Report of the Cold Fusion Research Laboratory 6-1, 1 (October, 2007)

Nuclear Chemistry in the Cold Fusion Phenomenon* Hideo Kozima Cold Fusion Research Laboratory http://www.geocities.jp/hjrfq930/ Yatsu 597-16, Aoi, Shizuoka, Shizuoka 421-1202, Japan * This paper is based on the note of an invited lecture given at the Nuclear Chemistry Branch of the Symposium on Radiochemistry (September 24 – 26, 2007, Shizuoka City) held by The Japan Society of Nuclear and Radiochemical Sciences,

Abstract The cold fusion phenomenon (CFP) is reorganized according to relevant branches of the natural science thus giving a new perspective to this phenomenon. At present stage of the investigation of the CFP, the nucleochemical approach is most promising to confirm the basis of this research field as we have tried for more than 14 years. In cooperation with physical and mathematical approaches, the nuclear chemistry has given a unified understanding of the CFP including diverse products of the nuclear transmutation and fascinating dynamical behavior of events. 1. Introduction

When Fleischmann et al. [1] announced the discovery of the “Cold Fusion” of two deuterons (or some other nuclear reactions) in palladium deuteride (PdDx) samples at near room temperature, they accepted the result as a proof showing a possible energy source with use of abundant deuterium. The experiment was motivated by an assumption that the crystal environment of transition-metal deuterides gives tremendous effects on d-d fusion reactions in them (“Fleischmann’s hypothesis”).

The experimental data sets obtained in these 18 years in this field [2, 3], however, have shown variety of events in the cold fusion phenomenon (CFP) which is out of range of explanation based on the Fleischmann’s hypothesis even if it is not possible to prove the hypothesis be effective by some tricks not known until now.

We, therefore, have to investigate the CFP by a standard way of scientific

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research based fundamentally on experimental results and established principles avoiding any presumptions contradicting to the existing science and biased by our desires of daily life. 2. The Cold Fusion Phenomenon

The cold fusion phenomenon (CFP) stands for “nuclear reactions and accompanying events occurring in solids with high densities of hydrogen isotopes (H and/or D) in ambient radiation including thermal and epithermal neutrons.” It should be emphasized that the CFP occurs not only in deuterium (D) but also protium (H) systems and also that the CFP occurs only if there are enough background thermal neutrons [2, 4].

A standard approach to a difficult problem in science is a trial-and-error method. In the trial-and-error approach, we have used often models in the history of science. In a model, there are always premises based on experimental results. These premises are not necessarily explained by existing principles of science or rather sometimes contradict them. A typical example of the contradiction is the stability of electron orbits in atoms in the Bohr’s atomic model.

We will use a model (TNCF model) [2, 4] based on experimental results assuming the existence of trapped-in-matter neutrons (quasi-free neutrons) with a density nn (or n in short when it is not confused with the symbol for a neutron) and their reactions with irregular nuclei in the crystal lattice. Number of reactions NnX (per unit time) between trapped thermal neutrons and a nucleus AZX may be calculated by the same formula as the usual collision process in a vacuum:

NnX = 0.35 nn vn nXVσnX, (0) 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, σnX is the cross section of the reaction.

Some examples of nuclear reactions are written down as follows: n + p = d + φ’s + Q, (1) n + d = t + φ’s + Q’, (2) t + d = 42He (3.5 MeV) + n (14.1 MeV), (3) where Q = 2.22 MeV and Q’ = 6.26 MeV.

In these reactions, φ’s denote phonons participating the nuclear reactions in solids replacing a photon (γ) in free space.

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Typical characteristics of experimental results are tabulated in Table 1. These characteristics are supplemented by another point of view to look at experimental data; they are classified by following branches of science 1) nuclear chemistry and electrochemistry, 2) nuclear physics 3) solid-state physics, and 4) nonlinear dynamics (complexity).

In short, the first point of view, nuclear chemistry and electrochemistry, sees the data phenomenologically and finds out qualitative and quantitative relations among events and also among products of the CFP. This point of view is explained more extensively in the next section.

The second point of view, nuclear physics, treats nuclear properties of relevant nuclei, a few initial steps of them have been explained in previous works [2, 5]. The halo nuclei and neutrons in around evaporation levels have been taken up in relation to the super-nuclear interaction between neutrons at different lattice nuclei (nuclei on lattice points).

Table 1 System and Obtained Evidences of the CFP. Host solids, agents, experimental methods, direct and indirect evidences of the cold fusion phenomenon. Q and NT express excess heat and the nuclear transmutation, respectively. Direct evidences of nuclear reactions in CFP are Energy (E) and position (r) dependences of reaction products, decrease of decay constants of radiative nuclides, decrease of fission threshold energy of compound nuclei (such as 4He* in reaction). Host solids Pd, Ti, Ni, KCl + LiCl, ReBa2Cu3O7,NaxWO3, KD2PO4,

TGS, SrCeaYbNBcOd

Agents n, d, p, 63Li, 103B, 39

19K, 8537Rb, 87

37Rb、(ion beam, O)

Experimental

methods

Electrolysis, Gas discharge, gas contact, (ion beam irradiation)

Direct Evidences

Gamma ray spectrum γ(ε), neutron energy spectrum n(ε),

Space distribution of NT products NT(r),

decrease of decay constants, lowering of fission threshold energy

Indirect

Evidences

Excess energy Q, number of neutrons Nn, amount of tritium atom Nt,

helium-4 atom NHe4, NT (NTD, NTF, NTA), X-ray spectrum X(ε)

Cumulative

Observables

NT(r), amount of tritium atom Nt, helium-4 NHe4,

Dissipative

Observables

Excess energy Q, neutron energy spectrum n(ε), number of neutrons Nn,

Gamma ray spectrum γ(ε), X-ray spectrum X(ε),

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The third point of view, solid-state physics, treats mainly wave functions of hydrogen isotopes in transition-metal hydrides and deuterides. The characteristics of fcc and hcp transition-metal hydrides/deuterides that are fundamentally different from those of bcc ones have been used to explain the characteristics of the CFP which occurs only in the former compounds [4].

The fourth point of view, nonlinear dynamics, is developed in recent works to explore the CFP as complexity [6 – 9]. In these works, dynamical properties of events in the CFP have been explained using concepts of the complexity. It seems that events of the CFP exhibit bifurcation and chaos principally in the same manner as in the recursion relations [10], especially in the logistic difference equations (l.d.e.) [11].

Fore any function with f(p) = p beff(p) like Fig. 1, it was shown that the recursion relations pn+1 = bf(pn) (i) is compatible and representative of the population (or density) variation [10].

Fig. 1. Dependence of f(p) = p beff(p) on p after Feigenbaum [1].

To investigate the structure of the recursion relations (or population (density) equations) (i), we can use the more concrete logistic difference equation (l.d.e.): xn+1 = λ xn(1 – xn ), (0 < x0 < 1, λ > 0) (ii) after J. Gleick [11].

Figure 2 is a bifurcation diagram of the l.d.e. with a parameter λ showing period-doubling and chaos [11, p. 71].

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Fig. 2. Bifurcation diagram to show period-doubling and chaos (From “Chaos” by J. Gleick [11]. p.71).

The main figure of Fig. 2 depicts x∞ (ordinate, xn at n = ∞) vs. the

parameter λ (abscissa) of the logistic difference equation, i.e. l.d.e. The inserted figures, a) Steady state, b) Period two, c) Period four, and d) Chaos, depict variations of xn with increase of suffix n (temporal variation if n increases with time) for four values of λ; a) 1 < λ < 3, b) 3 < λ < 3.4, c) λ ≃ 3.7, d) 4 < λ. The region a), b) and d) correspond to “Steady state”, “Period two” and “Chaotic region” in the main figure, respectively.

Fig. 3. Diagram showing the time evolution of the neutron emission from TiDx sample during the second run (April 15-16, 1989). The values indicated are integral counts over periods of ten minutes (Fig.3 of [12]).

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Fig. 4. Diagram showing the time evolution of the neutron emission from TiDx sample during the first run (April 7-10, 1989) [12]. The values indicated are integral counts over periods of ten minutes (Fig.2 of [12]).

It will be interesting to show some examples of events observed in the CFP in relation with complexity. The first experimental data set depicted in Figs. 3 and 4 shows neutron emission from TiDx samples obtained by De Ninno et al. [12]. A consistent explanation of Figs. 3 and 4 have been given using the TNCF model as manifestations of nonlinear dynamics in CF materials due to variation of the parameter n (density of the trapped neutrons) in the process of nuclear reactions in the material [8]. We may point out following characteristics of Figs. 3 and 4; The envelope of the diagram in Fig. 3 resembles the curve in Fig. 1 and the pattern of Fig. 4 with two kinds of peaks reminds us the bifurcation (period two) in Fig. 2.

Fig. 5. Temporal Variation of Excess Power, Uncertainty and Loading Ratio [13].

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Fig. 6 Variation of Excess Power with Loading Ratio [13] The second experimental data set cited here to show complexity in the CFP is obtained by McKubre et al. [12] and shown in Figs. 5 – 7. In these figures, variations of excess power from PdDx samples were depicted as functions of time, the loading ratio D/Pd, and cell current, respectively. The temporal variation exhibits similar characteristic behavior of the l.d.e. shown in the inserted figure “Chaos.”

Fig. 7 Variation of Excess Power with Cell Current [13] The distribution of experimental points for the loading ratio D/Pd larger than 0.91 in Fig. 6 resembles the chaotic region of the l.d.e. depicted in Fig. 2. The distribution of points in Fig. 7 also shows occurrence of the chaotic behavior of the CFP at specific values of a different parameter (in this case the “cell current”).

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Fig. 8. Excess power pulses and bursts during a 14 hour period of an experiment (070108) which lasted 12 days as a whole [7].

The third experimental data set shown in Figs. 8 and 9 is obtained by Dash et al. [6, 13] showing temporal and temperature variation of excess power generation in PdDx(Hy) samples. Variations of the excess power depicted in Figs. 8 and 9 show bifurcation of states with variation of parameters governing evolution of the system [7] as in the case of the l. d. e. as shown in Fig. 2. Fig. 8 is similar to the one (period two) of the inserted figures in Fig. 2.

Fig. 9. Distribution of the frequency NP (= y) producing excess power Pex (= x). To depict log-log

curve, values of NP and Pex were arbitrarily multiplied by 10n. (x = 100 in this figure corresponds to

Pex = 1 W) [7].

In Fig. 9, the bifurcation at “Period two” in Fig. 2 is reproduced by

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experimental data obtained by Dash et al. [7]. Thus, the controversial lack of the quantitative reproducibility in the CFP

is resolved negatively. The CFP essentially belongs to complexity without reproducibility and predictability. We can expect only qualitative or statistical reproducibility of events in the CFP. 3. Chemical Aspects of the Cold Fusion Phenomenon

The characteristics of the CFP showing nucleochemical properties described briefly in the previous section are explained in this section.

There are abundant data showing complex relations between nuclides prior-to-reaction and nuclides posterior-to-reaction in the CF system. To analyze these data, it is inevitable to use a specific point of view to make complex experimental facts tractable. We have used the TNCF model successfully for more than 13 years [2, 4] and use it in this paper, too. 3.1 Electrochemistry

It is a riddle of electrochemistry in the CFP that there exist preferable combinations of (host transition-metal)/(hydrogen isotope)/(electrolyte) in electrolytic systems [4].

The well-known combinations are Pd/D/Li and Ni/H/K (Na) [2, 4]. In some cases, Pd-D-H2SO4 system is effective [14] but details are not

well analyzed in this case leaving determination of optimum combination of metal/hydrogen isotope/electrolyte for the CFP unsolved.

Furthermore, the combination Ni/H is known to be effective in gas contact experiments [2]. 3.2 Nuclear Chemistry

Chemistry (or atomic chemistry) had been a main material science in the development of natural science started as the atomic theory by Democritus and others in Greek, developed as the alchemy by Paracelsus and others in the Middle Ages and accomplished around the last half of the 19th century when the essence of the periodic table of atoms was established by D.I. Mendeleev and J.L. Meyer in 1867. After then, atomic chemistry developed rapidly in experiment and in theory and included such radioactive elements as U, Th, Po, Ra, and so on in the final years of the 19th century. Based on chemical knowledge of atomic reactions, molecules and condensed matter,

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atomic physics has been developed throughout 20th century. On the other hand, it is possible to say that nuclear chemistry was

fundamentally born in 1913 when F. Soddy and K. Fajans discovered radioactive disintegration series based on the discovery of isotopes in 1906 – 1912 by B.B. Boltwood (identification of an element known as “ionium” (230Th) with thorium (Th), 1906), F. Soddy (recognition of elements of different atomic weights with identical (chemical) properties, 1910) and J.J. Thomson (recognition of 20Ne and 22Ne, 1912). (Later, F.W. Aston separated 20Ne and 22Ne in 1919.)

Due to fewer combinations of building blocks of nuclei (proton and neutron) compared with those of molecules (92 atoms), nuclear chemistry has drastically fewer objects compared to atomic chemistry but with a characteristic of the nuclear transmutations of nuclides by disintegration. Nuclear physics has been developed throughout the 20th century based on these facts to establish science of nuclei.

In the cold fusion phenomenon (CFP) which occurs in solids with complicated composition and structure, however, the situation has been somewhat different from nuclear reactions in free space where participating particles are well defined. Complication of experimental facts in the CFP needs chemical approaches at present stage of investigation as we show in this chapter. 3.2.1 Products of Nuclear Transmutation in the CFP and the Stability Law There are too many nuclear products generated in the CF materials in the CFP to be classified using knowledge of nuclear physics in free space. For nuclear transmutation, the accuracy of measurement is fairly high for the identification and quantitative determination of product nuclides as they are. cumulative observables.

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log H & Nob vs. Z

0

5

10

15

20

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37

Z

log

H &

Nob

b

log H

N ob

log H & Nob vs. Z-36

0

2

4

6

8

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46

Z - 36

log

H &

Nob

b

log H

Nob

Fig. 10 Stability effect of nuclear transmutation in the CFP. [2]

Figure 10 shows variety of nuclear products and the stability law for the production revealed by comparison with natural abundance of elements in universe [2]. In this figure, Nob(Z) represents number of observations of the element with atomic number Z and H(Z) is a relative abundance of the element in the universe. We see good correspondence between Nob(Z) and logH(Z) except several cases that have reasons of their discord [2]. 3.2.2 Correspondence between Occurrence of the CFP and Existence of Stable Isotopes – Energetics of nuclides related to the CFP–

It is interesting to notice that a situation where there occurs the CFP in solids with a nuclide AZX and there exist stable nuclides with differences of proton and nucleon numbers ⊿Z = 1 and ⊿A = 1 or 2, respectively; A+1Z+1X’ and A+2Z+1X’’. These nuclides are formed by absorption of a proton or a deuteron by the nuclide AZX, respectively. We investigate them concretely in relation with the CFP in this Section [15]. In tables 2 – 5, we tabulate data of ⊿Z = 1 nuclides for nuclides A22Ti, A28Ni, A46Pd and A78Pt that form stable fcc transition metals. Remarkable nuclides are boldfaced.

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Table 2. Characteristics of nuclides related to transition metal Ti. Tabulated are atomic number Z = 22 and 23, mass difference ⊿A = 0 – 2, and nuclide (natural abundance %).

Table 3. Characteristics of nuclides related to transition metal Ni. Tabulated are atomic number Z = 28 and 29, mass difference ⊿A = 0 – 2, nuclide (natural abundance %).

Table 2 shows that the 4822Ti (73.94%) can absorb a deuteron to form a

stable nuclide 5023V. This fact may be related to the experimental fact that deuterium works to produce CFP in experimental systems with Ti (TiDx), especially in gas contact experiment [12]. From this table, we can expect some effect of CFP in Ti-H systems, which are not well cultivated in CFP research up to now.

Table 3 shows that the 6228Ni (3.66%)can absorb a proton to form a stable nuclide 6329Cu. This fact may be related to the experimental fact that only protium works to produce CFP in experimental systems with Ni, especially in gas contact systems. In electrolytic systems, the combination Ni/H/K is very effective to give CFP. This shows also special chemical relation of NiHx and K to form surface layers on the sample. The CFP in the Ni-H system may be related to the fairly large cross section of neutron absorption by 3919K 2.1 b, abundance 93.1%). Table 4. Characteristics of nuclides related to transition metal Pd. Tabulated are atomic number Z = 46 and 47, mass difference ⊿A = 0 – 2, nuclide (natural abundance %).

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Table 4 shows that the nuclide 10546Pd (22.33%) can absorb a deuteron to form a stable nuclide 10747Ag, and 10646Pd (27.33%) and 10846Pd (26.71%) can absorb a proton to form stable nuclides 10747Ag and 10947Ag, respectively. This fact may be related to experimental facts that protium and/or deuterium work well to produce the CFP [1] in experimental systems with Pd [2, 14]. The combination Pd/D(H)/Li is very popular as a system for the CFP and shows special chemical relation of PdDx and Li to form surface layers on the sample. This may be also related to the large cross section for neutron absorption by 63Li (940.3 b, abundance 7.4%). Table 5. Characteristics of nuclides related to transition metal Pt. Tabulated are atomic number Z = 78 and 79, mass difference ⊿A = 0 – 2, nuclide (natural abundance %).

There are a few positive data in electrolytic systems with Pt cathodes and both H2O and D2O consistent with data given in Table 5.. 3.2.3 Nuclear reactions participating in the Nuclear Transmutation in the CFP To investigate such complex experimental data as shown in Fig. 10, we have to use a firm point of view based on several premises suggested by experimental results. We have proposed a model (TNCF model) with an adjustable parameter and given consistent explanation of several simultaneous events in many data sets. To investigate events where appear nuclear transmutations with large changes of proton and nucleon number, we extended the TNCF model to the neutron drop (ND) model. a) Neutron Drop (ND) Model [2]

In the neutron drop model which is proposed as an extension of the TNCF model and an application of quantum mechanical calculations, a neutron drop AZΔ in the cf-matter is considered instead of a neutron n. The neutron drop AZΔ is a compound state of nucleons composed of Z protons, Z electrons

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and (A–Z) neutrons stably exists in a cf-matter generated in surface/ boundary regions of CF materials [2].

To explain various nuclear products observed in CF experiments, it is necessary to assume multi-nucleon absorption by a nuclide AZX and succeeding nuclear processes including fission of the compound nucleus: AZΔ + A’Z’X → A – a Z – bΔ + A’+aZ’+bX*,

→ A – a Z – bΔ + A’– a’– a” Z”– b’– b”X’ + a’ b’X” + a” b”X”’. (4) The reaction equation showing beta decay is written down as follows when

m neutrons participate in formation of intermediate nucleus; AZΔ + A’Z’X → A – m ZΔ + A’ + mZ’X*→ A – m ZΔ + A’ + mZ’– 1X’ + e– + νe + Q', (5) where νe is an antiparticle of the electron neutrino.

If we consider the neutron drop, we have a freedom to feed several neutrons to a nuclide interacting with it. It is very powerful to explain nuclear transmutations with large changes of nucleon number A and proton number Z. b) Nuclear Transmutation by Decay, NTD There are many data sets explained by assuming alpha and beta decays of nuclides formed by following reactions supported by a neutron drop AZΔ; AZΔ + A’Z’X → A – m ZΔ + A’ + mZ’X* (6) A’ + mZ’X*→ A’ + mZ’– 1X’ + e– + νe + Q, (β) (7) A’ + mZ’X*→ A’ + m – 4Z’– 2X” + 42He + Q’, (α) (8) Concrete examples of this type observed in experiments are given as follows; ｎ + A46Pd → A+146Pd* → A+147Ag + e— + νe , (β)

115B → 83Li, (α) A13Al →A+114Si, (β) 3919K → 4020Ca, (β) A22Ti → A+123V, (β) A28Ni → A+129Cu, (β) A37Rb →A+138Sr, (β) 13455Cs → 13556Xe, (β+) A78Pt → A+179Au, (β) A79Au → A+180Hg. (β)

c) Decay Time Shortening There are several data sets explained only by an assumption where

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occurs the decay time shortening (τd ; decay constant in free space): 10746Pd* → 10747Ag (β). (τd = 1.3×109 y) 4019K* → 4020Ca (β). (τd = 6.5×106 y) 23592U* → 23190Th* (α). (τd = 1.0×109 y) 23892U* → 23490Th* (α). (τd = 6.5×109 y) Without the decay time shortening, it is difficult to explain existence of such nuclides as 10747Ag and 4020Ca in experimental system with a time constant of the observation of about several days. d) Nuclear Transmutation by Absorption, NTA

There are experimental data sets where occurs nuclear transmutation by absorption expressed as follows; AZΔ + A’Z’X → A – a Z – bΔ + A’+aZ’+bX, (9) where we observe A’+aZ’+bX leaving the neutron drop A – a Z – bΔ in the cf-matter.

Concrete data obtained are given as follows; A22Ti → A+A’24Cr, (ΔZ=2) A22Ti →A+A’26Fe, (ΔZ=4) A28Ni → A+A’30Zn, (ΔZ=2) A38Sr →A+A’42Mo, (ΔZ=4) A46Pd → A+A’48Cd, (ΔZ=2) A46Pd →A+A’50Sn, (ΔZ=4) A46Pd → A+A’56Ba, (ΔZ=10) A53Cs → A+A’59Pr, (ΔZ=6) A46Pd → A+A’82Pb, (ΔZ=36) A74W →A+A’82Pb. (ΔZ=8) e) Nuclear Transmutation by Fission, NTF

There are many data sets showing occurrence of the fission in the CFP. As we know well, the most popular simple example of the reaction (4) is the fission of 23592U induced by a neutron;

n ＋23592U → 23592U＊→ 14054Xe + 9438U + 2n + Q. More data sets of the type explained by Eq. (4) are given in the book [2]. Decrease or Disappearance of Fission Threshold Energy It should be noticed that the threshold energy for the fission reaction of a nuclide A’+aZ’+bX* in Eq. (4) might be drastically decreased in cf-matter from

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that in free space to reconcile the data with other events observed in the CFP. This characteristic of nuclear reactions in cf-matter is one of peculiarities of the CFP we have assumed in the TNCF and the ND models. f) Nuclear Transmutation by Transformation, NTT

There is a kind of nuclear transmutation where are generated nuclei with Z and A far from those of nuclides pre-existed in the system. Such reactions are most naturally explained by a transformation of a neutron drop AZΔ to a nucleus AZX without any change of A and Z: AZΔ → AZX. (10) Experimental data sets showing following nuclides may be naturally explained by the transformation (10) even if it is difficult to distinguish it from NTA; 126C, 2412Mg, 2814Si, 3216S, 3517Cl, 3717Cl, 4020Ca, 5626Fe, 5828Ni, 20882Pb. 4. Conclusion

The cold fusion phenomenon (CFP) has several typical characteristic phases in chemistry, physics and nonlinear dynamics. The events of the CFP included in these established research fields are at first sight dazzling and improbable to reconcile with known knowledge we have in these fields.

Using an appropriate point of view, we could give a unified phenomenological explanation for these events. In doing so, we have established the TNCF model with an adjustable parameter and several premises based on experimental facts. The key factor of the TNCF model is the trapped neutrons (quasi-free neutrons) with a density (adjustable parameter) nn (or n) in CF materials.

Furthermore, it have been assumed nuclear reactions in CF materials that are different from those in free space where a gamma photon is usually accompanied (cf. Eqs. (1) – (3)).

The chemical phase of the CFP includes compatibility of transition metal/hydrogen isotope/alkali metal and the stability effect explained in Section 3 and gives some insights into physical properties of CF materials; properties of halo nuclei, wavefunctions of neutrons in the evaporation levels, wavefunctions of protons/deuterons at interstices, super-nuclear interaction of neutrons in different lattice nuclei, formation of neutron bands at around

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zero energy level, accumulation of neutrons at surface/boundary regions, formation of neutron drops participating specific nuclear reactions in the cf-matter.

It is shown by recent investigation that characteristics simulated in nonlinear dynamics have been observed in the CFP [7 – 9].

Thus, chemical, physical and nonlinear-dynamical investigations of the CFP suggest that the science of this phenomenon should includes knowledge of nuclei of Ti, Ni, Pd and others in CF materials especially that of neutron wavefunctions of halo nuclei, wavefunctions of protons and deuterons at interstices which are not well explored in each field yet. Also, it should be emphasized that the CFP belongs essentially to complexity and has only qualitative or statistical reproducibility.

This work is partially supported by a grant from the New York Community

Trust. Appendix; Terminology CFP. Nuclear reactions and accompanying events occurring in solids with high densities of hydrogen isotopes (H and/or D) in ambient radiation including thermal and epithermal neutrons. CF materials. Materials where occurs the cold fusion phenomenon. cf-matter. A state of nuclides including neutron drops and lattice and alien nuclides formed at surface/boundary regions of CF materials where exists accumulated neutrons. neutron drop (ND). A compound nuclides composed of (A – Z) neutrons, Z protons and Z electrons expressed as AZΔ. TNCF model (trapped neutron catalyzed fusion model). A model based on the assumption that there are trapped neutrons (quasi-free neutrons) in solids with a number density nn (or n) reactive with nuclides at irregular position in the solids without emission of a photon as usual in free space.

References 1. M. Fleischmann, S. Pons and M. Hawkins, "Electrochemically induced Nuclear Fusion of Deuterium," J. Electroanal. Chem., 261, 301 – 308 (1989). 2. H. Kozima, The Science of the Cold Fusion Phenomenon, Elsevier Science, 2006. ISBN-10: 0-08-045110-1. 3. E. Storms, The Science of Low Energy Nuclear Reaction, World Scientific,

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Singapore, 2007. ISBN-10 981-270-620-8. 4. H. Kozima, Discovery of the Cold Fusion Phenomenon, Ohtake Shuppan, Tokyo, 1998. ISBN: 4-87186-044-2. 5. Kozima, H., “Quantum Physics of Cold Fusion Phenomenon,” Developments in Quantum Physics Researches – 2004, pp. 167 – 196, ed. V. Krasnoholovets, Nova Science Publishers, Inc., New York, 2004. ISBN 1-59454-003-9 6. H. Kozima, “Physics of the Cold Fusion Phenomenon” Proc. ICCF13 (to be published). 7. H. Kozima, W.-S. Zhang and J. Dash, “Precision Measurement of Excess Energy in Electrolytic System Pd/D/H2SO4 and Inverse-power Distribution of Energy Pulses vs. Excess Energy” Proc. ICCF13 (to be published). 8. H. Kozima, “The Cold Fusion Phenomenon as a Complexity (2) – Parameters Characterizing the System where occurs the Cold Fusion Phenomenon” Proc. JCF8, (2007, to be submitted). 9. H. Kozima, “The Cold Fusion Phenomenon as a Complexity (3) – Characteristics of the Complexity in the Cold Fusion Phenomenon” Proc. JCF8, (2007, to be submitted). 10. M.J. Feigenbaum, “Quantitative Universality for a Class of Nonlinear Transformations” J. Statistical Physics, 19, 25 – 52 (1978). 11. J. Gleick, Chaos, Penguin books, ISBN 0-14-00.9250-1 12. A. De Ninno, A. Frattolillo, G. Lollobattista, G. Martinio, M. Martone, M. Mori, S. Podda and F. Scaramuzzi, ”Evidence of Emission of Neutrons from a Titanium-Deuterium System,” Europhys. Lett. 9, 221 (1989) 13. M.C.H. McKubre, S. Crouch-Baker, A.M. Riley, S.I. Smedley and F.L. Tanzella, "Excess Power Observed in Electrochemical Studies of the D/Pd System," Proc. ICCF3 , pp. 5 – 19 (1993). 14. W.-S. Zhang and J. Dash, “Excess Heat Reproducibility and Evidence of Anomalous Elements after Electrolysis in Pd|D2O+H2SO4 Electrolytic Cells” Proc. ICCF13 (to be published). 15. H. Kozima, “Cold Fusion Phenomenon,” Rep. Fac. Science, Shizuoka University, 39, 21 – 90 (2005). The “References” in this paper is posted at the CFRL (Cold Fusion Research Laboratory) Website; http://www.geocities.jp/hjrfq930/Papers/paperd/RRefFull.htm

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