Proc. ICCF11 (Oct. 31 – Nov. 5, 2004, Marseille, France) to be published.

Cold Fusion Phenomenon and Solid State-Nuclear Physics

Hideo Kozima, Cold Fusion Research Laboratory,

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

E-mail; cf-lab.kozima@nifty.com, hjrfq930@ybb.ne.jp

The cold fusion phenomenon (CFP) is investigated in wide perspective of modern physics including physics of transition-metal hydrides, nuclear physics and the science of complexity using quantum mechanics. Characteristics of CFP including the stability effect in nuclear transmutation and the inverse power law of excess power generation are consistently explained using concepts of the cf-matter presented by the present author.

1. Introduction

We have investigated the cold fusion phenomenon (CFP) phenomenologically at first¹⁾ and then quantum mechanically.^2,3) Now, we are able to understand⁴⁾ total image of this complex phenomenon as a whole not disturbed by the Fleischmann’s hypothesis (immense acceleration of D-D fusion reaction rate in solid transition-metal deuterides) which lead to the pioneering work.⁵⁾

The cold fusion phenomenon is an outstanding phenomenon revealing complexity, a science closely related with self-organization and chaos, in solids corresponding to such meteorological and geophysical phenomena as the typhoon or hurricane and the earthquake. Its cause is defined by characteristics of the complex system and the phenomenon destined to be irreproducible in a strict sense conditioned by stochastic and/or chaotic processes occurring in microscopic atomic milieu in the sample. While atomic processes govern the cause, the effect of which is nuclear and therefore quantitative ratio of energies relevant with the effect and the cause reaches up to 10⁷. The effect accordingly is not completely averaged out as in atomic effects usual in solid-state physics and appears exotic for solid-state scientists. On the other hand, conventional mechanism of nuclear reactions between charged particles to overcome the Coulomb barrier is excluded in this situation: To realize mutual distance of about 1 fm where the nuclear force works, the kinetic energy of the mutual motion of two charged nuclei should be 10⁵ times larger than their thermal energy at the equilibrium state.

The largeness of the effects of about 10⁷ times that of the cause in energy scale and smallness of the effective process of about 10⁻⁵ times that of the cause in space dimension induce spectacular events rarely exist in nature. The chaotic nature of process producing CFP includes qualitative reproducibility but not quantitative which is popular in simple systems usually treated in modern physics. These features of CFP make it difficult to accept it in the field of scientific investigation for many scientists.

In this paper, we show a consistent explanation of the total feature of CFP using two laws discovered in the experimental data – the inverse power law and the stability effect of the nuclear transmutation – as clues to understand this complex phenomenon.

2. Solid State-Nuclear Physics of CFP Revealed by Experimental Data

Schematically, the characteristics of CFP are itemized as follows:

2-A. Phenomenological Characteristics of CFP^1,4)

A1. There are optimum combinations of the body material and hydrogen isotope. Experimental data in metal physics shows Pd-d and Ni-p satisfy this condition and are good combinations for CFP.

A2. Formation of composite system (inhomogeneous distribution of occluded hydrogen isotopes in a body metal) is a source of chaotic behavior in CFP.

A3. There are optimum combinations of the body material and the electrolyte metal to realize active nuclei in the appropriate surface/ boundary regions: e.g. Pd-Li, Ni-K, Na, Ti-Li,

A4. Production of tritium requires deuteron and that of ⁴He requires ⁶Li in the surface/ boundary regions.

A5. Nuclear reactions between a neutron drop (^A_ZΔ) and a nucleus (^A_ZX) occur in a chaotic state and production rates of new nuclides governed by their stability.

A6. CFP is fundamentally irreproducible and has at most qualitative reproducibility in short time range.

A7. The nuclear reactions may destroy necessary condition(s) for CFP and therefore CFP is fragile.

2-B. Microscopic Processes in CFP^2-4)

B1. Lattice nucleus should have neutron levels at around the zero energy level (the evaporation level). Pd, Ti and Ni satisfy this condition.

B2. Interstitial protons/deuterons with wide spread wave functions which interact with neutrons in lattice nuclei

B3. Super-nuclear interaction of neutrons in lattice nuclei mediated by interstitial protons/deuterons.

B4. Formation of neutron bands around zero level

B5. Formation of cf-matter at appropriate boundary/surface regions

B6. Neutron drops (in the cf-matter) – nucleus interaction

2-C. Realization of Necessary Conditions for Neutron Band Formation ^1,2)

C1. Ordered lattice nuclei with excited neutron levels around zero energy (evaporation level)

C2. Nearly saturated occluded proton/deuteron with wave functions spread out at lattice nuclei.

C3. Neutron (in a lattice nucleus) – proton/deuteron interaction by the nuclear force.

C4. Neutron (in a lattice nucleus) – neutron (in another lattice nucleus) interaction mediated by the occluded protons/deuterons (super-nuclear interaction)..

C5. Formation of neutron bands due to the super-nuclear interaction.

C6. Local coherence of neutron waves in a band at surface/boundary regions

C7. Enough number of neutrons in the band to realize cf-matter where are neutron drops composed of neutrons and a few protons

C8. Existence of exotic/disordered nuclei (active nuclei) at the surface/ boundary regions to realize CFP by interactions with the neutron drops.

2-D. On the Wave Functions of Protons/Deuterons in Transition-Metal Compounds⁴⁾

We give here short explanation of some properties of interstitial protons/deuterons with wide spread wave functions.

We know that CFP occurs only in fcc transition-metal hydrides and deuterides. In the transition-metal alloys, it is noticed that there are optimum combinations of metal and hydrogen isotopes: Some examples are Pd-d, Ni-p, and Ti-d, p.

Data of physical properties of transition-metal hydrides and deuterides show following nature of the wave functions of hydrogen isotopes. In PdH and PdD lattice, hydrogen or deuterium atoms occupy octahedral sites in ground states. In excited states, however, they are in tetrahedral sites and have more spread wave functions over several interstices.

There are several different characteristics in PdD and PdH. In PdD, Pd-D interaction is relatively weak and D-D interaction has following characteristics that the second neighbor D-D interactions is strong comparable to the first neighbor D-D interaction.

In PdH, H-Pd interaction is comparable to H-H interaction even if H-Pd distance (2.03 A) is less than that of H-H and the large value of the nuclear charge of Pd (Z = 46). Furthermore, it is probable that there is a repulsion of H atoms on next-nearest neighbor sites, which would overcompensate the attraction of nearest neighbor H atoms at high concentrations.

Activation energies for diffusion of D and H in Pd are 0.206 (T = 218 – 333 K) and 0.23 eV (T = 230 – 760 K), respectively.

These are some properties of Pd alloys, one of the most well investigated transition-metal hydrides and deuterides. Similar properties have been investigated in other alloys and they should be combined with data of CFP to elucidate quantum mechanical states of protons and deuterons in them.

2-E. Electrochemistry of CFP⁶⁾

It is now evident that the cold fusion phenomenon occurs mainly in surface/boundary regions of solid materials including high-density hydrogen isotopes.^1,6) Especially in electrolytic systems, we have noticed existence of optimum combinations of electrodes – electrolytes; some examples of them are Pd/D₂O + LiOD/Pt, Ni/ H₂O + KOH/Pt, A special case, in addition to the above ones, successively used by John Dash of Portland State University and others is a combination Pd/D₂O + H₂SO₄/Pt.

Unfortunately, this problem of optimum electrode - electrolyte combinations is not clarified yet. It is clear, however, that formation of surface layer with a composition appropriate to occlude hydrogen isotopes into cathode and to initiate nuclear reactions relevant with CFP is decisively important to realize CFP successfully.

3. Empirical Facts of CFP Showing Its Complexity

There are too abundant experimental data sets to catch physics behind them without a sound view point. From those data sets, we could deduce two laws related essence of CFP.

3.1 Inverse Power Law of the Excess Power Production⁴⁾

The data analysis of McKubre et al.⁷⁾ this section is far from complete. They will be able to give more extensive and complete analysis of their data along the same line of investigation. We tentatively counted number of observations N(P) from their Fig. 6 as shown in Table １ and made a data table to depict log N vs. log P graph as shown in Table 2.

Table 1. Gross number N(P) of measurement point for the excess power P (W) grossly counted from Fig. 6 of McKubre et al. (1993) using Pd wire with a dimension 1mm φ×36 cm (surface area of 11.3 cm²).

P(W)	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
N(P)	400	240	160	140	120	100	60	60	40	40
P(W)	1.1	1.2	1.3	1.4	1.5	1.6	1.7	1.8	1.9	2.0
N(P)	30	30	20	10	8	8	5	2	5	1

Table 2. Dependence of log N(P) on log P estimated from the data given in Table 1.

log P	-2.1	-1.7	-1.6	-1.5	-1.4	-1.3	-1.2	-1.15	+0.1	0.2	0.3
N(P)	400.	240	160	140	120	100	90	70	60	38	21
log N	2.6	2.4	2.2	2.15	2.08	2.00	1.95	1.86	1.78	1.58	1.32

The data given in Table 2 are plotted in Fig. 1.

Fig. 1. Plot of log N vs. log P from Table 2 showing linear dependence of log N on log P with a negative gradient with – 1, the inverse power law. Linear line is drawn for the benefit of eyes.

Inverse power law of excess power generation is clearly seen in the region from log P = - 1 to +0.1 (from 1 to 12 of the abscissa). The data depicted in Fig. 1 expresses that N(P) is inversely proportional to P:

N(P) = const. P^{– a} with a ≈ 1.

This characteristic expressed in the graph of the excess power spectrum reveals that CF system shows “the self-organized criticality.” This characteristic is common to many phenomena occurring in complex systems; most well known example is the 1/f noise of electric resistance noticed in 1925 by Johnson (the index a = 1).

Other examples include the intensity distribution of winds (a = 1, 5/3), frequency of earthquakes vs. their intensity (Gutemberg-Richter’s law, a = 0.47 – 0.73). The distribution of wind speeds at heights 80 and 150 meters were measured in Japan at the time of a typhoon. The index a were determined to be 1 and 5/3, respectively for the two heights.

Another interesting example of this behavior is the intensity of the cosmic ray measured at upper atmosphere. It obeys the 1/f-law. Interesting point is its relation with the fluctuation of the inter-galactic magnetic field that obeys also the 1/f-law. It is considered that the fluctuation of the intensity of cosmic ray reflects that of the magnetic field.

Figs. 2 and 3. Stability effect of nuclear transmutation.^3,4)

3.2 Stability Effect of Nuclear Transmutation of CFP^3,4)

The stability effect of nuclear transmutation in good coincidence with the abundance of elements in universe found in experimental data sets^3,4) shows clearly compound states of nucleons where it is easy to form stable configurations of nucleons. This is a complex many-body system looked at from a different point from that given in the preceding subsection about the inverse power law.

4. Discussion

Experimental data sets obtained in these 15 years after discovery of CFP⁵⁾ reach more than thousand, probably, and we have been staying too long in a state of poor prospect. In my opinion, the data obtained until now have not been fully utilized to give a sound perspective for future development of CFP research. Perhaps, it is useful to depart from the Fleischmann’s hypothesis for a while and to look whole situation from various points of view. We made a trial based on the two laws explained in this paper.

Now, we have to recall the statistical stability, a characteristic of the chaos, that the trajectory in the phase space of a chaotic system is unstable to a small perturbation and non-reproducible but a time average of a physical quantity on the trajectory is stable and is reproducible.

The most direct evidence of this nature is shown in Fig. 1 as the inverse power law of the excess power generation and less directly in Figs. 2 and 3 as the stability effect of nuclear transmutation in CFP.

As we have emphasized several times,^1–4) the system where occurs the cold fusion phenomenon has characteristics of complexity and phenomena occurring in them have inevitably qualitative reproducibility but not quantitative one.

Rather theoretical verification of the complexity of CFP is seen as follows. There are several situations in the process crucial to realize CFP. If other necessary conditions are fulfilled, it is necessary to have a) an appropriate distribution of protons/deuterons to realize the super-nuclear interaction (Chapter 2, B3, C4), b) an appropriate boundary/surface conditions to realize the local coherence, c) high density neutrons (B5, C6) to form the cf-matter including neutron drops (C7), and d) appropriate exotic nuclei to realize nuclear reactions with the neutron drops (B6, C8).

These conditions are possible to be realized as or closely related with self-organization from chaotic point of view.

We have to look at CFP from the above point of view if we notice existence of the two laws in CFP – the inverse power law and the stability effect of NT –. The necessary conditions for CFP explained in Chapter 2 from our point of view should be examined more carefully using experimental data to be performed on the new points of view.

It should be mentioned about a pioneering computer simulation on the self-organization in nuclear physics. Negele et al.⁸⁾ showed a formation of a regular lattice by self-organization in neutron star matter. This is an example of self-organization exactly corresponding to the situation c) discussed above.

References

1) H.　Kozima,　Discovery of the Cold Fusion Phenomenon, Ohtake

Shuppan Inc. Tokyo, 1998. Essential parts of this and following works by the author are accessible in the Cold Fusion Research Laboratory (CFRL) website: http://www.geocities.jp/hjrfq930/, http://web.pdx.edu/~pdx00210/

2) H. Kozima, “Quantum Physics of Cold Fusion Phenomenon” Developments in Quantum Physics, pp. 167 – 196, ed. F. Columbus and V. Krasnoholovets, Nova Science Publishers, Inc., New York, 2004.

3) H. Kozima, “Cf-Matter and the Cold Fusion Phenomenon,“ Proc. ICCF10 (to be published).

4) H. Kozima, “Cold Fusion Phenomenon” Rep. Fac. Science, Shizuoka University, 39, (2005) (to be published).

5) M. Fleischmann, S. Pons and M. Hawkins, "Electrochemically induced Nuclear Fusion of Deuterium" J. Electroanal. Chem.. 261, 301 (1989).

6) H. Kozima, "Electroanalytical Chemistry in Cold Fusion Phenomenon" Recent Res. Devel. Electroanal. Chem. 2, pp. 35 – 46, ed. S.G. Pandalai, Transworld Research Network, Trivandrum, India, 2000.

7) M.C.H. McKubre, S. Crouch-Baker, 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).

8) J.W. Negele and D. Vautherin, "Neutron Star Matter at Sub-nuclear Densities" Nuclear Physics, A207, 298 – 320 (1973).