Chapter 11     Cold Fusion Phenomenon is Explained by TNCF Model

In the preceding Chapters from 6 to 10, we have examined the experimental data sets in the cold fusion phenomenon obtained in this nine years spreading out into various events in solids not noticed until now. A. Einstein once compared a physicist with a detective in his famous book The Evolution of Physics written by him with L. Infeld. Knowing complicated facts in the cold fusion phenomenon introduced in these chapters, we are tempted to clarify necessary conditions of various events in them, to solve the many riddles contained in them, to determine sufficient conditions of the phenomenon and finally to built a new science of the solid state - nuclear physics. This is a challenging theme for genuine scientists who are always going to solve riddles of nature and society and to use the results to promote social welfare.

Why don't you start to a new spiritual adventure from now on as if you impersonate the talented detective Sherlock Holmes facing a new case.


11.1 The TNCF Model Trapped Neutron Catalyzed Fusion Model

To interpret various experimental data sets with poor reproducibility (or irreproducibility) and their absence in low background neutron environment, the author had the first idea to construct a model, named later the TNCF model, in August, 1993.[205] The TNCF model has several premises  based on the experimental data as explained in this section. These fundamental premises are symbolization of several necessary conditions\index{necessary condition} of the cold fusion phenomenon extracted from the pile of experimental data by the author's eyes. The necessary conditions clarified by now can be expressed as

1) existence of hydrogen isotopes (protium and/or deuterium) in appropriate solids (Pd, Ti, Ni, and so forth),

2) existence of the background thermal neutron,

3) existence of an appropriate alkali-metal layer (Li, K, Na and so forth) on the surface of the metal hydride (in the case of electrolytic system) and

4) inhomogeneous distribution of the hydrogen isotope in the solid. It should be emphasized that sufficient conditions of the cold fusion phenomenon are not determined yet although these necessary conditions have been recognized in the experimental data sets obtained hitherto.

The TNCF model has been applied to analyze more than fifty data sets until now obtained in various circumstances and materials and the results have been published one by one as cited in the third part of Chapter 18 (18.3). The results were published also in compiled forms recently.[255, 266, 270, 274]

The fundamental premises of the TNCF model, similar in its nature to 'the stationary electron orbits' in Bohr's model of hydrogen atom and 'the superfluid' in the two-fluid model (cf. Section 10.3), are the existence of quasi-stable trapped neutrons in cold fusion materials and their selective reaction with nuclei giving large perturbation on them.

In the model, there is one adjustable parameter nn, density of the trapped thermal neutron, which is used to analyze the cold fusion phenomenon containing several events specified by some physical quantities supposed to be results of various physical processes in the material. Some examples of these quantities are 1) gamma ray spectra, neutron energy spectra and distribution of transmuted nuclei in the material and 2) the excess heat, amounts of generated tritium and helium in a definite time, X ray and other charged particles if any. The quantities in group 1) are direct evidences of the cold fusion having direct information of the events and those in group 2) indirect evidences of the cold fusion showing accumulated results of the events.


The premises [241, 255, 270] in the TNCF model which connect nn and the observed quantities are explained in the next subsection. With these premises, more than fifty typical experimental data sets including those by Fleischmann et al.,[1] Morrey et al.,[1-4] Miles et al.,[18'] Storms et al.,[4] Gozzi et al.,[51'',51-3] Bush et al\citref [27''] and others were analyzed[229 232, 249, 265] successfully with consistency in them. The results are summarized as follows:

In the pioneering work[1] where observed the excess heat, tritium and neutron in the electrolytic system with Pd cathode in D2O + LiOD electrolytic solution (Pd/D/Li system), the controversial relations between these quantities were interpreted by our model[249] consistently with values of nn = 107 - 109 cm-3 if we permit inconsistency in the experimental results which showed lack of expected simultaneity of events from the model.

The difficulty to explain production of 42He in the electrolytic system of Pd/ D/ Li[1-4,14'',18',43'] were resolved by the reaction (5.3) between the trapped neutron and 63Li occurring in the surface layer of Li metal (and/or PdLix alloy) on the cathode. The parameter nn was determined[265,266,296] from the  data sets in these experiments as 108   1010 cm-3.

In the experiment[4] where observed the excess heat and tritium in Pd/D/Li system but without expected simultaneity, the parameter nn was determined[256] as 107 1011 cm-3 with the same reservation for the simultaneity of events. In the experiment[51''] where observed the excess heat, tritium and 4He in Pd/D/Li system, the data were interpreted[262] with nn = 1010 1011 cm-3 consistently altogether but again with the same reservation for the expected simultaneity of events.

In the experiment[27''] with Ni cathode and H2O + Rb2CO3 electrolytic solution, the excess heat and a nuclear transmutation (NT) from 8537Rb to 8638Sr  were observed. The result was explained consistently by the TNCF model[218,260] with nn = 1.4~107 cm-3.

Thus, it is possible to interpret various, sometimes more than two events in the cold fusion phenomenon consistently assuming only one adjustable parameter nn with a reservation of inexplicable problem of poor reproducibility and lack of simultaneity of several events. To understand these unexplained points more clearly, it will be necessary to take details of the object materials into the analyses on the TNCF model.

In this section, we will explain fundamental concepts of the TNCF model and relevant reactions in detail and renumber reactions listed in Chapter 5 for the later use.


11.1a Premises of the TNCF Model}


The TNCF model is a phenomenological one and the basic premises (assumptions) extracted from experimental data sets are summarized as follows:[241,255,266,274]


Premise 1. We assume a priori existence of the quasi-stable trapped neutron with a density nn in pertinent solids, to which the neutron is supplied essentially from the ambient neutron at first and then by breeding processes (explained below) in the sample.

The density nn is an adjustable parameter in the TNCF model which will be determined by an experimental data set using the supplementary premises which will be explained below concerning reactions of the trapped neutron with other particles in the solids. The quasi-stability of the trapped neutron means that the neutron trapped in the crystal does not decay until a strong perturbation destroys the stability while a free neutron decays with a time constant of 887.4 } 0.7 s.


Premise 2. The trapped neutron in a solid reacts with another nucleus in the surface layer\index{surface layer} of the solid, where it suffers a strong perturbation, as if they are in vacuum. We express this property by taking the parameter (the instability parameter) ƒÌ, defined in the relation (11.1) written down below, as ƒÌ = 1.


We have to mention here that the instability parameter ƒÌ in the surface layer is not known at all and it can be, as noticed recently, more than one (1 <ƒÌ) making the determined value of the parameter nn smaller. This ambiguity is suggested by various anomalous changes of decay character of radioactive isotopes and by unexpected fission products in the surface layer.


Premise 3. The trapped neutron reacts with another perturbing nucleus in volume by a reaction rate given in the relation (11.1) below with a value of the instability parameter\index{instability parameter}ƒÌ< 0.01 due to its stability in the volume (except in  special situations such as at very high temperature as 3000 K).


Following premises on the measured quantities of nuclear products and the excess heat are used to calculate reaction rates, for simplicity:


Premise 4. Product nuclei of a reaction lose all their kinetic energy in the sample except they go out without energy loss.


Premise 5. A nuclear product observed outside of the sample has the same energy as its initial (or original) one.


This means that if an energy spectrum of gamma-ray photon or neutron is observed outside, it reflects directly nuclear reactions in the solid sample. The same is for the distribution of the transmuted nucleus in the sample. Those spectra and the distributions of the transmuted nuclei are the direct information of the individual events of the nuclear reaction in the sample.


Premise 6. The amount of the excess heat\index{excess heat} is the total liberated energy in nuclear reactions dissipated in the sample except that brought out by nuclear products observed outside.


Premise 7. Tritium and helium measured in a system are accepted as all of them generated in the sample.


The amounts of the excess heat, tritium and helium are accumulated quantities reflecting nuclear reactions in the sample indirectly and are the indirect information of the individual events.


Premises about structure of the sample are expressed as follows:


Premise 8. In electrolytic experiments, the thickness l of the alkali metal layer on the cathode surface (surface layer)\index{surface layer} will be taken as l = 1 ƒÊm (though the experimental evidences show that it is 1 a 10 ƒÊm).


Premise 9. The mean free path or path length lt of the triton with an energy 2.7 MeV generated by n + 6Li fusion reaction will be taken as lt =  1 ƒÊm irrespective of material of the solid. Collision and fusion cross sections of the triton with nuclei in the sample will be taken as the same as those in vacuum.


Premise 10. Efficiency of detectors will be assumed as 100% except otherwise described, i.e. the observed quantities are the same as those generated in the sample and to be observed by the detector in experiments if there are no description of its efficiency.


A premise will be made to calculate the number of events NQ producing the excess heat Q.


Premise 11. In the calculation of the number of an event (a nuclear reaction) NQ producing the excess heat Q, the average energy liberated in the reactions is assumed as 5 MeV unless the reaction is identified: NQ = Excess heat Q (MeV)/ 5 (MeV).


Following relation combines two energy units, the million-electron-volt (MeV) and the joule (J):\index{energy unit}

 1 MeV = 1.6~10-13 J,  1 J = 6.25~1012 MeV.


The origin of the trapped neutron can be considered as 1) the ambient background neutrons, the existence of which have been recognized widely in public,[69] and 2) the neutrons breeded in the sample by chain nuclear reactions triggered by reactions of the trapped neutron with perturbing nuclei, proposed in the TNCF model.

We explain here the experimental bases of these premises briefly:


Premise 1. Possible existence of trapped neutron.

Cerofolini[39] and Lipson[15-3] observed temporal changes of neutron intensity irradiated to sample without change of total number (cf. Section 8.3).


Premises 2 and 3. Nuclear products induced by thermal neutrons.

Shani et al.[30], Yuhimchuk et al.[31], Celani et al.[32], Stella et al.[33] and Lipson et al.[15] had observed effects of natural or artificial thermal neutron on neutron emission in various materials (cf. Section 8.2).

Premises 2 and 8. Neutron reactions in the surface layer.

Morrey et al.,[1-4] Okamoto et al.,[12'',12-5]  Mizuno et al.[26-3] and Qiao et al.[57'] showed helium production and nuclear transmutation in the surface layers of Pd cathodes (and wire) with a thickness of from 1 to 40 ƒÊm.


Premise 3. Low reactivity of volume nuclei.

In addition to the data noticed in the preceding paragraph, Notoya et al.[35-3] observed nuclear transmutation and positron annihilation gamma in porous Ni sample which showed low reactivity of nucleus in volume of the sample.

Exception of the reaction rate in volume was illustrated in an experiment of Mo cathode at 3000 K where observed high production rate of tritium.[44 ` 44-4]


If the stability of the trapped neutron is lost by a large perturbation in the surface layer or in volume, the number of trigger reactions (per unit time) between trapped thermal neutrons and a nucleus AZM may be calculated by the same formula as the usual collision process in vacuum but an instability parameter ƒÌ:

 Pf =\ 0.35nnvnnMVƒÐnMƒÌ,

where  0.35nnvn  is the flow density of the trapped thermal neutron per unit area and time, nM is the density of the nucleus, V is the volume where the reaction occurs, ƒÐnM is the cross section of the reaction. The instability parameter ƒÌ as taken into the relation (11.1) expresses an order of the stability of the trapped neutron in the region as explained in premises 2 and 3, and also in the next paragraph.

In the electrolytic experiments, we have taken ƒÌ = 1 in the surface layer and ƒÌ = 0 in the volume except otherwise stated (Premises 2 and 3).

The values of ƒÌ = 0.01 instead of ƒÌ = 0 in the relation (11.1) will result in lower nn in the electrolytic data by a factor 2 than that determined with a value ƒÌ = 0 as had been used in our former analyses. (In this Chapter, we will cite previous results with ƒÌ = 0 as they were.)

In the case of a sample with a definite boundary layer surrounding a trapping region where is the thermal neutron, the volume V should be that of the boundary region where is the nucleus to react with the thermal neutron. On the other hand, in a sample without definite boundary layer but disordered array of minority species of lattice nuclei in the sample, the volume should be the whole volume of the sample.

If a fusion reaction occurs between a trapped thermal neutron and one of lattice nuclei AZM with a mass number A and an atomic number Z, there appears an excess energy Q and nuclear products as follows:

 n +AZM = A+1-bZ-aMf + baMff + Q,

where 00M = ƒÁ, ‚P0M = n, 11M = p, 21M = d, 31M = t, 42M = 4He, etc.

The liberated energy Q may be measured as the excess heat by the attenuation of the nuclear products, ƒÁ and charged particles, as generated in the reaction (5.2). Otherwise, the nuclear products may be observed outside with an energy (we assume it as the original one, hereafter) or may induce succeeding nuclear reactions (breeding reactions) with one of other nuclei in the sample.


Summary of the Analyses of Experimental Data

The results of analyses of more than 50 experimental results on the events obtained in the various cold fusion systems given in this chapter are tabulated in the following two tables Table 11.4 (p. *) and Table 11.5 (p.* ), one for systems with Pd and another for systems with Ni and others.


On the 'Seasonal effect' of NT (Added in the Second Printing.)

In the Proc. of ICCF7, there is a unique report by R.A. Monti[72] on the Nuclear Transmutation.

In this paper, R.A. Monti presented only results of his investigation done from 1992 to 1998 showing nuclear transmutation of stable and also unstable isotopes by means of ordinary chemical reactions. He also told about a paper presented at ICCF5 in 1995 (but not printed) where he had given a result on variation of the half lives of radioactive elements in cold fusion experiments.

His experiments have shown clearly a decrease of Pb and an increase of Ag with a decrease of Th or U. The observed change of those elements depended on the time when the experiments were performed. Monti has given an interpretation of this time dependence as follows:

"The 'seasonal effect' which I had already previously observed showed itself again. Even if I know it I had never written about it before. It was already difficult for the scientific community to get acquainted with the idea of Low Energy Transmutations. Imagine how easily a 'seasonal effect' in nuclear reactions could be accepted."

His result on the variation of radioactivity was too early to be printed in Proceedings of ICCF5. And also, his reference to constellation in regards to the 'seasonal effect' seems too outrageous as a scientific logic. From our point of view, however, density of the background neutron can surely be dependent on season which influences the cold fusion phenomenon and therefore NT.


11.14 Remaining Questions not Explained by the TNCF Model

There remain many questions about the model even if it has given satisfactory explanation for many events in the cold fusion phenomenon.

Following is a list of these questions to be solved or explained in future.

1. Physical basis of the neutron trapping mechanism

2. Stabilization of the trapped neutrons against beta‑decay (Elongation of life time)

3. Quasi‑stabilization of the trapped neutron against reaction with lattice nuclei

4. Neutron‑lattice nuclei interaction in a boundary layer

5. De‑stabilization of lattice nuclei in a boundary layer

6. Mechanism to initiate a trigger reaction

7. Role of channeling in the breeding reactions

8. Lack of reproducibility, explanation by stochastic formation of conditions for trapping, triggering and breeding reactions

9. Possible trapped neutron‑lattice nucleus reaction without photon emission

10. Role of photo‑disintegration of deuteron and nuclei

11. Lack of expected simultaneity of some events in experiments

12. Optimum values of nn = 108 ~ 1013 cm3.

13. Decay time shortening of nucleus in the surface layer

14. Induced nuclear fission of              nucleus in the surface layer

Some of these problems will be investigated in Chapter 12.