Cold Nuclear Fusion

Cold nuclear fusion

by E.N. Tsyganov
(UA9 collaboration) University of Texas Southwestern
Medical Center at Dallas, Texas, USA

Abstract
Recent accelerator experiments on fusion of various elements have clearly demonstrated that the effective cross-sections of these reactions depend on what material the target particle is placed in. In these experiments, there was a significant increase in the probability of interaction when target nuclei are imbedded in a conducting crystal or are a part of it. These experiments open a new perspective on the problem of so-called cold nuclear fusion.

Submitted to Physics of Atomic Nuclei/Yadernaya Fizika in Russian

Introduction
Experiments of Fleischmann and Pons made about 20 years ago [1], raised the question about the possibility of nuclear DD fusion at room temperature. Conflicting results of numerous experiments that followed, dampened the initial euphoria, and the scientific community quickly came to common belief, that the results of [1] are erroneous. One of the convincing arguments of skeptics was the lack in these experiments of evidence of nuclear decay products. It was assumed that “if there are no neutrons, therefore is no fusion.” However, quite a large international group of physicists, currently a total of about 100-150 people, continues to work in this direction. To date, these enthusiasts have accumulated considerable experience in the field. The leading group of physicists working in this direction, in our opinion, is the group led by Dr. M. McKubre [2]. Interesting results were also obtained in the group of Dr. Y. Arata [3]. Despite some setbacks with the repeatability of results, these researchers still believe in the existence of the effect of cold fusion, even though they do not fully understand its nature. Some time ago we proposed a possible mechanism to explain the results of cold fusion of deuterium [4]. This work considered a possible mechanism of acceleration of deuterium contaminant atoms in the crystals through the interaction of atoms with long-wavelength lattice vibrations in deformed parts of the crystal. Estimates have shown that even if a very small portion of the impurity atoms (~105) get involved in this process and acquires a few keV energy, this will be sufficient to describe the energy released in experiments [2]. This work also hypothesized that the lifetime of the intermediate nucleus increases with decreasing energy of its excitation, so that so-called “radiation-less cooling” of the excited nucleus becomes possible. In [5], we set out a more detailed examination of the process. Quite recently, a sharp increase of the probability of fusion of various elements was found in accelerator experiments for the cases when the target particles are either imbedded in a metal crystal or are a part of the conducting crystal. These experiments compel us to look afresh on the problem of cold fusion.

Recent experiments on fusion of elements on accelerators

For atom-atom collisions the expression of the probability of penetration through a Coulomb barrier for bare nuclei should be modified, because atomic electrons screen the repulsion effect of nuclear charge. Such a modification for the isolated atom collisions has been performed in H.J. Assenbaum and others [6] using static Born-Oppenheimer approximation. The experimental results that shed further light on this problem were obtained in relatively recent works C. Rolfs [7] and K. Czerski [8]. Review of earlier studies on this subject is contained in the work of L. Bogdanova [9]. In these studies a somewhat unusual phenomenon was observed: the sub-barrier fusion cross sections of elements depend strongly on the physical state of the matter in which these processes are taking place. Figure 1 (left) shows the experimental data [8], demonstrating the dependence of the astrophysical factor S(E) for the fusion of elements of sub-threshold nuclear reaction on the aggregate state of the matter that contains the target nucleus 7Li. The same figure (right) presents similar data [7] for the DD reaction, when the target nucleus was embedded in a zirconium crystal. It must be noted that the physical nature of the phenomenon of increasing cross synthesis of elements in the case where this process occurs in the conductor crystal lattice is still not completely clear.

Figure 1. Up – experimental data [8], showing the energy dependence of the S-factor for sub-threshold nuclear reaction on the aggregate state of matter that contains the nucleus 7Li. Down – the similar data [7] for the reaction of DD, when the target nucleus is placed in a crystal of zirconium. The data are well described by the introduction of the screening potential of about 300 eV.

The phenomenon is apparently due to the strong anisotropy of the electrical fields of the crystal lattice in the presence of free conduction electrons. Data for zirconium crystals for the DD reactions can be well described by the introduction of the screening potential of about 300 eV. It is natural to assume that the corresponding distance between of two atoms of deuterium in these circumstances is less than the molecular size of deuterium. In the case of the screening potential of 300 eV, the distance of convergence of deuterium atoms is ~510ˆ12 m, which is about an order of magnitude smaller than the size of a molecule of deuterium, where the screening potential is 27 eV. As it turned out, the reaction rate for DD fusion in these conditions is quite sufficient to describe the experimental results of McKubre and others [2]. Below we present the calculation of the rate process similar to the mu-catalysis where, instead of the exchange interaction by the muon, the factor of bringing together two deuterons is the effect of conduction electrons and the lattice of the crystal.

Calculation of the DD fusion rate for “Metal-Crystal” catalysis

The expression for the cross section of synthesis in the collision of two nuclei can be written as
where for the DD fusion
Here the energy E is shown in keV in the center of mass. S(E) astrophysical factor (at low energies it can be considered constant), the factor 1/E reflects de Broglie dependence of cross section on energy. The main energy dependence of the fusion is contained in an expression
that determines the probability of penetration of the deuteron through the Coulomb barrier. From the above expressions, it is evident that in the case of DD collisions and in the case of DDμcatalysis, the physics of the processes is the same. We use this fact to determine the probability of DD fusion in the case of the “metal-crystalline” DD-catalysis. In the case of DDμ- catalysis the size of the muon deuterium molecules (ion+) is ~5×10ˆ13m. Deuterium nuclei approach such a distance at a kinetic energy ~3 keV. Using the expression (1), we found that the ratio of σ(3.0 keV)/σ(0.3 keV) = 1.05×10ˆ16. It should be noted that for the free deuterium molecule this ratio [ σ(3.0keV)/σ(0.03keV)] is about 10ˆ73. Experimental estimations of the fusion rate for the (DDμ)+ case presented in the paper by Hale [10]:
Thus, we obtain for the “metal-crystalline” catalysis DD fusion rate (for zirconium case):
Is this enough to explain the experiments on cold fusion? We suppose that a screening potential for palladium is about the same as for zirconium. 1 cmˆ3 (12.6 g) of palladium contains 6.0210ˆ23(12.6/106.4) = 0.710ˆ23 atoms. Fraction of crystalline cells with dual (or more) the number of deuterium atoms at a ratio of D: Pd ~1:1 is the case in the experiments [2] ~0.25 (e.g., for Poisson distribution). Crystal cell containing deuterium atoms 0 or 1, in the sense of a fusion reaction, we consider as “passive”. Thus, the number of “active” deuterium cells in 1 cmˆ3 of palladium is equal to 1.810ˆ22. In this case, in a 1 cmˆ3 of palladium the reaction rate will be

this corresponds to the energy release of about 3 kW. This is quite sufficient to explain the results of McKubre group [2]. Most promising version for practical applications would be Platinum (Pt) crystals, where the screening potential for d(d,p)t fusion at room temperature is about 675 eV [11]. In this case, DD fusion rate would be:

The problem of “nonradiative” release of nuclear fusion energy

As we have already noted, the virtual absence of conventional nuclear decay products of the compound nucleus was widely regarded as one of the paradoxes of DD fusion with the formation of 4He in the experiments [2]. We proposed the explanation of this paradox in [4]. We believe that after penetration through the Coulomb barrier at low energies and the materialization of the two deuterons in a potential well, these deuterons retain their identity for some time. This time defines the frequency of further nuclear reactions. Figure 2 schematically illustrates the mechanism of this process. After penetration into the compound nucleus at a very low energy, the deuterons happen to be in a quasi-stabile state seating in the opposite potential wells. In principle, this system is a dual “electromagnetic-nuclear” oscillator. In this oscillator the total kinetic energy of the deuteron turns into potential energy of the oscillator, and vice versa. In the case of very low-energy, the amplitude of oscillations is small, and the reactions with nucleon exchange are suppressed.
Fig. 2. Schematic illustration of the mechanism of the nuclear decay frequency dependence on the compound nucleus 4He* excitation energy for the merging deuterons is presented. The diagram illustrates the shape of the potential well of the compound nucleus. The edges of the potential well are defined by the strong interaction, the dependence at short distances Coulomb repulsion.
The lifetime of the excited 4He* nucleus can be considered in the formalism of the usual radioactive decay. In this case,

Here ν is the decay frequency, i.e., the reciprocal of the decay time τ. According to our hypothesis, the decay rate is a function of excitation energy of the compound nucleus E. Approximating with the first two terms of the polynomial expansion, we have:
Here ν° is the decay frequency at asymptotically low excitation energy. According to quantum-mechanical considerations, the wave functions of deuterons do not completely disappear with decreasing energy, as illustrated by the introduction of the term ν°. The second term of the expansion describes the linear dependence of the frequency decay on the excitation energy. The characteristic nuclear frequency is usually about 10ˆ22 sˆ-1. In fusion reaction D+D4He there is a broad resonance at an energy around 8 MeV. Simple estimates by the width of the resonance and the uncertainty relation gives a lifetime of the intermediate state of about 0.810ˆ22 s. The “nuclear” reaction rate falls approximately linearly with decreasing energy. Apparently, a group of McKubre [2] operates in an effective energy range below 2 keV in the c.m.s. Thus, in these experiments, the excitation energy is at least 4×10ˆ3 times less than in the resonance region. We assume that the rate of nuclear decay is that many times smaller. The corresponding lifetime is less than 0.3×10ˆ18 s. This fall in the nuclear reaction rate has little effect on the ratio of output decay channels of the compound nucleus, but down to a certain limit. This limit is about 6 keV. A compound nucleus at this energy is no longer an isolated system, since virtual photons from the 4He* can reach to the nearest electron and carry the excitation energy of the compound nucleus. The total angular momentum carried by the virtual photons can be zero, so this process is not prohibited. For the distance to the nearest electron, we chose the radius of the electrons in the helium atom (3.1×10ˆ11 m). From the uncertainty relations, duration of this process is about 10ˆ-19 seconds. In the case of “metal-crystalline” catalysis the distance to the nearest electrons can be significantly less and the process of dissipation of energy will go faster. It is assumed that after an exchange of multiple virtual photons with the electrons of the environment the relatively small excitation energy of compound nucleus 4He* vanishes, and the frequency of the compound nucleus decaying with the emission of nucleons will be determined only by the term ν°. For convenience, we assume that this value is no more than 10ˆ12-10ˆ14 per second. In this case, the serial exchange of virtual photons with the electrons of the environment in a time of about 10ˆ-16 will lead to the loss of ~4 MeV from the compound nucleus (after which decays with emission of nucleons are energetically forbidden), and then additional exchange will lead to the loss of all of the free energy of the compound nucleus (24 MeV) and finally the nucleus will be in the 4He ground state. The energy dissipation mechanism of the compound nucleus 4He* with virtual photons, discussed above, naturally raises the question of the electromagnetic-nuclear structure of the excited compound nucleus.
Fig. 3. Possible energy diagram of the excited 4He* nucleus is presented.
Figure 3 represents a possible energy structure of the excited 4He* nucleus and changes of its spatial configuration in the process of releasing of excitation energy. Investigation of this process might be useful to study the quark-gluon dynamics and the structure of the nucleus.

Discussion

Perhaps, in this long-standing history of cold fusion, finally the mystery of this curious and enigmatic phenomenon is gradually being opened. Besides possible benefits that the practical application of this discovery will bring, the scientific community should take into account the sociological lessons that we have gained during such a long ordeal of rejection of this brilliant, though largely accidental, scientific discovery. We would like to express the special appreciation to the scientists that actively resisted the negative verdict imposed about twenty years ago on this topic by the vast majority of nuclear physicists.

Acknowledgements
The author thanks Prof. S.B. Dabagov, Dr. M. McKubre, Dr. F. Tanzela, Dr. V.A. Kuzmin, Prof. L.N. Bogdanova and Prof. T.V. Tetereva for help and valuable discussions. The author is grateful to Prof. V.G. Kadyshevsky, Prof. V.A. Rubakov, Prof. S.S. Gershtein, Prof. V.V. Belyaev, Prof. N.E. Tyurin, Prof. V.L. Aksenov, Prof. V.M. Samsonov, Prof. I.M. Gramenitsky, Prof. A.G. Olshevsky, Prof. V.G. Baryshevsky for their help and useful advice. I am grateful to Dr. VM. Golovatyuk, Prof. M.D. Bavizhev, Dr. N.I. Zimin, Prof. A.M. Taratin for their continued support. I am also grateful to Prof. A. Tollestrup, Prof. U. Amaldi, Prof. W. Scandale, Prof. A. Seiden, Prof. R. Carrigan, Prof. A. Korol, Prof. J. Hauptmann, Prof. V. Guidi, Prof. F. Sauli, Prof. G. Mitselmakher, Prof. A. Takahashi, and Prof. X. Artru for stimulating feedback. Continued support in this process was provided with my colleagues and the leadership of the University of Texas Southwestern Medical Center at Dallas, and I am especially grateful to Prof. R. Parkey, Prof. N. Rofsky, Prof. J. Anderson and Prof. G. Arbique. I express special thanks to my wife, N.A. Tsyganova for her stimulating ideas and uncompromising support.

References
1. M. Fleischmann, S. Pons, M. W. Anderson, L. J. Li, M. Hawkins, J. Electro anal. Chem. 287, 293 (1990).
2. M. C. H. McKubre, F. Tanzella, P. Tripodi, and P. Haglestein, In Proceedings of the 8th International Conference on Cold Fusion. 2000, Lerici (La Spezia), Ed. F. Scaramuzzi, (Italian Physical Society, Bologna, Italy, 2001), p 3; M. C. H. McKubre, In Condensed Matter Nuclear Science: Proceedings Of The 10th International Conference On Cold Fusion; Cambridge, Massachusetts, USA 21-29 August, 2003, Ed by P. L. Hagelstein and S. R. Chubb, (World Sci., Singapore, 2006). M. C. H. McKubre, “Review of experimental measurements involving dd reactions”, Presented at the Short Course on LENR for ICCF-10, August 25, 2003.
3. Y. Arata, Y. Zhang, “The special report on research project for creation of new energy”, J. High Temp. Soc. (1) (2008).
4. E. Tsyganov, in Physics of Atomic Nuclei, 2010, Vol. 73, No. 12, pp. 1981–1989. Original Russian text published in Yadernaya Fizika, 2010, Vol. 73, No. 12, pp. 2036–2044.
5. E.N. Tsyganov, “The mechanism of DD fusion in crystals”, submitted to IL NUOVO CIMENTO 34 (4-5) (2011), in Proceedings of the International Conference Channeling 2010 in Ferrara, Italy, October 3-8 2010.
6. H.J. Assenbaum, K. Langanke and C. Rolfs, Z. Phys. A – Atomic Nuclei 327, p. 461-468 (1987).
7. C. Rolfs, “Enhanced Electron Screening in Metals: A Plasma of the Poor Man”, Nuclear Physics News, Vol. 16, No. 2, 2006.
8. A. Huke, K. Czerski, P. Heide, G. Ruprecht, N. Targosz, and W. Zebrowski, “Enhancement of deuteron-fusion reactions in metals and experimental implications”, PHYSICAL REVIEW C 78, 015803 (2008).
9. L.N. Bogdanova, Proceedings of International Conference on Muon Catalyzed Fusion and Related Topics, Dubna, June 18–21, 2007, published by JINR, E4, 15-2008-70, p. 285-293
10. G.M. Hale, “Nuclear physics of the muon catalyzed d+d reactions”, Muon Catalyzed Fusion 5/6 (1990/91) p. 227-232.
11. F. Raiola (for the LUNA Collaboration), B. Burchard, Z. Fulop, et al., J. Phys. G: Nucl. Part. Phys.31, 1141 (2005); Eur. Phys. J. A 27, s01, 79 (2006).
by E.N. Tsyganov
(UA9 collaboration) University of Texas Southwestern
Medical Center at Dallas, Texas, USA

This hypothesis seems to be the starting point of this theory:

The problem of “nonradiative” release of nuclear fusion energy

As we have already noted, the virtual absence of conventional nuclear decay products of the compound nucleus was widely regarded as one of the paradoxes of DD fusion with the formation of 4He in the experiments [2]. We proposed the explanation of this paradox in [4]. We believe that after penetration through the Coulomb barrier at low energies and the materialization of the two deuterons in a potential well, these deuterons retain their identity for some time. This time defines the frequency of further nuclear reactions.

Until we have a good theory, it does not at all surprise me that experiments seems to be not repeatable.

Even something as the temperatures that a metal is forged in and allowed to cool might be enough to make or break the ability for the reactions to occur.

But I have little doubt now - very little, in fact, - that something is going on.

Pons and Fleischman may not have been the greatest theoretical nuclear physicists, but they were thermodynamic chemists par excellence!

"We believe that after penetration through the Coulomb barrier at low energies and the materialization of the two deuterons in a potential well, these deuterons retain their identity for some time."

"It is assumed that after an exchange of multiple virtual photons with the electrons of the environment the relatively small excitation energy of compound nucleus 4He* vanishes,"

"In this case, the serial exchange of virtual photons with the electrons of the environment "

This sounds more like a magic act. I had a debate a week or so ago with a poster who assured me that things cannot just 'materialize' or 'vanish'. That matter cannot be created or destroyed. I am sure my lack of experience in nuclear physics has led to misunderstanding of the 'terminology' in use in this article, but it seems that the verbs and adjectives they used are rather 'sketchy'.

Then again, We do not really understand gravity nor magnetism, so...

It is important to realize that while we typically think in Newtonian terms at our own scale, and more recently in Quantum terms, at the extremely small scale, there is also a “very small” scale that can produce some very exotic and counterintuitive effects.

For example, there is a variety of shrimp called a snapping shrimp, that has the remarkable ability to cause a tiny cavitation bubble that it uses to attack its prey. A tiny bubble that in a very small area creates an immense force, equal to 80 kilo-Pascal that can kill a small fish 4 cm away.

And that cavitation bubble, in a very small area, contains a temperature of over 4,700 C for a very brief moment. By comparison, the surface of the Sun is about 5,500 C.

I mention this as these oddities of the very small scale come into play when something like cold fusion is considered. This is because while we might be unaware of potent forces at the very small scale, they might be in play, bringing about very peculiar effects.

Thank you for responding and explaining things in laymen's terms.

In fact particles come into existence and vanish all the time. This is part of the essence of quantum mechanics.

Which is not really 'science', is it?

Our use of quantum 'theory' is to explain how it appears to us that when we observe the state of a particle, it is not there (really meaning it is not where we 'predicted' it would be), and therefore we conjecture that it is in exactly a 180 degree rotation away. Maybe the problem is that we assume the orbits of these particles are perfect circles. A look at the examples in our solar system, galaxy, and the rest of the Universe say that perfect circular orbits rarely exist.

It is virtual particles that come into existence in the nucleus that create the force called the strong force that keeps the nucleus from flying apart at near light speeds.

OK, 'virtual' (meaning not exactly 'real'?) magically wink into existence, because we need them to explain what it is that holds the Nucleus together. Much like the need for Black Holes at the center of galaxies. We can't explain why the stars in a galaxy stick together instead of spreading out and depopulating the galaxy. Since we 'misunderstand' gravity, and our 'understanding' of it says that you have to have X amount of matter to create the gravity needed, then we postulated the theory called 'black holes' to explain the fact that they do indeed stay formed as galaxies. What is at the center of a tornado, that keeps the moisture and dirt spinning round it at such high speeds, without instantly coming 'apart'?

Perhaps the reason they stick together is not due to black holes, but due to the same force that we call gravity, magnetism, and the strong/weak nuclear forces.

It all boils down to what the ancients understood. Balance. In this case, balance of electrical potentials. The Yin and Yang Symbol. The attempt by all particles to establish a balanced electrical field.

A battery with a positive charge will send that 'potential' to a negative ground (or does it go the other way?) because of the NEED to balance that potential back to zero. A balloon quickly rubbed will attract oppositely charged material. Same reason. Balance. That process of the attraction or repulsion is a force.

All things (particles) in the Universe, and the matter that they comprise,,, attempt to achieve balance. If they all did, I don't think the Universe (matter) would exist. It is the energy (force) created by this need to attain balance that powers the Universe. Due to the chaotic nature of the Universe, and constant 'change', nothing achieves that balance (perfection).

Why is it that we say gravity keeps the Moon orbiting round the Earth, but that it is not gravity that keeps the nucleus together, or the electrons in orbit?

It’s not magic, it’s more a limitation of an ability to describe a phenomenon with everyday day terms.

True. It also may be a limitation of 'our' ability to describe a phenomenon that is still outside our scientists' understanding.

Virtual particles are simply a way of describing energy without a particle to carry it. Hence around an electron there are a cloud of virtual particles that make the electron seem fuzzy until one attempts to penetrate deeper.

Hmmmm... Like photons being particles and waves? If the virtual particles are just energy with no particle to carry them, how do they cause a fuzziness? When you go deeper, what do you find?

Or the magnetic field would be another example of energy without particles moving about carrying the energy.

Are not all emissions of the electromagnetic spectrum 'energy' without particles?

Hmmmm... Like photons being particles and waves? If the virtual particles are just energy with no particle to carry them, how do they cause a fuzziness? When you go deeper, what do you find?

They come into existence and act like a particle until they disappear. What is at the heart of an electron? who knows?

“Are not all emissions of the electromagnetic spectrum ‘energy’ without particles?”

I'm not an expert (you could tell couldn't you?)but I suggest the photons act as particles.

There are many articles online that might be helpful to you, more so than I certainly.

Fascinating.

From wikipedia

http://en.wikipedia.org/wiki/Alpheidae

Snapping effect

The snapping shrimp competes with much larger animals like the Sperm Whale and Beluga Whale for the title of 'loudest animal in the sea'. The animal snaps a specialized claw shut to create a cavitation bubble that generates acoustic pressures of up to 80 kPa at a distance of 4 cm from the claw. As it extends out from the claw, the bubble reaches speeds of 60 miles per hour (97 km/h) and releases a sound reaching 218 decibels.[11] The pressure is strong enough to kill small fish.[12] It corresponds to a zero to peak pressure level of 218 decibels relative to one micropascal (dB re 1 μPa), equivalent to a zero to peak source level of 190 dB re 1 μPa at the standard reference distance of 1 m. Au and Banks measured peak to peak source levels between 185 and 190 dB re 1 μPa at 1 m, depending on the size of the claw.[13] Similar values are reported by Ferguson and Cleary.[14] The duration of the click is less than 1 millisecond.

The snap can also produce sonoluminescence from the collapsing cavitation bubble. As it collapses, the cavitation bubble reaches temperatures of over 5,000 K (4,700 °C).[15] In comparison, the surface temperature of the sun is estimated to be around 5,800 K (5,500 °C). The light is of lower intensity than the light produced by typical sonoluminescence and is not visible to the naked eye. It is most likely a by-product of the shock wave with no biological significance. However, it was the first known instance of an animal producing light by this effect. It has subsequently been discovered that another group of crustaceans, the mantis shrimp, contains species whose club-like forelimbs can strike so quickly and with such force as to induce sonoluminescent cavitation bubbles upon impact.[16]

The snapping is used for hunting (hence the alternative name "pistol shrimp"), as well as for communication. When feeding, the shrimp usually lies in an obscured spot, such as a burrow. The shrimp then extends its antennae outwards to determine if any fish are passing by. Once it feels movement, the shrimp inches out of its hiding place, pulls back its claw, and releases a "shot" which stuns the prey; the shrimp then pulls it to the burrow and feeds.

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