON) "…I didn’t say it was wrong" (Feb. 19, 2007)
(DTRA) Defense Threat Reduction Agency Experts' Panel: "New theory by Widom[-Larsen] shows promise; collective surface effects, not fusion." (June 29, 2007)
Hideo Kozima: [Kozima accepted the WL mechanism to produce neutrons. It supported his own neutron-based theory.] (Feb. 23, 2007)
Robert Deck: "The mechanism proposed in the Widom-Larsen papers provides a far more compelling explanation of the anomalous phenomenon observed in electrolytic chemical cells than previous theories." (March 14, 2007)
Dennis M. Bushnell (NASA): "Now, a Viable Theory" (See pg. 37) (Oct. 29, 2008)
Johns Hopkins University: "More recent research, notably by Lewis Larsen and Allan Widom ... indicates that the pheoomena are real but entirely different from the kind of atomic fusion reaction that occurs at immensely high temperatures inside the stars or in a hydrogen bomb."(2009)
Pat McDaniel (Sandia N.L., retired): "Widom Larsen theory is considered by many [people] in the government bureaucracy to explain LENR." (Aug. 4, 2009)
Joseph M. Zawodny (NASA) "All theories are based on the Strong Nuclear force and are variants of Cold Fusion except for one new theory. Widom-Larsen Theory is the first theory to not require 'new physics'.” (Aug. 12, 2009)
DTRA (Edward Toton and George Ullrich): "The Widom-Larsen (W-L) theory provides a self-consistent framework for addressing many long-standing issues about LENR." (March 31, 2010)
Randy Hekman (One of the Proposers of the 2004 DOE LENR Review) "This theory explains the data in ways that are totally consistent with accepted concepts of science." (Dec. 29, 2011)
Marty K. Bradley and Christopher K. Droney (Boeing) (May 2012) "The Widom-Larson theory appears to have the best current understanding."

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Citations in Other Published Papers or Books

Kozima, Hideo, "The Science of the Cold Fusion Phenomenon, ISBN 0-080-45110-1, Section, p. 95 (2006)
Daddi, Lino, "Virtual Neutrons In Orbital Capture And In Neutron Synthesis"
Daddi, Lino, "Hydrogen Miniatoms"

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In the News Media

New Energy Times Issue #13 (Krvit) - Nov. 10, 2005: "Newcomers to Condensed Matter Nuclear Science Rock the Boat"
New Energy Times Issue #15 (Krvit) - March 10, 2006: "Widom-Larsen Low Energy Nuclear Reaction Theory, Part 3"
New Energy Times Issue #21 (Krvit) - March 16, 2007 "Widom Larsen Theory Debate"
Chicago Tribune (Jon Van) - April 16, 2007: "Nuclear reactions may produce phones’ power
Institute of Science in Society (Mae-Wan Ho) - Oct. 23, 2007: "How Cold Fusion Works" (Feauturing Widom/Larsen, Krit Prasad Sinha and Andrew Meulenberg, Xing Zhong Li, Talbot Chubb)
Institute of Science in Society (Mae-Wan Ho) - Oct. 24, 2007: "Transmutation, The Alchemist Dream Come True"
New Energy Times Issue #26 (Krivit) - January 11, 2008: "The Widom-Larsen Not-Fusion Theory"
Larsen Interview with Sandy Andrews on Blogtalkradio -April 17 , 2010

“LENR is way bigger than IBM, way bigger than the United States,” Lewis Larsen, of Lattice Energy LLC, told Sandy Andrew of blogtalkradio on April 17.

Among the subjects they covered were the following: the differences among LENR, fusion and fission; an introduction to weak-interaction concepts and collective effects; possible practical implications of LENR and commercial applications; and examples of low-energy nuclear reactions going back a hundred years.

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