Deflation Fusion
Speculations Regarding the Nature of Cold Fusion
Horace Heffner October 17, 2007
PURPOSE
It is intended here to advance potential mechanisms underlying the
production of cold fusion and low energy nuclear reactions (LENR).
The possible existence of such mechanisms suggests new experiments
and improved techniques that may lead to a better understanding of
some of the anomalous behavior of these reactions, like unusual
branching ratios. It is also intended to derive some engineering
principles to utilize the mechanisms.
ELECTRON SCREENING IN FUSION REACTIONS
The term “electron screening” when applied to fusion reactions
typically has two meanings.
One type of electron screening is the effect of the distribution of
charge in the electron wave functions of orbital electrons between
two hydrogen nuclei. The charge of a single orbital electron is
spread over a large volume, compared to nuclear distances, thus this
screening is very tenuous. The electron screening in a hydrogen
molecule actually thins out if the two nuclei are brought closer
together than their average separation distance, thus increasing
their mutual repulsion, and restoring the molecular shape. This
orbital electron screening requires long tunneling distances of the
hydrogen nucleus to achieve fusion, due to the large size of the
orbital in comparison to the nucleus.
Another kind of electron screening can occur when most of the wave
function of one or two free electrons gets between two hydrogen
nuclei. This can only happen if the screening electron de Broglie
wavelength is small, therefor the momentum and thus energy of the
screening electron is high, well over 2000 eV. This kind of electron
screening happens with great frequency only in very hot dense
environments.
Electron screening fusion reactions can be called electron catalyzed
fusion. Proposed here is a third kind of electron catalyzed fusion,
called deflation fusion. It is not an electron screening reaction.
It is fusion occurring as the result of a multi-body quantum wave
function collapse simultaneously involving electron(s) and hydrogen
nuclei, especially deuterons. Wave function collapse is a term which
has meaning depending on the quantum interpretation invoked.
Regardless of interpretation, as applied here, it is a very real
phenomenon. Consider the electron capture reaction. An electron
with a wave function covering a volume thousands of times that of a
nucleus suddenly collapses to become part of the nucleus when the
electron capture reaction occurs. Similarly, in the photoelectric
effect, a photon from across the universe, having a wave function of
very large size, can collapse its entire energy and momentum onto one
tiny electron on one atom in order to eject it from its orbital. An
electron on one side of a Josephson junction has a wave function that
initially extends to the other side of the junction with only a small
(volume integral) probability. Yet, depending on the width of the
junction and the potential across the junction, once the electron
tunnels across, it builds a newly centered (center of mass) wave
function having a small probability of being where it was on the
other side. These are three examples of wave function collapse, where
a quantum wave function can suddenly change both location and locus
probability distribution dramatically. Such quantum wave function
collapse can happen and indeed happens when it is energetically
favorable for either electrons or nuclei.
Typically in deflation fusion the wave functions of an electron and
two hydrogen nuclei momentarily collapse into a small volume, their
centers of mass being co-located, to create an intermediate state.
Weak and/or strong nuclear reactions may occur in this intermediate
state. This process differs from an electron screening process,
where the screening occurs prior to tunneling, and does not involve
an electron in the nucleus. A key ingredient to making deflation
fusion occur is stressing the electron wave function so as to make
its collapse with two nearby nuclei energetically favorable. Another
key ingredient is creating a configuration in which it is more
energetically favorable for two nuclei to tunnel to an electron, or a
nucleus to tunnel to a nucleus-electron pair in close proximity,
than for the electron to tunnel toward one of the nuclei.
TWO BODY WAVE FUNCTION COLLAPSE
An electron wave function collapse upon a single nucleus, followed
by reverse tunneling, is much more likely than the 3 body events
discussed above, but it is an unnoticed event, an event without any
"ash" or consequences. When the reverse tunneling occurs, the final
state is identical to the initial state. Neutron creation is
energetically not favored from the two body event, because a neutron
has more energy than an electron plus a proton, and also because
neutron creation is a weak force interaction. A weak force
interaction is improbable, even if an energetic neutrino or energetic
nucleus supplies the energy, because weak reactions require a long
exposure time. Typically tunneling is a two way possibility. All
else being equal, the smaller the probability of a "tunneled to"
volume, the less apparent time available in that small volume state.
Still, the apparent time in even a very small probability state is
finite, and thus interactions, like strong or weak force
interactions, other tunneling, etc., are made possible from that
state, and their probabilities depend on the apparent percentage of
time in that state. This is how electron capture happens, which is
energetically favored in some nuclei, but not protium or deuterium
nuclei. Note that, for the sake of simplicity, tritium will not be
mentioned here except to note that it is essential to eventually test
any effective cold fusion cell type with a 50-50 deuterium-tritium mix.
Some quantum interpretations see the electron as a point particle and
its quantum waveform as in effect a probability distribution for its
whereabouts. More accepted interpretations see the quantum waveform
as merely a potentiality of particle existence in a given volume,
without actual existence unless a measurement is performed. This
latter view appears to the author to be wrong at least to the extent
portions of the quantum waveform, any selected volume of the electron
quantum waveform that is, exerts force as if there were partial
charge located in that volume, and the proportion of effective charge
in that volume corresponds to the electron occupation probability for
that volume. This apparent partial waveform charge accounts for
location of the nucleus at the "center of charge" of an atom,
dislocation of the center of charge in an electric field, the
converse effect, i.e. the piezoelectric effect, and electron
screening in hydrogen molecules.
A momentary state exists periodically for hydrogen nuclei and nearby
electrons in which a single small wave function exists for that state
and the nucleus plus electron can act as single small intermediate
state particle. (This state may be viewed alternatively under some
interpretations as a coexisting state, a partial existence
potentiality, or a state which manifests on observation with some
finite probability. ) Call this small wave function state a
deflated hydrogen state. That state, or particle, formed some times
under observation and wave function collapse, is not a neutron, not
a di-neutron, not a hydrino, not a hydrex,1 and not a protoneutron
as in the Mitchell Jones theory as discussed first on the newslist
sci.physics.fusion. The deflated hydrogen state differs from the
above listed particle concepts in that it represents a partial form
of existence of the involved electron-hydrogen nucleus pair. The
deflated hydrogen state (at least upon observation) exits for time
intervals in the attosecond range, but it is repeated at a high
apparent rate. Depending on the strength of the bond or resonance of
the deflated hydrogen state, this momentarily bound state may be an
intermediate state preceding deflation fusion. In other words, a
three body wave function collapse may consist of a multistage
process, a two body collapse to a deflated hydrogen state, possibly
followed by some very small attosecond order duration of motion of
the neutral charge deflated hydrogen, followed by tunneling of the
intermediate state particle to a second nucleus, or vice versa, or
even tunneling to or with a lattice nucleus. Cold fusion engineering
then consists of designing ways to increase the probability of and
thus the proportion of existence of the deflated state hydrogen, and
thus the probability of deflation fusion, or of increasing the
probability of multi-body wave function collapse.
Now that the deflated hydrogen state has been defined, it is easy to
see the ideal configuration to engineer is one in which tunneling
tends to occur in the deflated state, or tunneling to a site
momentarily occupied by a deflated state hydrogen tends to occur.
This is cold fusion.
It is not known the strength of the bond of the deflated hydrogen
state, or its distribution, and thus the respective probabilities of
one stage or two stage multi-body wave function collapse. It is
likely the bond is very weak and variable because the deflated
hydrogen state occurs extremely frequently and periodically. It
might be expected the deflated state happens with a probability being
roughly equal to the probability of the electron being in or highly
proximal to the hydrogen nucleus. The probability may in fact have
been observed to be much higher than this though. The deflated
hydrogen state may indeed provide an explanation for the missing
proton problem. 2 3 The probability of the deflated hydrogen state
in water and other compounds may be as high as 0.25. When viewed in
attosecond time frames, water is H1.5O, not H2O.
The electron hops into and out of, or otherwise coexists in, the
deflated hydrogen state without any change in energy or apparent
radiation. One way to visualize this state is that it is a partial
state of the involved electron which is not observed unless wave
function collapse occurs which precipitates a strong force reaction
fusion event with another nucleus, or interaction occurs with a
photon or particle, one possibly used to sense the state, or at least
lack of interaction from the state.
Another way to view the deflated state is it is a brief state which
is both energetically permitted and then ended by zero point field
interaction. As with the orbital itself, there is thus no resultant
radiation due to electron acceleration. Heisenberg is not violated
because the time intervals are so brief.
An electron easily tunnels back and forth between an orbital state,
or partial orbital state, and a deflated hydrogen state, i.e.
coexists in those states, because it is energetically possible. In
normal circumstances the deflated hydrogen state is not observed
because it is so brief, though with new technology it may be observed
because the deflated hydrogen state is neutral, thus the hydrogen
nucleus can in effect momentarily disappear periodically, or with
some probability, to a photon, neutron, or electron beam. There is
nothing that traps the electron in the nucleus in the deflated
hydrogen state because the potential energy change due to charge
location is offset by the uncertainty energy, in essence the energy
required to confine the electron to a small volume, zero point
energy. However, this energy balance changes if deflation fusion
ensues, because there are then two positive charges in the nucleus,
and the electron must inflate its way out of this fused nucleus by
accumulating zero point energy, and it radiates in the process.
It is reasonable to discuss or treat multi-body tunneling as a single
event or process because a two stage deflation fusion process in
which a deflated hydrogen is involved is essentially
indistinguishable in outcome from a single stage multi-body
collapse. Both can occur in attosecond range time intervals.
WHY KINETIC FUSION IS UNAFFECTED
The very brief existence of the deflated state explains why
kinetically induced fusion can not make use of the Coulomb barrier
being down , because there is insufficient time for a motional
approach of two nuclei before the barrier is back up. Even at an
energy of 2000 eV the proton has a velocity of 6x105 m/s, thus
travels only 6x10-13 m per attosecond. This is not enough to affect
to a practical degree the tunneling rate for hot fusion.
ELECTRON FUGACITY
Much discussion has occurred in the cold fusion (CF) and low energy
nuclear reaction (LENR) literature regarding the importance of
achieving high D/Pd atomic ratios, i.e. high hydrogen loading in CF
cathodes, and thus high hydrogen fugacity. Fugacity is similar to
pressure in that it is a measure of the energy required to add an
additional particle to a system. 4
Much work in the cold fusion field has, from early on, focused on the
difficulty of achieving high hydrogen fugacity5 because lattice
imperfections exist, electrode metals fail, diffusion occurs into
cracks and occlusions6 , and other sources of hydrogen loss exist.
Some work has focused on the importance of superimposed electrostatic
fields in or on cathodes, specifically that of S. Szpak, P. A. Mosier-
Boss, F. E. Gordon.7 This work noted structural and morphological
changes in electrode structure, dendrite growth, etc., in the
presence of strong electrostatic fields.
Despite an intense focus on hydrogen fugacity, and some work related
to superimposed electrostatic fields, no work has focused on electron
fugacity. This is a complex area due to the quantum mechanical
requirement for degenerate electrons to occupy ever higher energetic
states once their density passes a critical value, and no conduction
electron is free to "move" statistically speaking. 8
One aspect of achieving high loading coefficients is that conduction
band electrons, which are ionically bound to the adsorbed hydrogen in
the lattice, are bound to a specific location when the adsorbed
hydrogen reaches saturation and thus can no longer diffuse. In fact,
one means of measuring cathode loading is to measure cathode
conductivity. A key aspect of achieving high electron fugacity then,
when no other means is applied or even known to be of use, is to
achieve loading to the point no diffusion can occur. Cracked
electrodes, lattice imperfections, unsealed exposed surfaces, and
anything else that permits hydrogen diffusion leakage decreases
electron fugacity as well.
As hydrogen is loaded into Pd at a given temperature the conductivity
decreases to about H0.8Pd, and then increases with increased loading.
9 Beyond this point long range electron waveform interaction
appears to become significant. More importantly, the sensitivity of
lattice resistance to temperature begins to increase, especially near
H9.5Pd loading, due to the increased sensitivity of the energetic
long range electron wave function interaction to thermal disruption.
This suggests the possible utility of loading at high temperatures
and then reducing temperature to establish high electron fugacity and
the energetic long range electron wave functions capable of energy
focusing. In any event, these facts strongly indicate that both
conductivity and its relation to temperature should be studied in
relation to induced surface charge in thin films, and the existence
of the deflated hydrogen state should be investigated in relation to
these variables.
Though electron fugacity is highly related to hydrogen fugacity, they
are not synonymous. Electron fugacity at the surface of a metal
conductor clearly can be increased by increasing the magnitude of the
negative potential of the metal. This increase of negative potential
is synonymous with an increase in electron surface density. Excess
itinerant electrons migrate to the surface of a metal conductor - to
a point. When conduction bands at the surface fill up, addition
excess electrons are forced to lower levels. At very negative
potentials, orbitals of surface atoms deform out into the space
beyond the normal surface. When complete hydrogen saturation occurs
in a loaded cathode, additional conduction band electrons are forced
to occupy locations within the volume of the conductor. Therefore
the conduction bands at the surface fill up, pushing the excess
conduction band electrons deeper into the metal.
If sufficient electron fugacity is achieved in a given volume of a
lattice, then the addition of more electrons results in a higher
energy state of the electrons, not a higher temperature of the
electron "gas". It is at this point fusion may possibly be
catalyzed by electron fugacity. Increased electron quantum state and
reduced wavelength assists electron catalysis of fusion. The common 3
body tunneling deuteron reaction probabilities are energetically
increased:
D + e- + D ---> He + e- + energy
D + e- + D ---> T + p + e- + energy
D + e- + D ---> 3He + p + e- + energy
These reactions involve the simultaneous 2 body tunneling of an
electron and deuteron to the location of another deuteron, or vice
versa, i.e. a three body reaction. Similar reactions can involve
other isotope pairs or multiple isotope-electron reactions. When the
fugacity of both hydrogen and electrons reaches a critical point, the
addition of more energy to the lattice results in fusions. This is
an energy focusing effect. An increase in the group energy state,
i.e. group fugacity, can result in a pressure outlet involving only a
few members.
Note that the eventual escape of the catalytic electron from the
newly fused nucleus reduces the resultant nuclear temperature. The
electron populated nucleus can radiate. The branching ratios from an
electron catalyzed reaction will therefore differ from those of a
kinetic fusion reaction which does not involve a catalytic electron
in the initial bound state.
High surface electron fugacity of a cathode can be achieved by
increasing the negative potential of the cathode, and thus the
electrostatic field at the cathode surface. It can also be increased
in small locations by a bumpy or dendritic cathode surface.
An alternative way, or more importantly an incremental way, to
increase the electric field strength at an electrode surface is to
bounce a laser beam off of it at a low angle of deflection. Laser
stimulation of a very highly negative potential cathode surface may
work in a gas environment, provided the surface out gassing is
controlled by choice of a surface material with a low hydrogen
permeability and which sustains both a high hydrogen and high
electron fugacity by presenting an appropriately strong barrier to
diffusion. Such a surface can be fed adsorbed hydrogen via a proton
conducting backing like palladium. Laser stimulation of fusion on a
cathode surface in the presence of a magnetic field is well known and
is called the Letts-Cravens Effect.10 11
DEFLATED PAIRED STATE
In a high electron fugacity environment, excess electrons can be
expected to form pairs with other conduction band electrons,
including those which are ionically bound to hydrogen nuclei. These
pairs consist of electrons occupying the same quantum state with the
exception of opposed spins. Such a paring in fact creates a weak
bond between the paired state electrons. The existence of such pairs
in a highly loaded lattice provides a credible explanation for
increased conductivity at high electron fugacities, as well as the
increased sensitivity of conductivity to thermal disruption, though
this hypothesis requires experimental validation, especially at in
cathodes with high backside potentials. At high loading,
conductivity should vary depending on both temperature change and
large swings in cathode potential. The existence of weakly bound
paired electrons increases the probability of a deflated paired
state. In such a state two small wavelength electrons exist in the
nucleus. Such a state, having a negative charge, has a vastly
increased probability of tunneling to other nuclei, and of being a
target for tunneling nuclei.
SURFACE POTENTIAL
Surface potential at a conductor surface point P is defined here to
be with respect to the surface of some small volume (dx)3 of a
neutral matter, where there is no intervening conductive surface
surrounding P and separating P from the neutral matter. Neutral
matter is matter having an equal number of positive and negative
charges. Establishing and measuring potential in this context is
critical in achieving a desired or even known electron fugacity.
For this reason, conducting LENR experiments in Faraday Cages is
essential. The small volume of neutral matter that defines zero
potential can then be located within the Faraday cage metal itself.
It should be sufficient to use a grounded Faraday cage as ground
potential, i.e. potential zero, to achieve the electron fugacity
goals for various experiments.
BRANCHING RATIOS
If sufficient electron and deuteron fugacity is achieved the
probability of a three body electron tunneling reaction is
energetically increased. When the fugacity of both hydrogen and
electrons reaches a critical point, addition of more energy to the
lattice results in fusions. This is an energy focusing effect. An
increase in the group energy state, i.e. group fugacities, results in
a pressure outlet involving wave function collapse of relatively few
members, resulting in deflation fusion. Let us examine how this
deflation fusion process might change branching ratios.
The following are standard D + D hot fusion branching ratios:
D + D --> T(1.01 MeV) + p(3.03 MeV) (4.03 MeV, 50%)
D + D --> 3He(0.82 MeV) + n(2.45 MeV) (3.27 MeV, 50%)
D + D --> 4He( 76 keV) + gamma (23.8 MeV) (23.9 MeV, 1x10^-6)
The initial effect of an electron in a newly fused nucleus is to
reduce its potential energy in comparison to a hot fusion created
nucleus. The tunneling of two deuterons and an electron to a point
is the result of a wave function collapse. The amount of energy lost
in the wave function collapse is dependent on the size of the
combined intermediate result, which is a random variable.
From the electric potential energy Pe for separating an electron
from two deuterons we have:
Pe = k (-2q)(q)(1/r) = (2.88x10-9 eV m) (1/r)
which we can rearrange to obtain r for a given potential energy,
r = (2.88x10-9 eV m) (1/Pe)
and we have for 23.9 MeV:
r = (2.88x10-9 eV m) (1/(23.9x106 eV))
r = 1.2x10-16 m
which is about 10 times the diameter of a quark, and thus in the
realm of credibility. It is feasible for the wave function collapse
to initially consume all the available fusion energy.
If the three interacting particles collapse to a point, or even to
quark size, then all the 23.9 MeV available from ordinary hot fusion
(and more) is consumed. This is certainly an energetically favorable
tunneling reaction. Further, given that the collapsed intermediate
nucleus radius is variable in size, according to some probability
distribution, various total energy amounts are available per
reaction. We can also see that the neutron producing reaction, D + D
--> 3He + n, having the least energy available from the fusion
reaction (3.27 MeV), would necessarily be the least likely branch
path. Thus it is clear how the electron catalyzed deflation fusion
produces an initially cool nucleus, and favors the reaction D + D -->
He. However, the nucleus can't stay cool. The confined electron
gains energy from the vacuum, and from its immediate neighbors, which
also gain zero point energy due to the small nucleus size.12 The
electron gains zero point energy until it has sufficient energy to
tunnel out, and possibly take some kinetic energy with it also. In
the process of the electron gaining energy, while it is confined with
the nucleus hadrons and experiencing accelerations within the
energetic nucleus, the nucleus can be expected to radiate. This is
the bulk of the energy of cold fusion, of electron catalyzed
deflation fusion - protracted low energy gammas and beta radiation.
The most likely product is helium, and the second most likely
product, though comparatively rare, is tritium. The least likely
products are helium-3 and neutrons, though trace amounts of these
products are produced.
References and rich text version at:
http://www.mtaonline.net/~hheffner/DeflationFusion.pdf
Horace Heffner
http://www.mtaonline.net/~hheffner/
