Reports of CFRL (Cold Fusion Research Laboratory), 8-3, pp. 1 – 23 (September, 2008)
Phenomenology of the Cold Fusion Phenomenon*
Hideo
Kozima
Cold
Fusion Research Laboratory
*This paper is based on a presentation with the same
title given at “Workshop on Nuclear Transmutations” organized by G.H. Miley on
August 15 after ICCF14 (August 10 – 15, 2008,
“The
man of science must work with method. Science is built up of facts, as a house
is built of stones; but an accumulation of facts is no more a science than a
heap of stones is a house. Most important of all, the man of science must
exhibit foresight.” Henri Poincaré, Science
and Hypothesis, p. 141. translated by W.J.G., Dover Publications, Inc.
1952. Library of Congress Catalog Card Number 53-13673.
Abstract
Phenomenological approach to the
cold fusion phenomenon (CFP) is explained using experimental data sets as a
material to construct models and also using comparison of theoretical results
with experimental data as an evidence of success. Quantum mechanical
investigation of premises used in the models is given as a first step of
microscopic approach to this curious phenomenon including various events
related with nuclear reactions in room temperature solid materials.
1. Introduction
In these almost twenty years of
researches of the cold fusion phenomenon (CFP) in such materials (CF materials)
as transition-metal hydrides and deuterides, in hydrocarbons with a periodic
array of carbon atoms and in some biological systems, we have obtained a lot of
experimental data sets and have elaborated a few theoretical trials to explain
the curious facts revealed by the experimental data sets [1, 2, 3].
Generally speaking, the
experimental facts especially those of excess energy and several accumulative
observables such as transmuted nuclides are unquestionably revealed abnormal
behavior in the CF materials at around room temperature difficult to explain by
known knowledge of nuclear physics and solid-state physics.
We may specify the present stage
of the research in the CFP (CF research) as plenty of experimental facts lacking
satisfactory theory and we need such an effort as specified by H. Poincare’s
words cited in the head of this paper. Really, it is necessary to have an appropriate
design of the house and cement to combine distributed blocks together to construct
a building.
To make theoretical trials for a
consistent explanation of experimental facts with wide variety, we have to have
a strategy for the investigation. The methodology given in this paper is one of
such trials based on historical experience in nuclear physics and shows the
phenomenological approach including models is the most needed one at present.
There is a trial to formulate the
development of science as three steps called 1) phenomenological, 2) substantial,
and 3) essential ones (three-step hypothesis of science evolution). According
to this formalism, theoretical approach to a new problem starts with a
phenomenology based on experimental facts assuming hypothesis to explain them
using concepts of existing science, the next step uses a model combining old
concepts as a system of hypotheses and finally a theory develops a logical
system based on general principles accepted by the scientific world at the time.
Therefore, theoretical trials to
attack an inexplicable experimental data obtained in the CFP may be classified
into three categories; 1) hypothesis, 2) model and 3) theory as explained in
the previous book ([1], Appendix B) as cited in Appendix A of this paper.
In this paper, we give a
phenomenological explanation of the CFP, the first step of theoretical
development in the classification given above in addition to extensive
explanation of theoretical trials developed by now, especially putting weight
on problems under development in nuclear physics and solid-state physics.
2. Difficulty to Explain
Nuclear Reactions in Solids at around Room Temperature without Acceleration
Mechanisms
In nuclear physics, low energy
nuclear reactions in free space are a well investigated subject and detailed
knowledge has been accumulated in almost 80 years after discovery of the
neutron in 1932 when nuclear physics substantially was get started.
A nucleus (called a
nuclide to specify its constituent characterized by the number of protons Z,
the number of nucleons A, and the energy state) has a volume V
proportional to A and therefore the radius of the nucleus RN
is proportional to a cube root of A;
RN＝CA1/3.
(1)
The constant C has a value about 1 fm (femtometer or
fermi) = 10– 13 cm.
This means that
nucleons (protons and neutrons) are interacting with an attractive force called
the nuclear force with an action range of about 1 fm except the inter-nucleon
distance |r| is not too small (|r| ≥0.1 fm).
Let us consider an
interaction of two nuclei with proton numbers Z and Z’. When the
mutual distance |R| between two nuclides is larger than the
distance RN0 ≡ 1 fm (or 10–13 cm), the force
exerting between two nucleus is essentially the repulsive Coulomb force Fc
proportional to inverse square of the distance |R| due to the charges on
the nuclides;
Fc = c ZZ’e2/|
R |2,
with a constant c. When the
distance | R | diminishes to a magnitude of an order of RN0,
the nuclear force starts to work to attract each other and the two nuclei fuse.
Thermonuclear fusion reactors investigated for more than fifty years to realize
a sun on the earth are machines to realize d-d or d-t
fusion reactions effectively in plasmas with high density (1015 cm–
3) and temperature (108 degree Kelvin).
When the two nuclei
approach in the range of the nuclear force each other overcoming the repulsive
Coulomb force by some means, the two nuclei coalesce forming a compound,
intermediate nuclide, usually expressed by an asterisk on the shoulder like AZX*.
The compound nucleus AZX* stabilizes itself
through several branches as established in nuclear physics, emitting
electromagnetic radiation (γ ray) to become AZX, emitting
a light particle as n, p, heliuim-4 to become another nuclide, or
exerting a fission to become other nuclides.
In CF materials, if there occurs entirely different nuclear reactions from those
in the free space, we have different events in the process from the
initial to the final through the intermediate stage of the reaction. The
conceivable stage that differs from that in free space is one of followings;
(1) when two nuclei are approaching, (2) in the stage forming a compound
nucleus, (3) when a compound nucleus is formed, and (4) after a compound
nucleus is formed.
Let us investigate
possible effects of CF materials on these stages of nuclear processes. As an
example of illustrative investigation, we use the most popular case of PdD
crystal out of CF materials. The deuterons are in a special situation in this crystal
different from that in free space by factors listed as follows; (a) existence
of free electrons, (b) existence of nuclei of A46Pd (A =
102 – 110) on the lattice points (lattice nuclei), (c) existence of regularly
distributed other deuterons at interstices surrounded by lattice nuclei of Pd.
It is possible that
these factors cooperate to produce new effects, which might be stronger than
individual effects. We consider, however, only these factors individually in
this paper due to a common sense that a cooperative effect is not stronger than
effects induced by individual causes even if it has different characters from
them leaving existence of unexpected keys to overcome conventional difficulties
discussed below.
2.1 Electrons ([1] Section
3.4.2)
In quantum
mechanics, a particle can take restricted values of momentum p
and position r by the uncertainty principle different from in
classical mechanics where they can take arbitrary exact values. Let us consider
this situation in one-dimensional case, for simplicity.
In one dimensional
system, the uncertainties of the momentum Δｐ and the position Δx of a particle
with a mass m have to satisfy the uncertainty relation;
Δx・Δｐ ∼
ћ/2.
(2)
The constant ћ
is defined as the Planck constant ｈ divided by 2πand has a value;
ћ ＝
1.05×10– 34 J・s.
(3)
According to the
uncertainty relation (3.4-2), an uncertainty Δx of position and an
uncertainty Δｐ of momentum relate to each
other and they cannot decrease independently.
The momentum p
is related to the energy E of the particle by a relation;
Ｅ = p2/2m.
(4)
This means also an
uncertainty of energy ΔE of the particle is restricted by the
uncertainty of position Δx through the uncertainty of momentum Δｐ. If we confine a particle in a small
space thus making Δx small, then we have a larger value of the momentum
due to the increased Δｐ,
resulting in an increased value of the energy.
Let us consider a system composed of two
hydrogen atoms, (H + H). A hydrogen atom is composed of a proton and an
electron. When the mutual distance Ｒ
of two atoms decreases from infinity, two electrons behave as follows; when Ｒ is larger thanｒN ≡ 10–13 cm, a
distance where the nuclear interaction starts, the force exerting between
protons and electrons is only the attractive Coulomb force and a state with largerＲ is
more stable.
When the distance
Ｒ
becomes smaller to a value around the distance of stable interatomic distance Rmin
of hydrogen molecule H2, two electrons take longer time at the
position where they screen the repulsion of two protons as we know from quantum
mechanical calculation of the stable state of H2. In this state, two
electrons are confined with a high probability in a small space between two
protons; this restriction on their positions make their energy higher while the
screening of p-p repulsion make Coulomb energy lower and the balance of
these two effects determine Rmin.
Thus, the reason why there is a minimum energy state with an interatomic
distance Rmin. is explained by the uncertainty relation (2).
This reasoning by the energy balance forbid to make the interatomic distance
decrease further to an order of magnitude of ｒN ≡ 10–13 cm when
there are no strong force exerted to enforce two protons approach.
When the
inter-proton distance becomes close toｒN, by the screening effect of electrons decreasing the
Coulomb repulsion between two protons, we can calculate how high the energy is
of two electrons confined in the small space between two protons;
The electron has a light mass me
= 9.11×10–31
kg and the uncertainty principle Δx・Δｐ ∼ ћ makes the energy of an electron large when its position is confined
in a small range. In a hydrogen atom, an electron with the classical Bohr orbit
with a radius aH = ћ2/me2 (∼ Δx)
has a kinetic energy Ee as given by
Ee = Δｐ2/2m
∼ ћ2/m a2 ∼ 10
eV,
using
the ground state energy of hydrogen atom EH = e2/aH
= – 13.6 eV.
This estimation applies also
to D-D system instead of H-H system without any change of factors.
If an electron works to lower
the Coulomb barrier between two deuterons to make them fuse together, the
electron has to remain between them at a distance aboutｒN
∼ 10–5 aH
where the nuclear force works. Then, the energy of the electron becomes very
large,
Ee ∼ Δｐ2/2m
∼ 1010 ћ2/m a2
∼ 1010 |EH|
∼ 1011 eV (= 105
MeV),
showing
inability of its screening effect for the fusion reaction:
.
Thus, in a system
without special acceleration mechanism, it is impossible to expect d-d
fusion reactions to be realize by any screening effect of electrons in the
system.
There are several
trials to overcome the above explained shortage of the screening effect by
electrons as briefly introduced in Section 3.3.7 without respectable positive
results.
2.2 Phonons ([1] Section
3.4.3)
Let us consider PdD
crystal, one of the typical CF materials of fcc transition-metal
deuterides and hydrides, for example. The lattice structure of PdD is shown in
Fig. 2.2-2. Ions of Pd and deuterons are oscillating with thermal energy around
their equilibrium points, lattice points and interstitial sites, respectively.
The thermal motion
of ions and deuterons are equivalently described as oscillations of lattices of
Pd ions and deuterons as usually done in solid-state physics. The oscillation
of a lattice is quantized to be described by phonons, quasi-particles with
quasi-momenta and quantized energy. The phonon is treated in parallel to the
photon, the quantized state of the electromagnetic field. Physics of a system
composed of charged particles and electromagnetic fields is called Quantum
Electromagnetic Dynamics (QED), which inspired M. Fleischmann to expect
Fleischmann’s hypothesis [4].
There are several
researchers, including M. Fleischmann, who considered that phonons will help
realization of d-d fusion reactions in CF materials as photons worked to
explain such quantum electrodynamic effects as Lamb shift and abnormal magnetic
moment of an electron. The different characteristics of the photon and the
phonon make it difficult to show possibility of d-d (or p-d)
fusion reaction in CF material. With a following investigation, we can
understand the fundamental problems of their trials.
Let us consider two
examples of one-dimensional oscillation; a rubber string of continuous medium
and a line of mass points and springs combined alternatively. The wavelength of
the oscillation of the rubber string distributes from the maximum, twice the
length of the string, to the minimum, zero. This distribution of wavelengths
(or equally frequencies) is a characteristic of the continuous medium.
The latter is an
example of discontinuous medium like a crystal lattice. In this case, there is
a minimum wavelength, twice the distance between adjacent mass points. This is
a strong restriction of the oscillations to accelerate charged particles for
fusion overcoming the Coulomb repulsion between them in the medium as explained
below.
The idea of phonons
to accelerate two particles to approach (or to keep away from) each other is
easily seen by the phase difference of 180 degrees when the wavelength is
minimum. This is the case where the force becomes a maximum to change mutual
distance between adjacent particles in the discontinuous medium. In the
continuous medium, there is no finite minimum wavelength and therefore no
limitation for the degree of freedom of photons. This is the case of QED where
photons played decisive roles in several electromagnetic interactions between
charged particles.
Thus, we understand
why phonons do not play a spectacular role in assisting nuclear fusion
reactions of d-d or p-d pairs.
2.3 Electric Field ([1]
Section 3.4.4)
There are other
trials to use electromagnetic force to make d-d fusion reactions
feasible without any acceleration mechanism. In this case, the difference of
masses of the electron and nuclei, or typically the proton is an obstacle to
them.
The CF materials
are mainly metals in which free electrons are easy to move under an electric field.
If there is an electric field, a charged particle receives a force proportional
to its charge. When a particle receives a force, it means there is an
acceleration that is inversely proportional to its mass. The velocity gained in
a unit time is proportional to the acceleration exerted. Therefore, an electron
with mass me moves under an electric field about 1800 times
faster than a proton with a mass about 1800 times me. The
effect of the electric field therefore absorbed by electrons before it works on
deuterons or other charged particles.
Magnetic field has
usually weak effects to charged particles with small velocity and we need not
care much about it in CFP.
Thus, several
factors in CF materials that are not in the free space seem to have no respectable
effects on CFP. If these factors do not do fantastic effects on d-d
fusion reactions, it is far from expectation to have tremendous effects on
three or more particle fusion reactions as some researchers dream about.
There are several
standard treatments of d-d fusion reactions in CF materials by
physicists in nuclear physics and plasma physics denying increase of fusion
probability by huge orders of magnitude [5, 6, 7].
2.4 Neutrons – a Key Element
governing Nuclear Reactions at Low Energy
The neutron is a particle
unstable in a
n → p + e—＋νe + 0.782 MeV. (5)
The mass
of a neutron mn is 1.67×10–27 kg or 1837.6 me,
where me is the electron mass; 9.11×10–31 kg,
Wave
Nature of Neutron
It is well established now
that any microscopic particle has wave nature and it is true for the neutron,
too. This nature of the neutron is widely used in many applications as neutron
diffraction and neutron optics.
A neutron with a momentum p
has a characteristic wavelength (called de Broglie wave length)
λ = ℏ/|p| = ℏ/(2mn E)1/2
(6)
which
takes a value 1×10–8 cm for a kinetic energy of 88 meV and 1.80×10–8
cm for 25 meV (the thermal energy at 300 K).
Participation of neutrons in the
CFP has been investigated from the initial stage of investigation of this
curious phenomenon and several facts have been clarified. The first is the
positive evidence of neutron’s effect on the CFP as shown by Shani et al.,
Celani et al. and Lipson et al. ([2] Section 8.2). The second is the null
result without thermal neutrons as shown by Ishida, Jones et al., and Forsely
et al. ([2] Section 8.1, [1] Section 2.2.1.4). Finally, the success of models
with neutrons – TNCF model – shows indirectly the importance of neutrons
participating in the CFP.
Neutrons in relation to
the CFP
As given in Appendix B, there are
evidences to show that neutrons strongly participate in the CFP. Therefore, one
of most promising phenomenological approach to the theory of the CFP is a model
using neutrons as an agents catalyzing nuclear reactions in CF materials at
around room temperature.
3. On the Conceptual
Discrimination among Theory, Model and Hypothesis (Cf. Appendix A)
There have been proposed several
hypotheses, Models and Theories to explain the CFP in solid materials
classified into three types; a) Transition-metal deuterides/hydrides which are
further subdivided into two types a-1) transition-metal hydrides and a-2)
transition-metal deuterides, b) hydrocarbons with periodic array of carbon atoms
(XLPE and phenanthrene) and c) biological bodies.
The system b) has been
investigated recently and may give a bridge between systems a) and c) which
have been assumed almost independent each other.
However, there are a lot of
confusion in the field of the CFP due to the ambiguous usage of words; theory,
model and hypothesis. We have proposed to discriminate these terms to clarify
the confusion induced by the ambiguity of the terminology (cf. Appendix A).
There are
also differences of points of view to investigate the CFP.
Theories.
The first
point of view concentrates its effort to clarify the CFP in the materials a-1)
classified above and tries to prove possibility of a reaction
d + d
→ 4He + phonons (7)
in
CF materials. It is possible to say that almost all theoretical efforts have
been performed on this line of investigation until now.
To show the possibility of the
reaction (7), many theoretical efforts have been concentrated on effects of
phonons absent in free space without success (J. Schwinger, P. Hagelstein, H.
Hora, - - -).
Another
approach in this approach is extension of theoretical investigations in rather
simple situations to the complicated CF materials (X.Z. Li, Y.E. Kim, - - -).
Models.
The second theoretical approach is models using neutrons as a catalyst
for nuclear reactions in CF materials. Several models based on experimental
facts difficult to understand by common sense of modern physics have been
proposed with qualitative success (J. Fisher, H. Kozima, - - - ).
Hypotheses.
The third approach is rather
simple one. To explain contradictions of experimental facts with the knowledge
of nuclear physics, there have been proposed such easy-going hypotheses as nuclear
reactions between (or among) charged nuclides at around energies of eV or existence
of quasi-neutral particles composed of a proton and an electron contradicting
quantum mechanics.
These theoretical endeavors have
sometimes been called theories making discussions in this field ambiguous and
in confusion.
A theory is
based on principles with some simplifications of conditions in logical
deduction. Therefore, it is easy to judge the correctness of the theory by its
validity of the simplifications used in its logic.
A model uses premises or
assumptions based on experimental facts but sometimes contradicting common
sense of established sciences. The value of the model is not in these
assumptions but in its success to explain experimental facts as a whole.
On the contrary, a hypothesis is a
makeshift explanation of facts and sometimes ignores knowledge of established
sciences, in our case that of nuclear physics. The hypothesis just waits
irresponsibly theoretical proof to overcome the knowledge.
4. Phenomenological
Approach using Concepts without Contradiction to Knowledge of Physics (Premises of
the TNCF model are given in Appendix C)
4.1 Characteristics of
Experimental Facts ([1, 2])
It is possible to pick up characteristics
of the CFP observed in CF materials as follows:
1.
Enormous excess energy generation inexplicable by atomic processes.
2.
Nuclear transmutations generating almost all nuclides of elements on the
periodic table.
3.
Qualitative reproducibility of events or absence of quantitative
reproducibility.
4.
Sporadicity of occurrence of CF events.
5.
Necessity of thermal neutrons to induce the CFP. The CF events do not occur
without thermal neutrons and are enhanced by thermal neutrons.
6.
Compatibility among the host atom, the hydrogen isotope and the solute alkaline
metal. There are such favorable combination of them as Pd-D-Li; Ni-H-K; - - - .
7.
Minimum ratio of (hydrogen isotope)/(host atom) (D/Pd, H/Ni, - - - ). In the
case of PdDx, the minimum ratio is around 0.85, (D/Pd)min
≃ 0.85.
8.
Locality of the reactions. Transmutation products are localized at around
surface/boundary regions with a thickness of about 10 μm.
9.
Stability effect of transmuted nuclei (stable nuclides were produced much)
10.
Inverse-power law in frequency N(P) vs. intensity P of excess energy generation
N(P) = C/Pb
(b: a constant with a value 1.0
– 2.0, C: a constant)
11.
Bifurcation of effects (the intensity of an effect takes two branches in the
course of an experiment)
12.
Chaotic distribution of effects (the intensity of an effect distributes
chaotically between a minimum and a maximum)
13.
Explosions (as a positive feedback of an effect, excess energy production
increases without limit to destroy the experimental system)
4.2 Effects of Neutrons
There are experimental data
showing decisive effects of thermal neutrons on the CFP. They are tabulated as
follows:
1.
Positive evidence of neutron effect – Shani, Celani, Lipson {[2] Section 8.2}
2.
Null result without thermal neutrons – Ishida, Jones, ([2] Section 8.1)
3.
Success of models with neutrons – TNCF model.
4.3 Under developing
Area of Nuclear Physics and Solid-State Physics
There are fields not
well-developed until now in nuclear physics and in solid-state physics. The CFP
seems to have close relation with these fields under developing in recent
years. These fields are tabulated as follows:
1.
Exotic nuclei with far excess number of neutrons. The neutrons in these exotic
nuclei, low energy neutrons have wavefunctions extended out of the periphery of
the nucleus (especially for nuclides with medium mass numbers). Though the
investigation at present is confined only to such nuclides with small mass
numbers as 62He, 113Li, 144Be,
179F, we can expect similar situation for such nuclides
with medium mass numbers participating in the CFP as A6C,
A22Ti, A28Ni, A46Pd,
- - -.
2.
Nature of excited states of nucleons at around zero energy level in the exotic
nuclei.
3.
Delocalization of hydrogen isotopes in Ti, Ni, Pd, - - - (in contrast to
localized ones in Mo, Ta, V, - - - where are no CFP observed).
4.4 Phenomenological
TNCF Model and ND model assuming Thermal Neutrons in CF Materials ([1, 2], Cf. Appendix C)
Using premises (assumptions) based on these experimental facts
summarized in Subsections 4.1 – 4.3, we have constructed a model (TNCF model)
including thermal neutrons in CF materials with an adjustable parameter nn (density of the neutrons)
to explain experimental data obtained in various CF materials. Using the model,
we could semi-quantitatively explain several features of the CFP with values of
the parameter nn at around
108 – 1013 cm–3. To explain nuclear
transmutations with large change of mass numbers, the TNCF model was extended
to the ND model (neutron drop model) in which neutron drops composed of Z protons and (A – Z) neutrons AZΔ exist.
4.5 Quantum Mechanical
Explanation of Premises made in the Model
Neutrons in solids are not
fully investigated until now perhaps because of thee short lifetime of about
887 seconds in the free space. However, the wave nature of the low energy
neutron has been used more widely in technology (the neutron guide and others)
and science (the neutron trap to study nature of neutrons). From our point of
view, however, the research is in an infantile stage and we have much work to
do in studying neutron physics in solids, especially fcc
transition-metal hydrides and deuterides.
Thus, we can expect new states
of neutrons in transition-metal hydrides and deuterides when there is an
optimum situation where several conditions are fulfilled to realize the neutron
valence bands below zero as discussed above and also expect new phenomena
related to the neutron valence band.
Several words should be added
about the states of neutrons in the boundary regions in solids. At boundaries
of a crystal, there is aperiodicity of the crystal lattice and disturbance to
the neutron Bloch waves. There appear new states due to the disturbance such as
surface states different from the Bloch states with different energies. We
ignore, however, occurrence of these states in this treatment and confine our
investigation to the neutron Bloch waves.
As was noticed in [1, Chapter
2], there is much evidence of nuclear reactions in CFP that is difficult to
explain without participation of neutrons, including those called decay-time
shortening and NT in surface layers of electrodes in electrolytic systems and
in surface regions of cathodes in discharge systems. In the TNCF model, this
surface nature of CFP is taken into the model by the instability factor ξ
of the trapped neutron assuming a value 1 (ξ = 1) in the surface layer
and 0.01 (ξ = 0.01) in volume [1, Section 3.2].
4.6 Complexity in the
Cold Fusion Phenomenon revealed by Experimental Facts [8 – 11]
Comparing extensive experimental
data sets of the CFP with diagrams obtained in nonlinear dynamics, we can
confirm our intuitive idea of complexity in the CFP as fully explained in
recent papers [8 – 11]. This shows that a phenomenological approach to the CFP
is again useful to show another phase of events in the CFP rooted in nonlinear
interactions of components (or agents) in multi-component materials.
5. Possible explanations
of explosions in the CFP by the TNCF model [12, Sketch 2]
Using the phenomenological TNCF
model successful to explain many phases of the CFP, we could explain several
data of explosions observed in these almost 20 years in this field. It is
interesting to know that such an extraordinary events as chaotic behavior and
explosion observed in the CF research are able to understand from a unified
point of view. This is a triumph of a phenomenological approach and encourages
to work on this line of investigation.
6. Conclusion
Successful construction of models
based on curious experimental data is illustrated using explanation of many
experimental facts as evidences of usefulness of the models. Extraordinary
nature of the models is difficult to accept even if there are experimental
facts inexplicable by common sense of established branches of science. With a
unified explanation of various facts by the model, we are going to accept the
reality of the premises assumed in the models recognizing existence of under
developing fields in nuclear physics and in solid-state physics. We hope that
many serious investigators will give attention to the undeveloped
interdisciplinary area where occurs the CFP generating various nuclides and
excess energy.
Appendix A. On the Conceptual Discrimination among
Theory, Model and Hypothesis (Appendix B of [1])
There are theoretical trials to explain
curious events in CFP assuming new ideas independent of knowledge of science
developed in 20th century. In discussion of CFP, there was ambiguity
of concepts of theory, model and hypothesis that made discussion in confusion
in CF community and impossible communicate with scientists in other research
field. We propose here a standard usage of terminology in relation with
historical usage of theory, model and hypothesis. It should be noticed that the
proposal is not obligatory, as a matter-of-course.
A1. Theory
A theory is a system of logic based on
fundamental principles commonly accepted in modern physics. In the logic of a
theory, there are inevitably included restrictions (approximations) to confine
field of investigation to make the logic tractable. Therefore, validity of a
conclusion obtained in a theory definitely depends on the restrictions
(approximations) assumed in the logical development from principles to
conclusion. If the logic used in a theory is perfect, scientists who believe in
the principles will accept the conclusion of the theory without reservation.
BCS theory of superconductivity is a typical example of the theory.
In the case of such complex systems as
where CFP occurs, any theoretical task necessarily depends on restrictions or simplifications
of the real system to make the object tractable. We can say there is no
successful theory for CFP at present because of too complex situation of the
phenomenon where we cannot imagine physics of fundamental processes in CF
material.
A2. Model
A model is a system of premises (or
assumptions) based on some experimental facts sometimes containing adjustable
parameters. Value of a model is solely in its ability to explain other data
than those composing the basis of the model. If a model is successful, it shows
that the premises (or assumptions) of the model include reality in them even if
the premises (or assumptions) contradict an established principle and can be a
seed to find out a new principle. Bohr’s model of H-atom is a typical example of
the model, which included essence of quantum mechanics.
Even if the logic used to explain facts
successfully is flawless, the model is not necessarily accepted by people who
do not believe in the facts on which the premises of the model based. This
occurred in the history of investigation of the cold fusion phenomenon (CFP).
A3. Hypothesis
A hypothesis or an assumption is a
statement to explain an experimental data, which is not directly (or plainly)
explained by fundamental principles. A statement of a hypothesis may be deduced
from principles or not. In the latter case, the hypothesis may contribute to
find out a new principle as in the case of a model. Planck’s quantum hypothesis
of harmonic oscillator energy is a typical example of the hypothesis played a
decisive role in development of quantum physics.
Sometimes,
there occurs a situation where no dependable principles exist to fit for a
problem. In such a case, new premise(s) (as assumption(s) or hypothesis
(hypotheses) at first) is postulated to explain the problem in hand and the
conclusion of the theory based on the assumed premise is tested by comparison
with experimental data. When the conclusion is consistent with facts, then the
premise is accepted as a new principle of
science and there occurs a revolution of the science. The theory of special
relativity by A. Einstein is a typical example of the theory of this type.
Appendix B. Participation of Neutrons in the Cold Fusion
Phenomenon (Chapter 8 of [2] supplemented after publication)
As
was shown in Chapter 6, a premise of the early researchers in the cold fusion
phenomenon was d – d reactions (5.7) and (5.8) not saying
the reaction (5.9) with a small branching ratio compared with the former by a
factor of ∼10–7.
The trial to detect neutron with an energy 2.45 MeV in a condition of minimum
background (as insisted in the DOE report 1989 [RB5]) had been therefore their
main theme.
On the other
hand, there were a few people put their eyes on the effect of background
neutrons to the cold fusion phenomenon and they obtained positive results with
thermal neutrons. In this section, we introduce those works not historically
but logically first null results without background neutrons and then positive
results of them on the cold fusion phenomenon.
B1. Null Experimental
Results
S.E. Jones in
B1a. Data by S.E. Jones
et al. [RB1]
S.E. Jones had been trying to
check the generation of the 2.45 MeV neutron, gamma and X-ray from the
electrolytic cell used by them in the first report\citref{2} in an underground
laboratory where the background neutron was very few for more than a year.
Their presumption on the cold fusion phenomenon was d-d reactions (5.7) and (5.8), a natural result of Jones' career of
a researcher in the muon catalyzed fusion. Naturally enough from our point of
view, they failed to measure any nuclear products from the cell [RB1] and Jones
turned to criticize positive results of the cold fusion experiments.[RB2]
A null result obtained in an
experiment with a machine named Kamiokande installed in a 1000 m deep mine in
B1b. Data by L. Forsley
et al. [RB4]
L. Forsley et
al. tried to check the electrocatalytic reduction of radioactivity in U and Th
in a low background cave with null results. This result shows again important
decisive role of the background neutron to induce one of various events in the
CF phenomenon.
B1c. Data reported in
DOE Report} [RB5]
In the DOE
Report [RB5] (A Report of the Energy Research Advisory Board to the United
States Department of Energy, November 1989), there had been cited reports from
research groups in Institutions including such large Laboratories listed below
to deduce negative conclusion against CFP. The list of Institutions includes
ANL (Argonne National Lab.), AT&T Bell Labs., BNL (Brookhaven National
Lab.), Caltech, CRNL (Chalk River Nuclear Labs.), GMC (General Motors Corp.),
Harwell Lab. in
These reports with null results on
the excess heat and nuclear products (tritium, neutron and 4He) were
obtained under sophisticated experimental conditions with controlled low
background neutrons to gain high S/N ratio.
Thus, these experiments performed in Institutions with sufficient experts in
relevant branches of science and precise measurement facilities and obtained
null results might be divided into this Section although we have no detailed
data of them.
It is a
simple fact that those experiments showing null results are not disproving the
reality of the cold fusion phenomenon. This is too simple to understand and it
is also self-evident that scientific truth is not determined by popularity or
the decision by majority. This simple fact is sometimes forgotten in public by
some reason and majority of null results are used to deteriorate the cold
fusion research by some pseudo-scientists, with author's regret. A typical
example of this sort was the report at ICCF3,
In
After eleven
years' experiences endeavored by many sincere researchers in the world, we can
say now that the condition to obtain positive results in the cold fusion
research is complicated and is not easy to realize. It is possible to say with
confidence that one of the necessary conditions for the cold fusion phenomenon
is existence of background neutrons. The failure of early experiments done
impromptu was a natural result of rash trial and exclusion of the background
thermal neutrons from the experimental system.
Perhaps, the occurrence of the
cold fusion phenomenon is compared with the birth and growth of typhoon in the
As was
disclosed by investigation of chaos, it is clear that a macroscopic process
occurring in a complex system with a large number of degrees of freedom and
with nonlinear interactions is not absolutely determined by an initial state of
the system but deflect macroscopically by differential changes of microscopic
initial states which can not be fixed macroscopically. We have to see the cold
fusion phenomenon as such.
Now, we will
go further to learn the experimental results obtained with a lot of sun on the
Ocean near the Equator from those obtained in a season without sun.
B2. Effect of Thermal
Neutron
Even though
no cold fusion phenomenon observed in an environment without background
neutron, it is a jumping into a conclusion leading to a mistake if we deduce a
simple and direct relation between the background neutron and the cold fusion
phenomenon. There are, however, several experimental facts which show positive
but complex effects of the background neutron on the cold fusion.
B2a. Data by G. Shani et
al. [RB10]
The first
experimental evidence of an effect of the thermal neutron on the nuclear
reactions in solids was obtained by G. Shani et al. in
From their
result, Shani et al. deduced a conclusion that the cold fusion phenomenon
observed in solids is a result induced by the background neutron with a
negative nuance against its revolutionary character.
B2b. Data by A.A.
Yuhimchuk et al. [RB11]
Another
evidence of the effect of the background neutron on the cold fusion phenomenon
was obtained by A.A. Yuhimchuk et al. in
The
similarity of the two figures obtained in vanadium deuteride and depicted in
Fig. 8.1 shows that the neutron bursts observed and represented in Fig. 8.1 (b)
have been induced by the background neutrons represented in Fig. 8.1 (a). The
characteristic of this similarity in VD1.2 in contrast with effects
in palladium and titanium will be discussed in Chapters 11 and 12 (11.5 and
12.7a).
B2c.
Data by F. Celani et al. [RB12, 13]
F. Celani et al. of INFN
(Instituto Nazionale di Fisica Nucleare) in
B2d.
Data by B. Stella et al. [RB14]
B. Stella et
al. in
B2e. Data by A. Lipson
et al. [RB15,
16]
A. Lipson et
al. in Physico-chemical Institute,
When the number of the irradiated
thermal neutrons was increased to 100 times that of the background neutron,
then the number of the observed high energy neutron increased to 25 times from
4 times that of the irradiated thermal neutrons only when the temperature was
in the phase transition region. This data set show nonlinear dependence of the
neutron emission on the thermal neutron density. The experimental data given above
could be explained by the TNCF model on the same line given in Chapter 11
(11.2a).
Their experiment with a triglycine
sulfate (TGS) showed absorption of the thermal neutron by the sample and the
change of ferroelectricity of the sample. This data is treated in 8.3b in more
detail.
B2f. Data by Y. Oya et
al.
[RB17]
M. Okamoto and his collaborators
in Tokyo Institute of Technology (later in
There are
amazing similarity of the effects of the thermal neutron on the different
substances introduced in this section. It is difficult to conclude that these
results are obtained in accident. We will discuss its meaning in Chapter 11 in
detail.
The
experimental data sets introduced in this chapter seems to tell us that one of
the necessary conditions of the cold fusion phenomenon is existence of thermal
neutrons in the system. This is a background of the TNCF model proposed by the
author in 1995 and grown up to explain various phases of experimental data
obtained in cold fusion systems. The model itself will be explained and used in
Chapter 11 to analyze various experimental data sets of cold fusion events.
Reference to Appendix B.
RB1.
S.E. Jones, D.E. Jones, D.S. Shelton and S.F. Taylor, "Search for Neutron,
Gamma and X-Ray Emission from Pd/LiOD Electrolytic Cells: A Null Results",
Trans. Fusion Technol. 26, 143 (1994).
RB2.
S.E. Jones and L.D. Hansen, "Examination of Claims of Miles et al. in
Pons-Fleischmann-Type Cold Fusion Experiments", J. Phys. Chem. 99, 6766
(1995).
RB3.
T. Ishida, "Study of the Anomalous Nuclear Effects in Solid-Deuterium
Systems", Master Degree Thesis,
RB4. L. Forsley, R.
August, J. Jorne, J. Khim, F. Mis and F. Phillips, “Analyzing Nuclear Ash from
the Electrocatalytic Reduction of Radioactivity in Uranium and Thorium,” Proc.
ICCF7, pp.128 – 132 (1998)
RB5.
DOE Report 1989, Cold Fusion
Research, November 1989－A Report of the Energy Research Advisory Board
to the United States Department of Energy－(DOE Report 1989),
DOE/S-0071 (August, 1989) and DOE/S--0073, DE90, 005611.
RB6.
M. Fleischmann, S. Pons and M. Hawkins, "Electrochemically induced Nuclear
Fusion of Deuterium," J. Electroanal. Chem., 261, 301 – 308
(1989).
RB7.
S.E. Jones, E.P. Palmer, J.B. Czirr, D.L. Decker, G.L. Jensen, J.M. Thorne and
S.E. Tayler, "Observation of Cold Nuclear Fusion in Condensed
Matter," Nature 338, 737 – 740 (1989)
RB8.
Cooperative Research Team of JAERI, “In Search of Cold D – D Nuclear Fusion (I)
(in Japanese), JAERI-M 89-142 (1989)
RB9.
Cooperative Research Team of JAERI, “In Search of Cold D – D Nuclear Fusion
(II) (in Japanese), JAERI-M 90-134 (1990)
RB10.
G. Shani, C. Cohen, A. Grayevsky and S. Brokman, "Evidence for a
Background Neutron Enhanced Fusion in Deuterium Absorbed Palladium", Solid State Comm. 72, 53 (1989).
RB11.
A.A. Yuhimchuk, V.I. Tichonov, S.K.
RB12.
F. Celani, A. Spallone, L. Libaratori, F. Groce, A. Storelli, S. Fortunati, M.
Tului and
RB13.
F. Celani, A. Spallone, P. Tripodi, A. Petrocchi, D. Di Giacchino, P. Marini,
V. Di Stefano, M. Diocianiuti and A. Mancini, "Study of Deuterium Charging
Behavior in Palladium and Palladium Alloy Plates, Changing Surface Treatments
by \mikuro s Pulsed Electrolysis", Proc.
ICCF5 (April 9 - 13, 1995, Monte-Carlo, Monaco), p. 411 (1995).
RB14.
B. Stella, M. Corradi, F. Ferrarotto, V. Milone, F. Celani and A. Spallone,
"Evidence for Stimulated Emission of Neutrons in Deuterated
Palladium", Frontiers of Cold Fusion
(Proc. ICCF3) p.437, ed. H. Ikegami,
Universal Academy Press (Tokyo), 1993.
RB15.
A.G. Lipson, D.M. Sakov and E.I. Saunin, "Change in the Intensity of a
Neutron Flux as It Interacts with a K(SxD1–x)2PO4
RB16.
A.G. Lipson, D.M. Sakov and E.I. Saunin, "Suppression of Spontaneous
Deformation in Triglycine Sulfate
RB17.
Y. Oya, H. Ogawa, T. Ono, M. Aida and M. Okamoto, "Hydrogen Isotope Effect
Induced by Neutron Irradiation in Pd-LiOD(H) Electrolysis", Progress
in New Hydrogen Energy (Proc.
ICCF6), p. 370 (1996).
Appendix C. Premises of the TNCF Model and the
Neutron-Drop Model
C1. TNCF (trapped
neutron catalyzed fusion) Model ([1] Section 3.2)
The TNCF model is a
phenomenological one and the basic premises (assumptions) extracted from
experimental data sets are summarized as follows [C1]:
Premise 1. We assume a priori existence of
the quasi-stable trapped thermal neutrons 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 in a sample is an
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
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 neutron in the free space decays with a time
constant of 887.4±0.7 s (the half-life 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 occurs as if they are in the free
space. We express this property by taking the parameter (the instability
parameter) ξ as 1, which is defined in the relation (3.2-1) written down
below (ξ= 1).
We have to mention here that the instability
parameter ξ in the surface/boundary regions is not known at all and it
can be larger than one (1 <ξ) making the determined value of the
parameter nn smaller (as noticed recently). This ambiguity is
suggested by various anomalous changes of decay characters of radioactive
isotopes and by unexpected fission products in surface/boundary regions.
Furthermore, this characteristic behavior of ξ may be a manifestation of formation of the
cf-matter in the surface/boundary regions as explained in Section 3.7.3, from
our present knowledge of CFP.
Premise
3. The trapped thermal neutron
reacts with another perturbing nucleus in volume by a reaction rate given in
the relation (3.2-1) below with a value of the instability parameter ξ<
0.01 due to its stability in the volume (except in special situations such as
at very high temperature as 3000 K). It is assumed also that the nuclear cross
sections determined in the free space are applicable to reactions between the
trapped neutrons and other nuclides. (This premise corresponds to the cf-matter
without neutron drops in volume of samples, in the recent neutron drop model.)
Following common 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 sample solid. The same is for the distribution of a 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 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 individual nuclear reactions in the
sample indirectly and are the indirect information of the individual
events.
Premises about the 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) will be taken as ℓ = 1 μm (though the experimental
evidence shows that it is 1 - 10 μm).
Premise
9. The mean free path or path
length ℓt of the triton with an energy 2.7 MeV generated by
the n - 6Li fusion reaction will be taken as ℓt
= 1 μm 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 the free space.
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 detectors
in experiments if there is no description of their efficiencies.
A premise will be made to calculate the number of
events NQ producing excess heat Q.
Premise
11. In the calculation of the
number of an event (a nuclear reaction) NQ producing excess
heat Q, the average energy liberated in a reaction is assumed as 5 MeV
unless the reaction is identified:
NQ =
Excess heat Q (MeV)/ 5 (MeV).
C2. Neutron Drop Model
([1] Section 3.7)
When
there are neutron drops in cf-matter formed around surface/boundary regions by
the mechanism discussed above, we can use the neutron drop AZΔ and a small
neutron-proton cluster AZδin the nuclear reactions as a
simultaneous feeder of several nucleons to nuclides;
AZΔ+ A’Z’X
→ A – a Z– zΔ+ A’ + a Z’ + zX’*,
→ A – a Z– zΔ + A’ + a– a’ Z’ + z– z’X’’+ a’z’X’’’,
(3.7-18)
A’Z’Δ+ A+ 1 ZX*
→ A’Z’Δ* + A +
1ＺX → A’Z’Δ+ A + 1ＺX + x,
(3.7-19)
A’Z’δ+ AZX
→ A + A’Z + Z’X* → A + A’Z +
Z’X + x.
(3.7-20)
The neutron-proton
cluster AZδ is supposed to be a unit of nucleons absorbed
at the same time by a nuclide to form a new nuclide as in Eq. (3.7-20).
In the reactions
(3.7-19) and (3.7-20), the symbol x means not a γ photon in the free space but
another particle (a neutron or a neutron-proton cluster) in cf-matter [C2].
References to Appendix C
RC1. H. Kozima, Discovery of
the Cold Fusion Phenomenon (Ohtake Shuppan Inc., 1998). ISBN 4-87186-044-2.
The “References” in this book is posted at the Cold Fusion Research Laboratory
(CFRL) Website; http://www.geocities.jp/hjrfq930/Books/bookse/bookse.html
RC2. Kozima, H., “Quantum Physics
of Cold Fusion Phenomenon,” Developments in Quantum Physics Researches –
2004, pp. 167 – 196, ed. V. Krasnoholovets, Nova Science Publishers, Inc.,
References
1.
H. Kozima, The Science of the Cold Fusion
Phenomenon, Elsevier Science, 2006. ISBN-10: 0-08-045110-1. Table of
References of this book is posted at following pages of the CFRL website;
http://www.geocities.jp/hjrfq930/Books/bookse/bookse03/bookse03ref.htm
2.
H. Kozima, Discovery of the Cold Fusion
Phenomenon, Ohtake Shuppan,
http://www.geocities.jp/hjrfq930/Books/bookse/bookse01/refer1.htm
3.
E. Storms, The Science of Low Energy
Nuclear Reaction – A Comprehensive Compilation of Evidence and Explanations
about Cold Fusion –, World Scientific,
4. M. Fleischmann, S.
Pons and M. Hawkins, "Electrochemically induced Nuclear Fusion of
Deuterium," J. Electroanal. Chem., 261, 301 – 308 (1989).
5. A.J. Leggett and G. Baym,
"Exact Upper Bound on Barrier Penetration Probabilities in Many-Body
Systems: Application to 'Cold Fusion',” Phys. Rev. Letters, 63,
191 - 194 (1989).
6.
M.A. Alberg, L.
Wilets, J.J. Rehr and J. Mustre de Leon, “Upper Limits to Fusion Rate of
Isotopic Hydrogen Molecules in Pd,” Phys. Rev. C41, 2544 (1990).
7.
8.
Hideo Kozima, “Complexity in
the Cold Fusion Phenomenon” Proc. ICCF14 (August 10 – 15, 2008,
9.
H. Kozima, “The Cold Fusion Phenomenon as a Complexity (1) – Complexity in the
Cold Fusion Phenomenon” Proc. JCF6,
pp. 72 – 77 (2005) and also Reports of
CFRL (Cold Fusion Research Laboratory), 7-1, pp. 1 – 7 (2007);
http://www.geocities.jp/hjrfq930/Papers/paperr/paperr.html
10.
H. Kozima, “The Cold Fusion Phenomenon as a Complexity (2) – Parameters
Characterizing Cold Fusion Systems” Proc.
JCF8, pp. 79 – 84 (2008) and also Reports
of CFRL (Cold Fusion Research Laboratory), 7-2, pp. 1 – 8 (2007);
http://www.geocities.jp/hjrfq930/Papers/paperr/paperr12.pdf
.
11.
H. Kozima, “The Cold Fusion Phenomenon as a Complexity (3) – Characteristics of
the Complexity in the CFP“ Proc. JCF8,
pp. 85 – 91 (2008) and also Reports of
CFRL (Cold Fusion Research Laboratory), 7-3, pp. 1 – 7 (2007);
http://www.geocities.jp/hjrfq930/Papers/paperr/paperr13.pdf