Cold Fusion Phenomenon in Protium Systems

 

Hideo Kozima

Cold Fusion Research Laboratory,

Yatsu 597-16, Aoi, Shizuoka, Shizuoka 421-1202, Japan

 

1. Introduction

   The discovery of the cold fusion phenomenon (CFP) in a deuterium system was announced by M. Fleischmann, S. Pons and M. Hawkins [1.1] in 1989. They proclaimed observation of enormous heat generation, large amount of tritium and a little neutron in a electrolytic system of Pd cathode, Pt anode and electrolytic solution D2O + LiOD (Pd/ D(Li)/Pt system).

   The experimental result obtained by Fleischmann et al. [1.1] is inexplicable properly by known chemical reactions in the system but also is not consistent with probable nuclear reactions they presupposed in advance. They had expected a large effect of Pd lattice to induce the d-d fusion reactions in the palladium deuterides PdDx (x ≈ 1.0) (the Fleischmannfs hypothesis) [1.2].

   The experimental data sets obtained since 1989, however, have shown that the Fleischmannfs hypothesis is not fundamental as a cause of the cold fusion phenomenon (CFP) or the nuclear reactions occurring in solids, mainly in transition-metal hydrides/deuterides. There are many evidences telling us that the Fleischmannfs hypothesis does not work to explain experimental results obtained in various materials at various conditions.

   The most unexpected results have been obtained as the CFP in protium systems not including deuterium. The experimental data sets in protium systems of electrolytic and gas contact systems have been obtained as early as 1991 up to now increasing its number and variety.

The existence of three statistical laws [1.3] among observables noticed in experimental data sets obtained both in protium and deuterium systems is another evidence showing that the true cause (or causes) of the CFP is (are) not so simple as the Fleischmannfs hypothesis.

Despite these facts showing inapplicability of the Fleischmannfs hypothesis to the CFP, there are still trials to explain a part of the data obtained in the deuterium system by the d-d fusion reactions putting aside the data obtained in protium systems. One of the typical trials of this type was presented by Hagelstein et al. [1.4] as a proposal to ask reconsideration of the evaluation of DOE given in 1989 [1.5]. The answer of DOE [1.6] to this proposal has denied the proposed explanation of the d-d fusion reactions in cold fusion (CF) materials assumed by the authors. A report by S.B. Krivit [1.7] may be helpful to understand the situation.

In this paper, we take up the CFP in protium systems to show essential features of the CFP and an explanation of nuclear reactions in systems with hydrogen isotopes along the line presented in the former book [1.8].

 

2. Phenomenological Approach to the CFP

   As briefly explained in Introduction, there are many various experimental data sets obtained in deuterium and protium systems as compiled in several books [1.8, 2.1, 2.2]. There may be various points of view to investigate such a complex phenomenon as the cold fusion phenomenon (CFP) that occurs in condensed matters with various components and structures including hydrogen isotopes. It will be reasonable to investigate the phenomenon phenomenologically based on the experimental facts at first if the orthodox approach using existing theories does not work effectively.

   We have constructed a phenomenological model based on experimental data sets obtained in deuterium and protium systems and therefore applicable to the CFP in both systems [1.8, 2.1, 2.3, 2.4]. We give a brief introduction of the model in this section to use it in explanation of interesting experimental data sets obtained in protium systems given in the next section.

The TNCF (trapped neutron catalyzed fusion) model was established to explain curious experimental data showing nuclear reactions in near-room temperature solids without any remarkable acceleration mechanism. Existence of a dense neutron gas (trapped neutrons with a density nn) which has a usual interaction with alien nuclides in the solids has been assumed. After a successful application of the model to many experimental facts, the model has developed into the so-called ND (neutron drop) model to include simultaneous absorption and emission of nuclides with several neutrons. In this model, a neutron drop AZ (a group of Z protons and (A – Zjneutrons) has been assumed to participate the nuclear reactions where new nuclides appears as a result of nuclear transmutation. Some details of the models are given below.

There has been also noticed existence of several laws or regularities between observables in the CFP showing statistical nature of the phenomenon. In trials to understand new phenomenon inexplicable by known theories, we have to rely on any clue that seems to show some essence of the truth buried in the multitude of complex experimental facts. The statistical laws are naturally understood by complex nature of the system of the CF materials [1.3, 2.4, 2.5].

A quantal trial to understand the bases of the TNCF and ND models has been developed using novel investigation on the nature of exotic nuclei and wavefunctions of occluded protons and deuterons [1.8, 2.3].

 

 2.1 TNCF (trapped neutron catalyzed fusion) Model

The TNCF model is a phenomenological one and the basic premises (assumptions) extracted from experimental data sets are summarized as follows [1.8, 2.1]:

Premise 1. We assume a priori existence of the quasi-stable trapped thermal neutrons with a density nn in pertinent solids (CF materials).

Existence of the state in the solid where the trapped neutron exists is expressed as formation of cf-matter in the solid in the later version of the model.

The density nn of the trapped neutrons in a CF material is a single adjustable parameter in the TNCF model, which will be determined by an experimental data set using the common supplementary premises, which will be explained below concerning reactions of the trapped neutron with other nuclei in the solids. The quasi-stability of the trapped neutron means that the neutron trapped in the crystal does not decay automatically until a strong perturbation destroys its stability while a neutron in the free space decays with the time constant of 887.4 } 0.7 s (the half-life 1/2 of 615 s).

Premise 2. The trapped thermal neutron in a solid reacts with another nucleus in the surface/boundary regions of the solid, where it suffers a strong perturbation. The reaction of the trapped neutron with another nucleus in these regions is assumed to be characterized by the same reaction cross-section as that determined in the free space except that the released energy is dissipated in the solid (i.e. not emitted out as a photon) as expressed in Eq. (2.2) below.

Premise 3. The trapped thermal neutron reacts with another perturbing nucleus in the sample by a reaction rate given in the relation (2.3) below.

To calculate reaction rates (2.3), following common premises on the measured quantities are assumed.

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.

Those energy spectra of the nuclear products and the distributions of the transmuted nuclei are the direct information of the individual events of the nuclear reactions in the sample.

Premise 6. The amount of the 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.

Premise 11. In the calculation of the number of an event (a nuclear reaction) NQ producing excess energy Q, we assume that the average energy liberated in a reaction is 5 MeV unless the reaction is identified:

NQ Excess energy Q (MeV)/ 5 (MeV).                                (2.1)

Nuclear reaction formula and reaction probability in the CF material are assumed as follows.

If a fusion reaction occurs between a trapped thermal neutron and one of lattice nuclei AZX, there appears an excess energy Q (as thermal energy of the lattice) and nuclear products as follows:

n + AZX = A+1 – b Z – aX' + baX'' + Q,                                         (2.2)

where 00X , 10X n, 11X p, 21X d, 31X t, 42X 42He, etc. The product nuclides on the right-side of Eq. (2.2) are assumed to be in the ground state dissipating their internal excitation energy to the lattice, i.e. not emitting a gamma photon as usual in free space.

If the stability of the trapped neutron is lost by a large perturbation in the surface/boundary regions or in volume, the number Pf of reactions (2.2) between trapped thermal neutrons and a nucleus AZX is assumed to be calculated by the same formula as the usual collision process in the free space (but with an instability parameter that is omitted hear for simplicity);

Pf = 0.35 nn vn nX V nX,                                                       (2.3)

where 0.35 nn vn is the flow density of the trapped thermal neutrons per unit area and time, nX is the density of the nucleus AZX , V is the volume where the reaction occurs, nX is the cross section of the reaction.

Several conclusions are deduced from the premises in the TNCF model:

Numerical relations between the numbers of events in the CFP.

When a concrete reaction formula is applied to Eq. (2.2), we can predict a relation between numbers Nxf and Nxh of products Xf and Xh as

Nxf = Nxh = NQ                                                                        (2.4)

For instance, the following reaction between a neutron and a lithium nucleus 63Li

   n + 63Li = 42He (2.1 MeV) + t (2.7 MeV)                            (2.5)

gives a theoretical relation between Nt , NHe4,@and NQ (using the definition of NQ (2.1));

    Nt = NHe4NQ.                                                                       (2.6)

   If we have an experimental relation

Nx|ex = m ex Nxf|ex@(m ex : numerical parameter)                (2.7)

for the numbers of reactions Nx and Nxf for two observables x and xf, we can compare the experimental relation (2.7) with the following theoretical relation (2.8):

       Nx|th = m th Nxf|th (m th : numerical parameter),                       (2.8)

The coincidence of mth and mex gives verification of the model with a single adjustable parameter nn.

Gammaless stabilization of excited nuclei.

In the cf-matter relevant to the existence of the trapped neutrons, the nuclides on the lattice points (lattice nuclei) or in the boundary/surface region are interacting with trapped neutrons. The interaction stabilizes the nuclei in excited states dissipating energy to the lattice as assumed in Eq. (2.2) where product nuclei are in the ground states.

Decay constant reduction

In addition to this stabilization of their excited states of product nuclei, we assume the decay-time (or decay constant) reduction of radioactive nuclei generated by a reaction similar to (2.2). For instance, we assume the rapid decay of 4019K* in the reaction;

    n + 3919K = 4019K* = 4020Ca + e + e + Q,                              (2.9)

where e@is the anti-particle of the electron neutrino and Q = 2.78 MeV. In the free space, the decay constant of the radioactive nuclide 4019K is 1.28~109 years.

 

2.2. Neutron Drop Model

   The TNCF model proposed in the year of 1994 had been successful to give reasonable explanation for relations between events by coincidence of the factor m th@and m ex in Eqs. (2.7) and (2.8) adjusting the single parameter nn in the range of 108 – 1013 cm–3.

   However, there are several facts inexplicable by the simple assumptions made in the TNCF model. One of the difficulties to explain by the simple version of the TNCF model is generation of nuclides with mass and proton numbers shifted largely from original nuclides in the system. To remedy this defect of the model, we assumed a formation of the cf-matter, a dense neutron-proton liquid, at surface/boundary regions in CF materials developing the assumption of the trapped neutrons distributed uniformly in the TNCF model.

When there are neutron drops AZ composed of Z protons and (A – Z) neutrons in the cf-matter, we can use the neutron drop (and a small neutron-proton cluster AZ) in the nuclear reactions as a simultaneous feeder of several nucleons to nuclides;

AZ+ AfZfX A – a Z– z+ Af + a Zf + zXf*,

A – a Z– z + Af + a– af Zf + z– zfXff+ afzfXfff,       (2.10)

AfZf+ A+ 1 ZX* AfZf* + A + 1yX AfZf+ A + 1yX + x,            (2.11)

AfZf+ AZX A + AfZ + ZfX* A + AfZ + ZfX + x.                             (2.12)

The neutron-proton cluster AZ is supposed to be a small neutron drop absorbed at one time by a nucleus to form a new nuclide as in Eq. (2.11). In the reactions (2.11)  (2.12), the symbol x means not a in the free space but another particle (phonon or phonons) in the crystal lattice including the cf-matter.

We use the name gneutron drop (ND)h model for the new model explained above where we assume existence of the cf-matter and simultaneous absorption of the cluster AZ.

 

2.3 Statistical Laws between Observables in the Cold Fusion Phenomenon

  There have been found several statistical laws between observables deduced as a natural result of scientific endeavors, i.e. a conversation with nature [1.8, 2.5]; (1) the inverse-power law for the frequency- intensity relation in excess power production, (2) the stability law for generation of new nuclides by the nuclear transmutation (NT), (3) the bifurcation law showing recursion and chaotic behaviors of effects in the course of experiments.

2-3-1 Inverse-Power Law

From the explanations of experimental data sets, it became clear that various events with tremendous diversity measured in these more than 20 years show that the CFP is a result of processes induced by complex nuclear reactions in CF materials that outweigh such simple mechanisms as assumed by Fleischmann.

From our point of view, the CFP is determined by complexity of the material where it occurs and therefore inevitably has characteristics of chaotic systems. Due to the inability to control microscopic processes completely, there is a diversity of microscopic conditions in CF materials. Furthermore, the gigantic effects of the CFP generated by nuclear reactions magnify microscopic variety or uncertainty in CF materials. In this sense, the CFP is fundamentally irreproducible or qualitatively reproducible and sporadic.

Thus, we can expect a fluctuational feature, well known as 1/f fluctuation in many macroscopic phenomena, in the CFP which reflects microscopic fluctuations common in every complex system. In reality, we have shown the 1/f fluctuation of the excess energy production in data sets obtained in these 20 years [1.8, 2.5].

2-3-2 Stability Law

There are several data showing correspondence of the amount of NT products and stability of nuclei [1.8]. These data show clearly that the more stable a nuclide is, the greater quantity of that nuclide is generated by the nuclear transmutation in the CFP.

The most remarkable statistical data is seen in overall correspondence between the frequency Nob observing elements in the CFP and the relative abundance H (expressed as log10H) of elements in the universe.

Therefore, it is possible to conclude that the good qualitative coincidence of Nob and log10H discussed above is an evidence showing similarity of mechanisms working in CF materials and in the stars to produce new nuclides. Nuclear processes related to NTs in the CFP are fundamentally a low energy version of the processes producing nuclides in the stars. The more stable a nuclide is, the more frequently it is produced.

Detailed investigation of these features [1.8, 2.3] will help to explore dynamics of nuclear interactions in the CF materials.

2-3-3 Bifurcation Law

   The diversity of experimental data obtained in the research of the CFP has sometimes caused disbelief of scientists outside the CF research. The diversity of experimental data is inherent in systems characterized by complexity as many examples show as the earthquake. It is helpful to investigate the data from the viewpoint of complexity and to see similarity between the CFP and behavior of recursion equations as discussed in the paper [2.5].

 

3. Experimental Facts

   Soon after the publications of remarkable papers on the deuterium systems by Fleischmann et al. [1.1], Jones et al. [3.1] (neutron emission spectrum from Ti/D(Li)/Au system), and De Ninno et al. [3.2] (neutron emission from Ti/D2 system), searches of the CFP have started in protium systems.

   The first successful observation of the cold fusion phenomenon including nuclear transmutation (NT) in protium systems may be, as far as the author knows, the report by Mills et al. [3.3]. They observed large excess heat from an electrolytic system Ni/(H2O + K2CO3)/Pt. Soon after this work, Bush [3.4] performed experiments with an electrolytic system Ni/(H2O + K2CO3)/Pt observing excess heat and correlated production of calcium Ca.

It is interesting to notice that the work by Mills and Kneizys [3.3] had been motivated by an unbelievable assumption that hydrogen atoms undergo transitions to quantized energy levels of lower energy than the conventional ground state. R.T. Bush [3.4] followed them assuming the galkali-hydrogen fusion,h i.e. a fusion of the nuclei of the alkali atoms with the simplest of the alkali-type nuclides, namely, protons, deuterons, and tritons. This assumption is the extension of the d-d fusion reactions in solids (the Fleischmannfs hypothesis [1.1]) and is more difficult to realize in solids at near-room temperature.

However, a discovery of new phenomenon is not necessarily guided by correct expectations as the history of science have shown frequently. We would like to accept the experimental facts irrespective of the motivations by which the facts were obtained.

The research of the CFP in protium systems has been taken up by researchers in Hokkaido University in Japan. Ohmori et al. [3.5] observed excess heat in Ni(Au, Ag, Sn)/(H2O + K2CO3)/Pt system and also Notoya [3.6] observed excess heat in Ni/(H2O + K2CO3)/Pt system. Further, Bush et al. [3.7, 3.8] performed experiments with various electrolytes including lithium (Li), sodium (Na), potassium (K), rubidium (Rb) and cesium (Cs) and observed production of 2412Mg, 4020Ca and 8638Sr in the case of Na, K and Rb electrolytes, respectively, together with the excess heat. Similar electrolytic experiments with light water and transition metal or noble metal cathodes have been performed until now. Dash et al. [3.9] observed nuclear transmutations correlated to excess heat generation in a Pd/(H2O + H2SO4)/Pt system. On the other hand, Miley et al. [3.10] observed NT in the nickel layer of their multilayered cathode surface in (Cu/Ni/Pd)/(H2O + H2SO4)/Pt system.

We will investigate their implications taking up several typical data sets in subsection 3.1.

   There have been performed experiments of another type, the so-called gas contact system, mainly in Italy. In this case, transition-metal samples with large surface area have been made contact with gases of hydrogen isotopes. Focardi et al. [3.11] performed experiment with Ni/H2 system for the excess heat measurement like that of the Ti/D2 system with titanium shavings by De Ninno et al. [3.2] for the neutron emission.

It is noticed that remarkable experimental data in protium systems have been obtained mainly with nickel (Ni) metal samples in gas contact experiments in accordance with effective Ni cathodes in electrolytic experiments (e.g. Ni/H(K)/Pt combination). Some typical data sets are introduced in Section 3.2.

It is a characteristic of the researches in the CFP that a specific group has persisted in doing experiments with the same system. The groups mentioned above have engaged in the experiment of protium system for a long period sometimes more than ten years obtaining positive results.

   Recently, there have been reported strange phenomena of nuclear transmutations (NTs) in systems with organic polymers. The first report of this type is the observation of nuclear transmutations by Kumazawa et al. [3.12] in cross-linked polyethylene (XLPE (CH2)n) used in the shield of high-frequency electric cable. Another direct evidence of nuclear reactions in polyethylene CR39 (C12H18O7) has been reported recently by Oriani [3.13]. He observed evidence of energetic charged particles generated in the CR39 polymer after electrolysis experiments in which the polymers were used for detection of charged particles emitted from metal cathodes. Experimental data sets and their explanations by our model are given in section 3.3.

 

3.1 Cold Fusion Phenomenon in Electrolytic Protium Systems

   There have been published many experimental data sets by the electrolytic method showing positive results of the CFP in protium systems. We take up only several data sets where observed the nuclear products in addition to excess energy discarding data sets where measured only the excess energy. Then, we can show the effectiveness of our phenomenological approach by a consistent explanation of simultaneously observed several events adjusting the single parameter nn.

3.1.1 Data sets by Bush [3.4, 2.1]

The data set by R.T. Bush [3.4] was analyzed using the TNCF model [2.1]. The TNCF model predicts following reactions with the liberated energy Q (1/2: half-life time) between the trapped neutron and alkali metals:

n + 2311Na @2411Na* 2412Mg + e + e + Q,  (1/2 = 15.0 h),        (3.1)

n + 3919K 4019K* 4020Ca + e + e + Q,     (1/2 = 1.2 ~ 109 y)      (3.2)

In these reactions, the absorption cross sections are 0.82 and 3.2 b, and the liberated energies Q (including accompanying gamma in free space) are 2.72 and 2.78 MeV, respectively.

If we can assume that the decay time of the second reaction of 1.2 ~ 109 y is largely reduced by the interaction with the cf-matter to a value of the order of few hundred hours (let us take as 102 h), the experimental data showing generations of 2412Mg and 4020Ca are explained by the TNCF model with values of the parameter nn of 5.3 ~ 1011 and 5.3 ~ 1010 cm–3, respectively. The difference of one order of magnitude in the determined parameter nn for the experiments with different electrolytes Na and K could be accepted tolerable considering uncertainty in measured values of the excess heat and sporadic nature of nuclides detection in the experiment.

3.1.2 Data sets by Bush and Eagleton [3.7, 2.1]

 The data set by R.T. Bush and R. Eagleton [3.7] was analyzed using the TNCF model [2.1]. The experimental observation of the excess heat and the nuclear transmutation of A37Rb into A+138Sr (A = 85 and 87) in Ni/(H2O + RbCO3)/Pt system was analyzed using the reaction

n + A37Rb @A+137Rb* A+138Sr + e + e + Qi,    (i)   (A = 85 and 87).   (3.3)

The excess energy Qi (i = 1 and 2 for A = 85 and 87, respectively) is 1.77 and 5.32 MeV and the decay times i = 18.6 d and 17.8 min, respectively.

   The experimental data of 8637Sr/ 8837Sr ratio after the experiment and excess energy production were consistently explained by the TNCF model within a numerical factor of 3 [2.1 Section 11.11b].

3.1.3 Data sets by Miley et al. [3.10, 2.1]

According to the recipe of the TNCF model given in Section 2, we analyzed experimental data obtained by Miley et al. in the Ni thin-film on the microspheres in the so-called Patterson Power Cell [3.10].

   Generation of new nuclides of A24Cr (A = 52, 53), 5525Mn, A26Fe (A = 54, 56, 57), 5927Co, A29Cu (A = 63, 65) is semi-quantitatively explained by the TNCF model (discarding data of small amount Zn and large but Pd related Ag isotopes).

@The production ratio 1 : 0.27 : 0.12 of A28Ni (A = 59, 63, 65) observed by the experiment is compared with the theoretically expected ratio 1 : 0.17 : 0.57 ~ 10–2. The excess power 0.5 } 0.4 W measured by the experiment is compared with the theoretical value 0.12 W.

   Thus, the data set obtained by Miley et al. [3.10] is consistently and semi-quantitatively explained by the TNCF model [2.1].

These results given in this subsection might be accepted to indicate that the Premises assumed in the model reflect some phases of the hidden truth in the physical processes of the cold fusion phenomenon.

 

3.2 Cold Fusion Phenomenon in Hydrogen Gas Contact Systems

   Experiments with nickel samples in contact with hydrogen gas have been solely performed by Italian group for a long period from 1994 [3.11]. They have published several reports by the year 2010. We take up only three papers [3.12 – 3.14] to show complex nature of the phenomenon even in the relatively simple Ni-H system.

3.2.1 Data sets by Focardi et al. [3.11 – 3.14]

   Researchers in Bologna and Siena Universities in Italy have been working with Ni-H system for more than 10 years obtaining interesting data sets. We analyze some recent ones of their data sets explained in papers presented at ICCF11 [3.12 – 3.14].

   The Ni and Ni alloy (e.g. Ni7.6Cr20.6Fe70.4Mn1.4) samples were annealed in hydrogen gas of 102 to 103 mbar at the temperature of 400 to 700 K. They have observed the excess energy production, particle emissions, surface morphology, and appearance of new elements in the surface layer of a few micrometers width.

   It is interesting to notice that the hydrogen loading to the sample depends drastically on the states of the sample.

   The excess energy has been measured in Ni and Ni alloy samples. For instance, a Ni tab sample (99.5 % purity) with geometry 200~12~1 mm3 produced excess power of average about 20 W with a maximum of 25 W for about 35 days.

   The photon emission from some samples of the same shape as the above one has been observed in the energy range of 0.5 and 2.75 MeV.

   Surface morphology and elemental change in the surface layer of a few m depth have been investigated. The surface of the Ni alloy rod sample has shown the morphological alteration along the sample depending on its position in the experimental cell. New elements Cu and Zn in Ni alloy rod and Cr and Mn in Ni slab have been detected. The densities of the newly appeared and original elements in the surface layers have varied from a site to another. The distribution of elements Ni, Cr, Fe and Mn have changed along the rod by about 20 % and the maximum values of the change are about 80 % for Cr and Fe.

   In another experiment, they observed neutron emission in Ni-H system [3.12].

   The experimental data have shown astonishing variety of events in Ni and Ni alloy samples in contact with H2 gas. The variety is expressed by the researchersf concluding words cited below.

gVery interesting and complex phenomena can arise in Ni-H system. On the other hand, these experiments seem to indicate that other poorly understood parameters must be controlled to obtain similar experimental results. In particular, surface structure and geometry of cells are critical for loading and exciting nickel samples.h [3.12]

gthese experiments show the complexity of phenomena involved in the physics of the Ni-H system. Further investigations are needed in order to throw light on these phenomena.h [3.14]

   The experimental data sets obtained by Focardi et al. [3.12 – 3.14] clearly show the irreproducibility, a characteristic of complexity claimed by us [1.8, 2.3, 2.4, 2.5].

   Despite the lack of quantitative relations between various observables in these data sets of Ni-H systems obtained by Focardi et al., we may give a suggestive comments on the nuclear transmutation observed in the Ni alloy sample [3.13]. The experimental data shows a large peak of Cu localized in a narrow zone of the surface of the sample.

The appearance of the copper may be explained by following nuclear reactions of Ni isotopes A28Ni (A = 59, 60, 61, 62 and 64) with natural abundances of 67.88, 26.23, 1.19, 3.66 and 1.08 %, respectively.

n +@5828Ni = 5928Ni* (67.88 %)                                          (3.4)

n +@6028Ni = 6128Ni* (26.23%)                                          (3.5)

n +@6128Ni = 6228Ni* (1.19 %)                                           (3.6)

n +@6228Ni = 6328Ni* (3.66 %)                                           (3.7)

n +@6428Ni = 6528Ni* (1.08 %)                                           (3.8)

The fusion cross sections of these reactions for a thermal neutron are 4.6, 2.9, 2.5, 15 and 1.8 b, respectively. Because the fusion products 6128Ni* and 6228Ni* are stable, we discard them from our analysis although there remains possibility of their destabilization by interaction with the cf-matter.

Then, the fusion products 5928Ni*, 6328Ni*, 6528Ni* could be candidates responsible to NT observed in the experiment. They decay by following schemes with their half-lives 1/2 in parentheses;

5928Ni* = 5927Co – e, (1/2 = 7.6 ~ 104 y)                                      (3.9)

6328Ni* = 6329Cu + e +e + Q@(Q = 65 keV), (1/2 = 102 y)          (3.10)

6528Ni* = 6529Cu + e +e + Q@(Q = 2.14 MeV). (1/2 = 2.5 h)      (3.11)

Thus, the copper isotopes produced in the reactions (3.10) and (3.11) may give an explanation of the experimental result if there are decay constant reduction for the reaction (3.10). The reason of missing cobalt in the experiment may show that the electron capture reaction (3.9) is not influenced by the existence of the cf-matter due to the weak ne interaction.

 

3.3 Cold Fusion Phenomenon in Systems with Organic Polymers

   Nuclear reactions in room-temperature materials observed at first as the cold fusion by Fleischmann et al. [1.1] in the Pd/D(Li)/Pt system in 1989 have been observed in various materials including other transition-metal deuterides and hydrides. The most fantastic of the materials is polymers, cross-linked polyethylene (XLPE) used in electric cables [3.15] and CR39 used as a detector for energetic particles [3.16]. We show in this section that the nuclear transmutations observed in these polymers are explained by the TNCF and ND models as a kind of the CFP in polymers.

3.3.1 Data sets by Kumazawa et al. [3.15, 3.17, 3.18]

   In the investigation of water tree formation in XLPE ((CH2)n with n >> 1) by Kumazawa et al. [3.15], they used (I) Original sample of XLPE films, (II) Blank samples dipped in electrolytic solutions of (a) KCl, (b) NaCl, and (c) AgNO3 in light water, and (III) Experimental samples applied electric fields with high-frequency (2.4–3.0 kHz) and high-voltage (3.0 – 4.0 kV/mm) furthermore.

   Some of the remarkable experimental results obtained in the Experimental samples are summarized as follows.

In the case (a) (KCl),

(1) K decreased and Ca increased,

(2) 56Fe decreased and 57Fe increased,

(3) 64Zn increased while other isotopes of Zn decreased.

In the case (b) (NaCl),

(4) Mg decreased and Al increased in which the gross weight of the two elements was hardly different compared to the Blank or the Original samples.

In the case (c) (AgNO3),

(5) Fe decreased and Ni increased,

(6) New elements Li, Na, Pb and Bi were detected, and

(7) There are changes of elements in both regions with and without water trees.

   Furthermore, there are interesting features of the blank samples (II) in the case (a).

(8) In Blank samples, Mg and Ca are increased from those in the Original one while Fe is decreased.

In this XLPE system, it is possible to consider that the regular array of carbon nuclei 126C and the combined hydrogen 11H in the polymer play the same role as the lattice of transition-metal nuclei, e.g. Ni in nickel hydride, and occluded H to form a cf-matter at boundaries of the ordered region (spherulite). Then, we can apply our models to analyze the NTs in XLPE.

   The complex events of nuclear transmutation obtained in the XLPE were analyzed using the TNCF and ND models giving qualitative explanation of the experimental result [3.17, 3.18]. It is shown that the water tree in XLPE is induced by the NT in the sample, at least partially.

3.3.2 Data sets by Oriani [3.16]

   A high polymeric material called CR39 (C12H18O7) has recently been used in nuclear science and cold fusion researches to detect and record emission of charged particles and very energetic neutrons. Detection of charged particle emitted from CF materials using the CR39 has been performed by many researchers including Yamada et al. [3.19].

Oriani [3.16] tried to confirm production of charged particles in an electrolytic system Ni/(H2O + Li2SO4)/Pt using CR39 film. He confirmed that the nuclear reaction of some sort has been generated in the course of electrolysis of solutions of lithium salts in either heavy or light water. Furthermore, it is interesting to notice that the damage trail in the CR39 film chips showing evidence of charged particle emission begins (1) at external surface of the chips attached on the Ni cathodes as well as (2) within the interior of the thickness of the chips.

   This result (2) shows clearly the occurrence of nuclear reactions in CR39 polymers similar to the data obtained in XLPE by Kumazawa et al. In the case of XLPE, the occurrence of the nuclear reaction is confined to boundary regions of spherulites. On the other hand, it is not specified where the charged particle starts in the CR39 chips from. The following sentence in the paper [3.16] by Oriani suggests us possible mechanism of nuclear reactions at boundaries of polymerized and disordered (poorly polymerized) regions similar to the case of XLPE at boundary regions of spherulites; gThe polymerization process can leave poorly polymerized regions.h If it is so, the grouping of etch pits observed by Oriani may reflect the structure of the polymerized regions in the CR39 tips.

 

4. Discussion

   As the three statistical laws explained in Section 2 tell us clearly, the cold fusion phenomenon (CFP), or so-called low energy nuclear reaction (LENR), is a manifestation of complexity in the CF materials [1.3, 2.4, 2.5]. Therefore, the lack of quantitative reproducibility, one of the main reasons of rejection of the CFP by some scientists, is a fundamental characteristic of this phenomenon.

   The phenomenological models, TNCF and ND models, devised to explain experimental results have given consistent explanation of various events observed in CF systems as explained in papers and books given by the author [1.8, 2.1, 3.17, 3.18]. It is natural to investigate the bases of the models from modern point of view of physics and chemistry established in 20th century. Quantum mechanical trial to explore a new state of the cf-matter in solids composed of a transition metal lattice, occluded hydrogen isotopes and gtrapped neutronsh has been developed by us in these 10 years and presented in papers and books [1.8, 2.3, 2.4].

   The experimental data sets obtained in protium systems from 1991 until now have given another evidence of the complex nature of the cold fusion phenomenon (CFP), which has been discovered in 1989 and supposed at first as a result of simple d-d fusion reactions in transition-metal deuterides assisted by their environment. The data sets, a part of which introduced in this paper, have shown necessity of more experimental data and a point of view that can explain exclusively whole complex data sets obtained in protium and deuterium systems if we intend to understand these data sets as a whole as phases of the hidden nature of materials made of the lattice of transition-metal or carbon atoms interlaced by another lattice of hydrogen isotopes.

   It is interesting to notice another characteristic of the CFP that the host nuclei A22Ti (A = 46 – 50), A28Ni (A = 58, 60 – 62, 64) and A46Pd (A = 102, 104 – 106, 108, 110) in transition-metal deuterides/hydrides and also carbon nuclei A6C (A = 12, 13jin XLPE and CR39 have positive values of the neutron affinity (NA) defined by us [1.8, 2.1, 2.3]. The average neutron affinities <NA> of elements C, Ti, Ni and Pd with natural abundances are 2.19, 0.96, 3.84 and 0.27, respectively.

The necessary conditions for the formation of the cf-matter, then, may be listed as follows; (1) the ordered array of host nuclei AZX with positive neutron affinities@<NA>, (2) the ordered array of protons/deuterons A1H (A = 1, 2) interlaced with that of host nuclei, and (3) the interaction of two host nuclei (AZX)i and (AZX)j at adjacent lattice points R i and R j mediated by a proton/deuteron A1H (A = 1/2) interacting with both AZXfs (super-nuclear interaction [1.8]). The co-deposition of Pd and D on substrate metals of Cu, Au or Ni used by Szpak et al. (e.g. [3.20]) seems very effective to realize high quality ordered lattices of Pd and D satisfying the necessary conditions (1) – (3) described above and favorable for the formation of the cf-matter and therefore for the CFP.

   The trial to develop scientific approaches by phenomenological models and by quantal investigations [1.8, 2.1, 2.3 – 2.5, 3.21] may serve a first step to the science of the CFP as we have shown in this paper using interesting experimental data sets obtained in protium systems.

 

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