Science in Society Archive

How Cold Fusion Works

Many ways for atomic nuclei to come close coherently and fuse together in condensed matter. Dr. Mae-Wan Ho

Cold fusion with ease

The surprising thing about cold fusion is how easily it could be made to happen, and in many different forms [1, 2] (see From Cold Fusion to Condensed Matter Nuclear Science and Transmutation, the Alchemists’ Dream Come True? SiS 36). This is in striking contrast to hot fusion, which requires temperatures of millions of degrees K.

The key to cold fusion is that it happens in condensed matter. Simply put, there are many ways for nuclei to come together coherently and fuse in condensed matter. Cold fusion is friendly fusion, and does not need to be forced by thermonuclear temperatures. 

First of all, the hydrogen or deuterium nuclei are trapped in the host lattice, and hence much closer together than they would otherwise be in the gas phase. Under these conditions, quantum effects take over. Energy levels are no longer discrete; instead, they merge into broad bands. Coherent vibrations of the trapped nuclei, the electron cloud and the host lattice interact, all of which conspire to let nuclei slip under the Coulomb barrier and fuse together.

Delocalised and overlapping wave functions in condensed matter

Retired physicist from the US Naval Research Laboratory Talbot Chubb describes cold fusion as using a “catalysed configuration” to replace the need for high-energy collision between particles in hot fusion [3].

In the typical experiments where deuterium is absorbed or generated in a palladium electrode, the deuterons (nuclei of deuterium) become delocalised as waves with periods of the host lattice; this is referred to as a ‘Bloch state’. Bloch states enable the waves of different deuterons to overlap, and at a certain point when the kinetic energy of the vibrations becomes greater than the potential energy of the Coulomb barrier, the latter becomes irrelevant and two deuteron waves fuse into one. The electrons will also be delocalised as Bloch waves and will serve to shield the like charges of the nuclei and enable them to come closer together, thus facilitating the fusion.

Two deuterons fusing together gives helium-4 and excess energy of 23.8 MeV. The excess energy is transferred to the host lattice as phonons (sound waves) and dissipated as heat. This could explain the results of many cold fusion experiments, including that of Fleishmann and Pons [4] that started the whole field.

However, it was already apparent in the Fleishmann and Pons experiments that excess heat was produced in at least two ways: a predictable steady state (when helium-4 could well be produced), and unpredictable bursts of intense activity associated with the production of tritium.

Electron capture for nuclear transmutation

Allen Widom at Northeastern University Boston and Lewis Larsen of Lattice Energy have recently proposed a mechanism that could account for a wide range of fusion and transmutation reactions, electron capture by protons or deuterons [4].

In nuclear physics, it is very well known that a proton can capture a negatively charged lepton (light particle) and produce a neutron and a neutrino, and a common form of nuclear transmutation in condensed matter can be understood in term of this reaction.

An electron that wanders into a nucleus with Z (atomic number) protons and N (= A (atomic mass) – Z) neutrons can be captured, producing a neutrino and leaving behind a nucleus with Z-1 protons and N+1 neutrons. There is no Coulomb barrier in this process, which makes it much more likely than other reactions. In fact, a strong Coulomb attraction between an electron and a nucleus favours electron capture for nuclear transformation.

While lepton capture is known to occur in the case of muons (leptons) mixed into hydrogen systems, it is regarded as difficult for electrons to be captured by protons. For the reaction to happen, the lepton must be sufficiently massive, such that in energy terms, Mlc2 > Mnc2-Mpc2 ~ 1.293MeV ~2.531Mec2 (where MlMnMpand Me are the mass of the lepton, neutron, proton and electron respectively, and c is the speed of light). The muon is more than sufficiently massive to be captured by the proton, but not the electron, which needs to be at least 2.531 times as massive.

However, the electron mass in condensed matter can be modified by local electromagnetic field fluctuations. For example, laser light fields can “dress” an electron with additional mass. The surface states of metal hydrides are very important in this respect.

Collective surface oscillations of charged ions are involved in the weak interactions responsible for electron capture in condensed matter. The radiation frequencies of these oscillation range from the infrared to the soft X-ray spectra. The surface protons are oscillating coherently, contributing to the large magnitude of electromagnetic fluctuations. The neutrons produced by electron capture have an ultra low momentum (with long wavelength) due to the size of the coherence domain of the oscillating protons, estimated to vary from about one to ten microns in length. The long final state neutron wavelength allows for a large neutron wave function overlap with many protons, which increases the coherent neutron production rate.

It is estimated that the electron mass enhancement due to the electromagnetic field fluctuations (collective proton oscillations) on the surface of palladium hydride is about 20.6 fold, which is much more than enough for electron capture by proton or deuteron. The proton field oscillations can be amplified by shining a laser light on the palladium surface, which can enhance the production of neutrons that in turn catalyse other reactions.

The neutron, n, can fuse with other nuclei in transmutation reactions. Lithium (Li) is present in the electrolyte. A Li ion near to the hydride (electrode surface) could initiate a chain of reactions as follows:

                        6Li3  + n  →  7Li3

                        7Li+ n  →  8Li3

                        8Li3 →  8Be+ e- (electron) +v (neutrino)

                        8Be4 →  4He4He2

                                                            Q ~ 26.9 MeV

A large amount of energy, 26.9 MeV is generated by this chain of reactions.

Having produced 4He2, further neutrons may react to build heavy helium isotopes, and regenerate Li as follows.

                        4He2  + n  →  5He2

                        5He2  + n  →  6He2

                        6He2   →  6Li+ e+ v

                                                            Q ~2.95MeV

Other possibilities include direct lithium reactions

                        6Li3  + n  →  4He3H1

                        3H1   →  3He+ e+ v

                                                            Q ~ 4.29 MeV

These examples show that a final product, such as 4He2, does not necessarily constitute evidence for the direct fusion of two deuterons, which requires tunnelling through a high Coulomb barrier (see above). More importantly, final products such as helium-3 and tritium are also possible, as have been detected in many experiments.

Widom and Larsen are latecomers to the cold fusion field, and it is not clear to what extent their theory is accepted. I find it quite convincing especially for the low energy transmutation of elements [2], though it doesn’t necessarily exclude other mechanisms that depend equally on quantum coherence.


Krit Prasad Sinha and Andrew Meulenberg at the Indian Institute of Science Banagalore, India, propose the formation of deuteride or hydride (D- or H-) ions due to interactions of the deuterium or hydrogen with the phonon vibrations of the host lattice. ‘Local charged bosons’ (lochons) or local electron pairs can form on D+ to give D- [5-7].

At the same time, the collective motion of the deuterons driven by the phonons can introduce ‘breathing’ modes in the Pd lattice. If these breathing modes are resonant with the deuteron motion, they enhance deuteron migration and the rapid refilling and regeneration of the active sites. If the resonant vibration is anti-phase, the Pd atoms could move apart as adjacent deuterons come together, thus allowing direct collision of the deuterons while an electron cloud helps screen the repulsion due to the deuterons’ positive charges.

The formation of D- reverses the normal electrical repulsion between D+ ions, as D- and D+ can attract each other. The D+D- equilibrium positions in the lattice are much closer together than in free molecular D2 because of the increased effective electron mass from phonon interaction, reducing the electron distribution size into the sub-nanometre range, and therefore the point at which the attraction begins to diminish. The paired D+D- system has a much reduced zero-force distance (~2 nm) relative to that of a D2 molecule (~7 nm). All that conspires to increase the probability of fusion.

The D- and D+ fuse to form 4He2 releasing a large amount of energy, 23.8MeV, which is carried by the alpha particle and the ejected electron pair. Sinha and Meulenberg calculated a reaction rate of about 1.5 x1011 s-1. This is comparable to the muon-catalysed reactions giving tritium plus proton (T + p) or 3He + n processes (see previous section).

This mechanism too, could be greatly enhanced by laser stimulation.

Selective resonant tunnelling

In November 1989, the Energy Research Advisory Board of the Department of Energy in the United States made five recommendations, among them, to check for excess tritium in the electrolyte  in which cold fusion was supposed to have occurred. However, the amount of tritium generated did not tally with neutron emission. The expected 14 MeV neutron was not detected.

But tritium has appeared since in experiments in Japan, Italy, Russia, USA, Canada, India and China, and according to Li Xing Zhong at Tsinghua University Beijing China, it is one of the strongest pieces of evidence for condensed matter nuclear reactions, as it implies a new mechanism operating at low energy: selective resonance tunnelling [8].

A harmonic circuit is able to pick up the specific frequency from the air, but when the signal is weak, the resistance of the circuit must be low. It is the same with resonance tunnelling of the Coulomb barrier. At low energy, the Coulomb barrier is thick and high, hence the incident deuteron wave in the nuclear well is very weak. The amplitude of the weak penetrating wave may be enhanced by the resonance effect when the phase of the reflected wave inside the nuclear well is the same as that of the incident wave. This is resonant tunnelling. The damping must be weak, which is due to the fusion reaction itself, because the deuteron wave function disappears on fusion. Thus, this fusion reaction rate cannot be very fast, or it will kill the resonant effect. On the other hand, the rate cannot be too small, or it will give no fusion. As a result, the life-time of the deuteron wave function cannot be too large or too small. There is an optimum tlife to match a specific Coulomb barrier:

tlife ~q2tflight

q is a very large number for a thick and high Coulomb barrier, of the order of 1022 to 1031 or greater here. (1/q2 is the ‘Gamow penetration factor’, the kinetic energy of the approaching nuclei relative to the energy of repulsion between the nuclei); tflight is the flight time inside the nuclear well for the penetrating deuteron, and is of the order of 10-23s.

The reason there is no neutron emission from resonant tunnelling at low energy is because the lifetime for a neutron emission process is too short at around 10-23 s. Only the weak interactions (b-decay or k-capture, loss or gain of electron) might possibly provide the lifetime necessary.

Thus, selective resonant tunnelling provides the mechanism for penetrating the Coulomb barrier, and its selectivity explains why there are no neutron or gamma radiations after the resonant tunnelling at low energy.

If weak interaction is the only possible reactions for the resonant tunnelling at low energy, the possible reactions are between a proton p and a deuteron d:

p + d   →  T + e+ (positron) + ne

p + d       →        T  + ne

                        k capture

Usually the positron decay is faster than k-capture, the capture of an electron. In the case of resonant tunnelling, positron decay is too fast to meet the matching condition, so only k-capture is possible. This is consistent with experimental results. The annihilation of positron would produce 0.511MeV gamma radiation. But this is not observed in any tritium production experiments. The hydrophilic nature of the heavy water might explain the contamination by light water in the electrolytic cells, and that would be the source of protons for the resonant tunnelling reactions.

Solid state provides an energy band for deuterons or protons, thereby increasing the possibility of overlap with the resonant tunnelling state. Certain metals (Pd, Ni, Ti etc.) are particularly good because of their ability to absorb hydrogen, thereby filling this energy band to capacity.

Article first published 23/10/07


  1. Ho MW. From cold fusion to condensed matter nuclear science. Science in Society 36 (to appear),
  2. Ho MW. Transmutation, the alchemists’ dream come true? Science in Society 36 (to appear),
  3. Chubb T. Catalytic fusion and the interface between insulators and transition metals. ICCF12 Proceedings, 2005,
  4. Widom A and Larsen L. Ultra low mometum neutron catalyse nuclear reactions on metallic hydride surfaces. Physical Journal C 2006, DOI10.1140/epjc/s2006-02479-8.
  5. Sinha KP. A theoretical model for low-energy nuclear reactions in a solid matrix. Infinite Energy 29, 1-4, 1999.
  6. Sinha KP and Meulenberg A. Laser stimulation of low-energy nuclear reactions in deuterated palladium. Current Science 2006, 91, 907-12.
  7. Sinha KP and Meulenberg A. Lochon catalysed D-D fusion in deuterated palladium in the solid state, 2007, IOP,
  8. Li XZ, Liu B, Wei QM, Zeng SX and Cao DX. A Chinese view on summary of condensed matter nuclear science. J Fusion Energy 2004, 23(3) 217-21.

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