Branch Ratio Variance and Deflation Fusion Oct, 2009
If any byproduct of a fusion event, such as a neutron, is formed on a
stochastic basis, i.e. having energy or observed frequency
representing a sample from a random distribution, then other products
of the same fusion process must also be forming in a stochastic
basis. Descriptions of such events and products then are best
specified using probability distributions, i.e. stochastic
variables. The proportions of product types produced from fusion are
random variables, thus indicating underlying stochastic processes.
The proportions of byproducts produced from given inputs to fusion
events, i.e. the branching ratios, are stochastic variables affected
by the environment and circumstances in which the fusion occurs. One
of the most distinguishing differences between hot and cold fusion
are their branching ratios, the probability of a given reaction
pathway. It is well known that in deuteron-deuteron fusion, (D-D
fusion) that the D(D,p)T and D(D,n)He3 reactions are suppressed in
the cold fusion variety of reactions, leaving the D(D,gamma)He4
reaction to dominate, but with the gamma energy released in small
difficult to detect increments, possibly spread throughout the
condensed matter lattice which makes cold fusion possible. The
energy released by cold fusion is thus difficult to measure except
through calorimetry.
The varying of the branching ratios for D-D reactions, between hot
and cold fusion, indicates stochastic variables are at work in the
process. A key variable appears to be the mean net reaction
energy. In order to suppress the D(D,p)T and D(D,n)He3 reactions,
and drive most everything toward the D(D,gamma)He4 reaction, the mean
energy available from cold fusion must be offset in the negative
direction from that available from purely kinetic fusion. We can see
this from the energy available from each of the hot fusion branches:
D(D,p)T 4.03 MeV
D(D,n)He3 3.27 MeV
D(D,gamma)He4 23.9 MeV
If the D(D,gamma)He4 branch is highly favored and the D(D,p)T and D
(D,n) He3 reactions highly suppressed, it is reasonable to expect the
lower energy branches are being energetically suppressed by a lack of
energy to make them feasible. This requires an energy deficit to
occur in the combined intermediate reaction state designated here as
He*. He* is the intermediate state just prior to branch selection
mechanics taking effect. Highly suppressing both the D(D,p)T and D
(D,n)He3 reactions requires a mean energy deficit greater than 4 MeV.
Assume for a moment the energy of He* in a cold fusion reaction is
somehow offset by a random variable E(m,s) having a distribution with
mean m and standard deviation s which are functions of the
environment and circumstances of the reaction, and m is a negative
number, an energy deficit. That is to say the branch selected is
determined or limited in frequency by energy Q' = Q + E(m,s), where E
(m,s) is due to the circumstances of the reaction and m is negative.
It is suggested here that E(m,s) exists for cold fusion reactions,
and therefore E(m,s) is not related to any high energy kinetics of
the reactants. Further, E(m,s) results from energy transactions with
the vacuum, and varies across time throughout the reaction, and may
result in an apparent violation of conservation of energy at the
completion of the reaction. Note that there therefore can also be a
fourth hidden branch to the D-D reaction, D(D,D)D, i.e. one where no
reaction occurs even though the intermediate state He* forms, or
approximately forms. Such a pathway only has meaning if the vacuum
energy involved does not net to zero. Such a null product reaction
is more likely to be meaningful and probable for prospective weak
reactions or interactions, like p(p,p)p, which may be responsible for
excess heat production in nickel-hydrogen experiments, but outside
the scope of this discussion.
The energy variability, as described by the magnitude of s, arises
from vacuum phenomena. In part it arises from the nuclear
temperatures of the inputs to the reaction, which have Boltzman
distributions. Nuclear temperatures are sustained by uncertainty.
See: Heffner, "Nuclear ZPE Tapping", May 2007,
http://mtaonline.net/~hheffner/NuclearZPEtapping.pdf
Beyond this input variability, an additional mechanism has been
proposed to cause variability, the size of the He* that results from
the tunneling and wave function collapse that results in cold
fusion. This is described in: Heffner, "Speculations Regarding the
Nature of Cold Fusion", October, 2007,
http://www.mtaonline.net/%7Ehheffner/DeflationFusion2.pdf
An additional variability in the apparent net reaction energy is the
amount of nuclear heat left remaining in the reaction products. It
is notable that the heat in the input nuclei adds to the net energy
of the reaction, while the heat in the product nuclei and the heat
given to the vacuum, in the fusion producing wave function collapse,
subtract from the net energy of reaction, but all these factors
contribute to the variability of the reaction energy.
If in a given environment we suppose m = -5 MeV, and s = 0.25 MeV, we
can see the mean resulting energies available from a D-D fusion event
is given by
D(D,p)T -0.97 MeV
D(D,n)He3 -1.73 MeV
D(D,gamma)He4 18.9 MeV
We can thus see why the D(D,p)T and D(D,n)He3 branches would be
suppressed, and why the D(D,gamma)He4 average energy to be sensed by
calorimetry would be less than 23.9 MeV per helium atom produced.
Further, we can see that tritium production would be a 4 sigma
exception event, and neutron production would be a 7 sigma exception
event. The mean apparent energy produced per reaction would be Q' =
18.9 MeV, assuming the deficit energy is not returned in whole or in
part from the vacuum, by some mechanism, subsequent to or independent
of the branch determination mechanics. Knowing the branching ratios
in a given environment then provides a means of computing m and s.
It is notable that slight changes in either m or s can result in
dramatic effects on the observed branching ratios.
The small wavelength electron(s) trapped in the post fusion He*
nucleus are able to return some energy, which is continually acquired
from the vacuum in the form of nuclear heat, by radiating while they
acquire enough wavelength, i.e. size, to escape the nucleus and gain
orbital status. It is also feasible that vacuum transactions, such
as the creation of neutrinos, can siphon off trapped electron energy,
and thus some of the final heat detectable by calorimetry.
Therefore, m can not be determined simply by measuring the enthalpy
of cold fusion reactions.
Note that the average energy deficit does not have the same negative
magnitude (i.e. m is not a large negative value) in hot fusion
reactions because there is no electron in the excited He*
intermediate product reducing the amount of available potential
energy. A catalytic electron has an influence on both the kinetic
and potential energy of the nucleus, and this influence varies with
time. In addition, the input particles to a hot fusion event have a
high kinetic energy which is needed to overcome the Coulomb barrier.
That energy compresses the nuclear electrostatic field prior to final
tunneling and the energy of that field compression is released as
heat when the tunneling and fusion occurs. When cold fusion occurs
the event is initiated by tunneling of a neutral entity, deflated
hydrogen, over a much longer distance that the tunneling that
produces hot fusion.
The lattice is important to cold fusion because it creates an
environment where the electron can have a high frequency of
occurrence in the nucleus. Cold fusion in a vacuum or plasma
environment is unlikely because the deflated state, the electron in
the hydrogen nucleus, exists too briefly for the kinetic approach of
a charged nucleus to the deflated nucleus or vice versa. The deflated
state is too brief to provide electron catalysis for high energy
vacuum collisions except at energies so extreme fusion is otherwise
expected. The deflated state might be created with significant
frequency in a plasma magnetic pinch with sufficient current density.
Deflated state particles, being neutral, have only magnetic energy,
dipole attraction, to make their long range tunneling feasible, thus
when they tunnel their most likely targets are the much closer
lattice nuclei, which present no Coulomb barrier to them. The
catalytic electrons in that case, i.e. the case of lattice element
fusion, should tend to end up undergoing a weak reaction, so the
event amounts to a neutron addition to the lattice element. Lattice
site to lattice site hydrogen tunneling (diffusion) is Coulomb
repulsion driven. The sites to which hydrogen atoms are driven to
tunnel to are either unoccupied by hydrogen or momentarily occupied
by deflated state hydrogen. There is thus typically only one
catalytic electron per fusion.
In the deflated state the electron has the kinetic energy to hop back
to its chemical energy orbital existence. However, if a deuteron
tunnels to the deflated state deuteron, fusing, the charge of the
nucleus just doubled. The electron is now energetically trapped in
the deflated state. The energy it subtracts from the nucleus depends
on the distance of the electron from the nucleus at the time of the
collapse, i.e. its size, which is a random variable.
From the electric potential energy Pe for separating an electron
from two newly fused deuterons at radius r 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
In other words, the full energy of the fusion can be removed by the
presence of an electron of this size. Given the kinetic energy of
the deflated state electron the product of the wave function collapse
would have to be half that size to momentarily absorb all the energy,
but this is not important because the deflated state electron would
instantaneously begin to expand and radiate due to vacuum energy, the
energy of uncertainty.
Though it is brief, the deflated state repeats rapidly enough (has
sufficient observation probability) when in an appropriate lattice
environment to make fusion observable. This assumption is based on
the experimental evidence that water becomes H1.5O (as opposed to
H2O) when observed by sufficiently fast sensing methods, i.e. at
attosecond speeds.
The deflated state may not be a true "state" at all in the
conventional sense. It is merely easy to conceptualize in that
fashion. Quantum waveforms only speak of potentialities for
existence with associated probabilities, not necessarily true
existence. In the lattice the deflated state is a dual state with
the orbital state. It merely has some probability of observing upon
wave function collapse. There may even be no observable velocity or
duration for change of state. The same might be said for the fusing
of the nuclei. Prior to the fusion, the possibility of the fusion
may only be a potentiality that manifests with some probability.
The wave function collapse itself is clearly theoretically likely to
be able to exceed the speed of light, because the quantum wave
function of a particle theoretically extends to infinity.
It may take string theory to fully understand cold fusion. However,
it is fairly easy to understand how electron catalysis reduces the
mean energy available from fusion, and how that affects the branching
ratio of cold fusion vs hot fusion. The effect of the catalytic
electron is difficult to detect in D-D fusion reactions. However,
manifestations of the difference in E(m,s) in cold fusion reactions
may be revealed in tritium fusion (e.g. T-D reactions) because high
energy neutrons are always produced, high enough energy that their
energy spectrum should reveal the presence of a negative m resulting
from electron catalyzed fusion.
One of the most useful experimental techniques, not so much for
generating energy, but for diagnostic purposes, might be light
tritium doping. Consider the SPAWAR article:
http://www.springerlink.com/content/022501181p3h764l/
"The presence of three alpha-particle tracks outgoing from a single
point is diagnostic of the 12C(n,n′)3alpha carbon breakup reaction
and suggests that DT reactions that produce ≥9.6 MeV neutrons are
occurring inside the Pd lattice. To our knowledge, this is the first
report of the production of energetic (≥9.6 MeV) neutrons in the
Pd–D system."
This is a peer reviewed article by credible researchers. Their data
and conclusion should be taken seriously.
There in fact is experimental data corroborating the lattice DT
hypothesis feasibility. Here is an article relating to T2O + D2O
electrolysis with some rare (8 +-4 counts per second) 10 MeV plus
neutrons found: Quote:
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Rusov VD, Zelentsova TN, Semenov MYu, Radin IV, Babikova
YuF Kruglyak YuA;
Pis'ma Zh. Tekh. Fiz. 15(#19) (1989) 9--13 {In Russian}
"Fast neutron recording by dielectric track detectors in a palladium-
deuterated -tritiated water system in an electrolytic cell".
** Experimental, alloy, electrolysis, neutrons, res0
Used a 50:50 mix of D2O and T2O, a "corrugated" alloy
(Pd 72, Ag 25, Au 3) electrode, 10 mA/cm**2 and
"200 V" cell voltage (no electrolyte!). A polymer
track detector (CR-39) (1-5 E-04 track/n sensitivity)
was used to detect the integrated neutron flux from
possible cold fusion of light nuclei. Some rare
high-energy (>10 MeV) neutrons (8+-4/s) were found.
071989|101989
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
End quote.
The above summary was taken from Dieter Britz's site:
http://www.chem.au.dk/~db/fusion/alpha_R
The above experiment provides a solid indication of a nominal amount
of D-T fusion even though there is no indication whatsoever that
proper lattice conditions for cold fusion were established. If
repeatable, that is a landmark achievement because it proves fusion
from chemical conditions. Hopefully with what is known today the
results can be greatly improved.
The SPAWAR data does indeed suggest high energy neutrons from a DT
reaction. The source of the tritium in SPAWAR experiments logically
can be expected to be DD fusion, and thus of a low probability
because the concentration of tritium (or possibly some form of
tritium precursor) is very low. It should be no surprise that tritium
can be produced in small quantities via cold fusion reactions.
The conclusion of the Boss et al article implies the need for
repeating exactly the same experiment using D2O + T2O (actually just
a trace amount of TDO) instead of just D2O. If the flux of high
energy neutrons does not increase, then the conclusion is suspect.
Otherwise, this will provide some confirmation of the Boss et al
conclusion. More importantly, if high energy neutrons can be
reliably produced using the more sophisticated, successful, and
controlled protocol as used by Boss et al, this could provide a solid
starting point for narrowing down the underlying physics. A tritium
atom does not differ significantly from a deuterium atom with respect
to the Coulomb barrier. Whatever mechanism permits deuterium to
defeat the Coulomb barrier should also permit tritium to do so
also. The difference may be that the cross section is larger and
the signature unmistakable and highly repeatable.
Though the use of tritium can only be done in the US by licensed
labs, and practical devices would preferably be deuterium only,
tritium doping experiments may provide a necessary step in the
progress toward practical devices.
Because the tritium available in the SPAWAR D loaded cathode must be
nominal in the extreme, and likely primarily there due to DD fusion,
the cross section for lattice based DT fusion has to be enormous,
much larger than 100 times the DD cross section (if cross section is
even a valid concept for lattice assisted fusion) to support the DT
hypothesis. The tritium must be used up very quickly after forming.
Perhaps lattice half-life (LHL) would be a better concept than cross
section, in loaded lattices, because the term cross section pre-
supposes a collision, kinetic interaction, hot fusion. LHL is a term
which would have meaning only in the context of a specific degree of
lattice loading. I expect when highly confirmed theories of LENR are
available such a term could be defined including a formula component
descriptive of lattice loading conditions.
If Boss et al are correct in their deductions of the source of high
energy neutrons, then a huge breakthrough is at hand. If
contradictions are found in the D-T hypothesis, or unexpected energy
spectra are identified, it does not necessarily mean that increasing
the D-T reaction rate is not useful, and it does not mean huge
benefits cannot be obtained by increasing the miniscule T
concentration even by a factor of a few orders of magnitude. Tritium
doping should be useful for analyzing and improving any CF protocol,
especially those capable of producing excess heat.
Lattice assisted DD fusion nearly eliminates the neutron forming
branch, but there is no reason to believe that lattice assisted D-T
fusion will nearly fully suppress neutron generation. In the case of
D-D fusion there are three branch possibilities, two of which create
no neutrons. Given that a lattice assisted D-D fusion nucleus is not
created by energetic kinetic action, but rather by electron
catalysis, it should be no surprise the branch producing the highest
energy is highly favored, namely D+D->He4, and the other feasible
branches highly suppressed. There is no probable similar
alternative branch for the D-T or T-T fusion that creates no
neutrons. All the tritium fusion reactions create neutrons. Tritium
doping is thus extremely useful for diagnosing whether excess heat is
from actual fusion or from some other source.
Tritium doping provides a window into what is happening in the
lattice, via the energy spectrum of the resulting high energy
neutrons. It certainly is not logical that D-D fusion can occur in a
lattice assisted manner and yet D-T or even T-T fusion can not. The
Coulomb barrier is the same. Tritium likely provides a large
tunneling target because the D-T hot fusion cross section is large.
If D-T fusion is indeed in fact occurring in the lattice, as Boss et
al hypothesize, it is therefore unreasonable to not expect neutron
generation. However, the mechanism of fusion in the lattice is
energetically different from hot fusion, and I would expect the
neutron energy to differ. In fact I would expect high energy
neutrons to exhibit a spectrum of kinetic energies for reasons I have
posted here and published regarding the "Deflation Fusion" scenario.
Under that or any electron catalysis scenario, I would in fact not
expect 14 MeV neutrons from D-T fusion reactions, while a significant
number above 6 MeV could be expected, with a fuzzy peak.
Tritium doping should (a) produce highly repeatable and
incontrovertible proof of nuclear reactions and (b) provide an
effective means of quickly measuring reaction rates while dynamically
varying experimental conditions.
If tritium doping is used, then lattice assisted fusion should also
result in the p-T reactions: T(p,n)3He and T(p,gamma)4He. The latter
reaction might be considered as unlikely as D(D,gamma)4He is
conventionally considered to be due to initial kinetic energy
requirements and lack of an inertial pair to distribute resulting
kinetic energy. However, under the deflation fusion scenario, or some
other electron catalyzed fusion scenarios, the nucleus enclosed
electron provides a means of releasing radiant energy and momentum in
small increments, and high initial energies are not required to
trigger the reaction. The T(p,n)3He reaction requires from 1 to 5
MeV kinetic energy to pull off as hot fusion. Given that electron
catalyzed fusion reactions result in highly de-energized nuclei, and
the resulting radiant energy is largely from the vacuum, it may be
that T(p,n)3He is feasible as a cold electron catalyzed reaction. If
lattice assisted D-T reactions can occur with much higher observed
frequencies than expected for the reactant concentrations, as
possibly indicated in SPAWAR results, then p-T reactions may also
have a higher frequency than expected for the reactant
concentrations. Protium from ambient humidity can be expected to
contaminate D2O cells, especially long running open cells. This
could account for highly variable neutron production over long run
times. In a D2O experiment an initial period is required to build up
trace T and another period is required to build up p. The SPAWAR
CR-39 could possibly have 3He tracks resulting from T(p,n)3He or D
(D,n)3He reactions, as well as neutron reaction induced tracks. All
this indicates that tritium doping of even all protium based
experiments may not provide adequate controls.
If lattice fusion reactions should produce high energy particles,
especially third particle Bose condensate stimulation based reactions
(as opposed to low energy electron catalyzed reactions) produce high
energy particles, and conditions for producing many small Bose
condensates exist, then it is clear that unexpected chain reactions
can result. The D(D,n)3He reaction, for example, produces two
particles for each reaction. It is thus important to diagnose
exactly what conditions in the lattice are producing energetic
results in what proportions. It seems feasible that both 3rd particle
seeded Bose condensate collapse mechanisms as well as electron
catalyzed fusion mechanisms can be at work in differing proportions
in differing experiments, or a given experiment at differing times.
What has been missing is a means to diagnose these kinds of things.
Tritium doping may well lead to such a diagnostic capability. Third
particle stimulated Bose condensate reactions are described here:
http://mtaonline.net/~hheffner/BoseHyp.pdf
X-ray stimulation may provide good chances of robust cold fusion
effects if the right lattice conditions are created. Deflation
fusion is driven by (1) creating the deflated state with high
probability, and (2) maximizing tunneling rate in the lattice. X-ray
stimulation can be used to increase the latter. X-ray stimulation
might be combined with radioisotpe lattice doping. Impurities like B,
SI, and C, are known to create interstitial locations wherein
"trapped hydrogen can jump between a limited number of sites without
diffusing away from the trapping atom." (see Topics in Applied
Physics, Volume 73, Hydrogen in Metals II, p. 76.) Also worthy of
note is the fact (noted on p. 77), regarding hydrogen motion between
double well potentials between two nearest neighbor tetrahedral
sites, that tunneling is the dominating transport mechanism, with
coherent tunneling occurring at less than 10 K, and incoherent
tunneling occurring above a temperature of 10 K. Further, "tunneling
dynamics is strongly affected by a nonadiabatic interaction of the
hydrogen with the conduction electrons." Given the existence of such
trapping sites, it appears beneficial to find a way to stimulate a
high tunneling rate, using a method not involving diffusion, but
rather conduction band electron stimulation. The best method of
doing this may be use of coherent x-rays, probably from a wiggler, as
that would be capable of producing a volume effect. Even if
effective at producing fusion the problem then might be too high a
requirement for energy in. It may be that a resonant ultrasound
vibration could be set up to stimulate tunneling without excessive
diffusion. Phonons should stimulate significant conduction band -
partial orbital state changes for ionically bound electrons. Overall
lattice stimulation by x-rays, sound, or high frequency current
stimulation, should avoid the helium blocking of diffusion problem,
as fusion would be triggered throughout the lattice without the need
for other than the initial loading diffusion. This then would
provide a volume effect instead of a surface effect. It also would
enable loading at a high temperature and cooling a bit to increase
orbital stressing without worries about reduced diffusion rates.
The problem of course is finding the right mix of all these things.
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
