Nickel Transmutation And Excess Heat Model
Using Reversible Thermodynamics: The
Least Action Nuclear
Process (LANP) Model
Presented at ICCF-17, published in J. Condensed Matter Nucl. Sci, 13(2014)
Daniel S. Szumski1
1Independent Scholar, USA
Abstract— This research develops the Least Action Nuclear Process (LANP) model
of cold fusion, by assuming that the process is thermodynamically reversible. This requires: 1) one element of new
physical theory, a far-from-equilibrium blackbody equation having a second temperature scale, and 2) a nuclear reaction
selection method based in the Principle of Least Action. The model appears to predict nuclear transmutations observed in
Miley's nickel microspheres, without false positives, and provides a plausible explanation of loading and ignition
processes, excess heat, no excess heat, and the absence of gamma radiation. The model shows how solar core
temperatures can exist in a laboratory temperature device. This presentation is abstracted from a larger technical
Index Terms— LANP model, theory, Least Action, reversible process.
During the last two decades it has become evident that low energy nuclear reactions are occurring in
Fleischmann-Pons(F-P) electrolytic cells(1). These reactions are unprecedented in nuclear physics, and are at least for
now, hidden from understanding because a suitable theoretical framework has not been forthcoming(2). The degree to which
new physics underlies these experimental observations is not known. But, among theoreticians it is considered more
likely that the present conundrum will be resolved by extensions of known physical principles.
This research endeavors to provide insight into three theoretical issues. First, it explores a mechanism for
accumulating the ignition energy. Second, it explores how this energy might be stored until the moment of ignition. And
third, it proposes how the accumulated energy partitions to specific nuclear transformations, and not others. The goal
here is to show how a different view of heat processes, one that includes both irreversible and reversible thermodynamics,
might inspire a comprehensive cold fusion theory.
B. Theory of Heat
Heat exists in two domains that continually exchange energy as any arbitrary thermal system tends toward new
quasi-equilibrium states. These are the domain of molecular motion, and the domain of heat radiation. The first might be
referred to as the mass domain. It was Helmholtz who first showed that molecular motion is equivalent to heat; an
observation that is central to what follows.
Heat energy also exists in the radiation domain. The theoretical framework describing equilibrium conditions there
bears the revered names of Rayleigh, Wien, and Planck. Planck's equation(3) describes the equilibrium temperature
dependence of blackbody spectral emittance.
Reversible thermodynamic processes are believed to be rare in nature. These are processes that produce a net zero free
energy change, and are described by the thermodynamic treatment of Helmholtz, but not that of Gibbs. In all cases,
reversible processes can be completely described by the Principle of Least Action(4).
I have proposed(5) a mathematical form for the blackbody spectral distribution that permits a glimpse into its
non-equilibrium, and far-from-equilibrium characteristics.
Blackbody spectra = Emittance (Rayleigh Law)/Absorbtance (Ref. ), where:
where: Tm is the thermodynamic temperature. TR is a new quantity called the
radiation temperature, and exists where the number of quanta is equal to or greater than 1. Planck's equilibrium
equation is given by:
The non-equilibrium form in Equation (1) is close to, but not exactly Planck's at equilibrium.
This theory suggests that independent temperature scales might represent the mass and radiation domains. Figure 1
illustrates characteristics of the far-from-equilibrium, blackbody radiation spectra.
Fig. 1. Heat transfer occurs between the two domains as the far-from-equilibrium state decays to
a new equilibrium (transfer channel is Wein frequency). Illustration of non-equilibrium changes in the heat radiation
spectra (Equation 1). Case A represents instantaneous mass domain heating (i.e. friction) at constant radiation
temperature. Case B represents adiabatic heat accumulation at a constant thermodynamic temperature.
Curve A, refers to the transient initial condition where heating is initiated by increasing molecular motion, for
example, by frictional input of heat. If an identical amount of heat is initially added to the radiation domain alone
(i.e., higher energy radiation), Tm is initially constant, and the Wein frequency increase shifts the
emittance spectra to higher frequencies (curve B). Both of these cases decay to equilibrium spectra similar to, but with
higher total energy than the initial equilibrium case. At the new equilibrium condition, the mass and radiation
temperatures become identical, and it is not possible to determine from which of the two domains the original heating
took place. However, as will be shown in what follows, there are circumstances under which the second of these spectra
might be held in a far-from-equilibrium state, and in this way store vast amounts of energy in a nickel or palladium
cathode that is apparently at about 60°C.
C. Consider A Thermodynamically Reversible Process
In thermodynamically reversible processes, be they chemical or nuclear, all of the process energy must be in a usable
form. Thermal motion is specifically excluded, or it must be quieted; i.e., converted to radiation domain energy, as it
enters the reaction space. In our case, a deuteron's kinetic energy is captured ('quieted') as it is absorbed from the
heavy water into the metal lattice, adding to the internal lattice energy, and more specifically storing that captured
kinetic energy in excited electron and excited nuclear states.
To place an order of magnitude estimate on this energy storage, we will use the 0.2cm diameter x 10cm Pd electrode
from Fleischmann and Pons 1989 experiments. The surface area of the cathode is 6.28 x 10-4meters. Assuming
-phase absorption approximating
-Pd D0.85, and having a lattice
parameter of 0.405nm, the number of filled sites at the surface of the cathode, is approximated as 3.26 x 1015sites
in a single atomic layer at the cathode surface. If we assume that the average deuteron velocity is 0.2m/sec, the average
kinetic energy of the deuterons in the cell can be calculated as 6.68 x 10-22erg, or a total of 2.2 x
10-6erg = 1.35 MeV in a single surface atomic layer. Thus, deuterium's 'quieted' thermal motion is more than
sufficient for ignition. Where the electrode is being loaded in a deuterium gas environment the average molecular energy is
at, or 6.89 x 10-14erg.
The loading energetics for metal hydrides are well understood [6,7,8] and the research reported here takes no issue
with the known thermodynamics. Nevertheless, this theory is alone in associating the cold fusion ignition and process
energy with the loading process. All other theoretical constructs take the matrix loading as a given, and then look for the
ignition energy within the metal hydride matrix.
Hydrogen storage within the lattice structure is known to occur in distinct thermodynamic phases:
. These are known to be thermodynamically
reversible . Let us now look at that next step.
How is this energy stored during the loading phase of the experiment? We will begin by assuming that deuterium loading
is a singular, multi-site, reversible process. During loading, no energy is lost to thermal motion. Thus, the stored energy
is either entirely in the radiation domain, or it moves to another energy type where it can be held in a completely reversible
state. We will partition this energy storage into two components. The first is the mechanical work involved in expanding the
metal lattice by up to 15% to accommodate high deuterium loadings. This is an adiabatic volume expansion, and thus, a
reversible process. The second is the adiabatic storage of radiation domain energy to achieve ignition energies.
It appears to me that the best explanation for the lower bound for energy storage is within discrete covalent bonds; each
covalent electron pair alternately absorbing and emitting electro-magnetic energy that remains in a wholly reversible state.
As the total energy storage increases further, excited nuclear states become active bringing the reversibly stored cathode
energy to gamma levels, where Mossbauer resonance, a reversible process, prevails, and energy storage occurs as resonant gamma
exchange. This energy is stored entirely within the atomic structure of the lattice, and without any external manifestation.
It is masked from observation.
In order to inquire about temperatures achieved in this reversible energy storage, we note that temperature is a
derivative[4, p. 105], dQ/dt, measuring the emittance from any closed volume contained completely within the
nickel electrode's interior, and where the Joules/sec crossing the surface area of that volume completely describes its
temperature. If our free body volume is around one of the electrons participating in covalent bond resonant energy storage,
the temperature is above the ambient thermodynamic temperature, Tm, but relatively small. However, as the
frequency of the shared photon approaches gamma energies, the exchange takes place between nuclei, and the heat derivative,
and thus the temperature within the volume containing one of these nuclei can become enormous, approaching and exceeding solar
The spectra labeled B in Figure 1 represents the distribution of energy levels corresponding to this storage of heat energy.
Eventually, the Wein Frequency reaches gamma intensities, and the radiation temperature approximates that in the solar core,
about 107 as illustrated in Figure 2. The Figure contrasts the temperature regime (Tm and
TR) that this theory postulates to that in the solar core. It suggests that the energy spectra required for
ignition in the Tokamak is about four orders of magnitude higher than that operative in the F&P cell, and much larger on a
total energy basis. In essence, the cold fusion process takes an energy shortcut around the enormous kinetic energy required
for thermonuclear fusion. In this way, we see that the LANP is actually quite hot.
Fig. 2. Comparison of theoretical radiation temperature structure in the F&P electrode with the
solar core temperature. Both exhibit radiation temperature, but very different thermodynamic temperatures.
But, where are the Gamma emissions? We need to recall that we are dealing here with an extension of blackbody theory wherein
electromagnetic energy of all wavelengths is emitted and absorbed within the lattice. The mass quantities involved in this
absorption and emission are presumed to be electrons at the low energy end of the spectrum, and atomic nuclei as the energies
increase through gamma intensities. Mass changes from any overall reaction occur as gamma emissions into the blackbody spectral
distribution. Gamma emission and absorption are intrinsic to this system, internal to it, and in effect masked by it.
Let's return to the mechanism of thermo-nuclear fusion/fission under these conditions. Miley's data from electrolysis of
nickel coated microspheres(9) provides a suitable data set for analysis. I have inventoried what I believed are the most likely
nuclear reactions occurring in the nickel coated microspheres. A small sampling of the 210 reactions (column 1) analyzed during
this research is presented in Table 1. Isotope data is extracted from Wikipedia (10). The second and third columns are the
initial isotope formed, and the final stable product(s) of its decay. The last column is the total mass change in the nuclear
reaction sequence that ends with the isotope in column 3.
Overall the data analysis shows that the reactions producing the lower atomic weight portion of the final electrode
composition are: 1) fusion reactions of initial electrode isotopes (including impurities) with one or more deuterons, 2) fission
reactions of initial electrode isotopes or isotopes that were absent from Miley's table, or 3) alpha decay. Some of the higher
atomic weight isotopes result from fusion reactions involving nickel-nickel and nickel-impurities with deuterium nuclei. Because
the initial electrode is severely neutron deficient relative to the final electrode, many of the high nuclear weight products
probably have their origin in more complex stellar nucleosynthesis reactions. One thing is clear: neutron production
is fundamental to the underlying nuclear process.
Many of these nuclear reactions have multiple isotope end points, and many of those are not in Miley's Table 3. I have
identified one rule that determines which of these multiple isotope products will occur: all fusion and fission reactions
that can occur, are candidates. The one that actually produces a product along any reaction pathway is the reaction sequence
that satisfies the Principle of Least Action (smallest overall mass change).
For each reaction shown, the isotope product that satisfies this condition is in bold type . Consider the
nuclear reaction involving Miley's nickel electrode and one of its impurities: . It normally produces 38 intermediate radioactive isotopes and 7 stable isotope
products, three of which are in Miley's Table 3:15163Eu,16564Gdand16366Dy.The results obtained from this reaction
sequence are shown in Table 1 where the Principle of Least Action correctly selects
for16366Dy,but not along the normal decay pathway.
Instead, the Principle of Least Action selects
for16769Erwith a mass change of +0.0775065 amu. This
is followed by alpha decay to 16366Dy,still within
the domain of reversible thermodynamics. The energy change drops accordingly to +0.0767937 amu. The overall mass change which
normally manifests as gamma absorption, occurs instead as Mossbauer resonance; part of the far-from-equilibrium blackbody
I have chosen to call this mode of nuclear decay, where no intermediate radioactive products occur, and where half-life time
delays are nonexistent, sigma-decay.
We are finally ready to look at the issue of excess heat generated in Miley's experiment. The LANP reversibility constraint
requires that the core process be adiabatic. Therefore, we need to explore the limits of that process to identify the step at
which it crosses over the line into the domain of irreversibility.
Because there are both exothermal(- mass change) and endothermal(+ mass change) reactions occurring, the excess heat is probably
a net heat measure, and most probably has it origin in the circumstance where the far-from-equilibrium spectrum is already filled
at the gamma emission's frequency, and the energy must instead flow into the spectra's mass domain. There it enters the domain of
irreversible processes, and results in an increase in Tm. The transfer function that re-distributes the gamma
energy is theorized to be Equation (2). Furthermore, experiments where no excess heat is observed could be either: 1) dominated by
endothermal reactions, or 2) have a net zero heat production. The electrodes from these 'failed' experiments need to be checked for
transmutation products. It is entirely possible that these experiments were successful in some way other than excess heat
The LANP theory is unique in its ability to describe many of the unexplained phenomena occurring in a F&P electrolytic cell
- A mechanism for loading energy into the metal hydride lattice,
- A mechanism for storing that energy until ignition,
- A theoretical basis for the fusion temperature requirement and how it is masked,
- A mechanism for selecting products that do and do not occur,
- An explanation for the absence of radioactivity.
The theory also has appeal in that it is not nickel specific, or even metal lattice specific, and it provides a plausible
mechanism for the solar temperatures that thermonuclear fusion is know to require. LANP is a very hot process.
The mechanism that causes excess heat may require more detailed work, particularly with the nuclear event sequence that fills the
far-from equilibrium spectra, and the meaning of equation (2), including its more rigorous derivation. Nevertheless, the model
demands additional study and experimental work. It answers too many questions to be dismissed.
On the other hand, theoreticians and experimentalists in the field should contain their exuberance for this, or any other
promising model. This field is simply too controversial to allow missteps, or premature dialog with the non-scientific community.
Places where LANP departs from current theory, and more importantly, from common sense, need immediate study. For example, is
it even plausible that all of the intermediate radioactive decay steps, and half-life constrains of -decay can be bypassed by
LANP. The absence of any radiation signature in F&P cells, and the observed transmutation products make that conclusion tantalizing.
And yet, it is contrary to everything that we currently know about nuclear processes. The same is true of more fundamental aspect of
the theory such as its claim of reversibility. This one feature of the theory is without precedent in modern science, and will be
attacked vigorously in peer review. Perpetual motion machines, quite simply, are not supposed to exist. Even more implausible is the
claim that stellar and supernova processes might occur within a laboratory device.
These claims are almost untenable, and yet they seem to constitute a cohesive theoretical framework that is consistent with the
data. We should be very careful not to give LANP too much credibility at this point in its short life, and instead design a scientific
plan to achieve rigorous experimental proof one way or the other.
- Fleischmann, M., S. Pons, M. Hawkins, "Electrochemically Induced Nuclear Fusion of Deuterium", J Electroanal. Chem., vol 261, p.
301 and errata in vol. 263, 1989.
- Hagelstein, et al, "Input to Theory from Experiment in the Fleischmann-Pons Effect". ICCF-14 International Conference on Condensed
Matter Nuclear Science, Washington, DC., 2008.
- Planck, M., "Verhandlunger der Deutschen Physikalischen Gesellschaft" vol. 2, 237, 1900, or in English translation: Planck's
Original Papers in Quantum Physics, Volume 1 of Classic Papers in Physics, H. Kangro ed., Wiley, New York, 1972.
- Planck, M., Eight Lectures in Theoretical Physics, 1909, translated by A.P. Wills, Columbia U Press, NY 1915.
- Szumski, D.S., "Theory of Heat I - Non-equilibrium, Non-quantum Blackbody Radiation Equation Reveals a Second Temperature Scale",
Unpublished manuscript, 2012.
- Gibb, T. R., Primary Solid Hydrides, in Progress in Organic Chemistry, Cotton, F.A. ed, J Wiley & Sons, NY, 1962.
- Libowitz, G.G., The Solid State Chemistry of Binary Metal Hydrides, W A Benjamin, NY, 1965.
- Storms, E., "The Science of Low Energy Nuclear Reaction", World Scientific Publishing Company, 2007.
- Miley, G., J Patterson, "Nuclear Transmutations in thin-Film Nickel Coatings Undergoing Electrolysis", J. New Energy, vol. 1,
no. 3, pp. 5-38, 1996.
- Isotopes of element in Wikipedia, Retrieved 1/04-07/12 from http://en.wikipedia.org
Appendix A - The Tunneling Issue
The fundamental problem in cold fusion theory is overcoming the coulomb barrier between reacting nuclei. The barrier can be
represented by the electro-static potential energy:
where k is Coulomb's constant, e is the elementary charge, l is the charge separation, and
Z1, Z1 are the atomic numbers of the interacting nuclei. Overcoming this potential barrier
for deuterium-deuterium fusion requires kinetic energies in the MeV range, essentially solar surface temperatures.
Parmenter and Lamb  showed how dual deuterons in a single potential well might achieve the required resonant energies in the
presence of large numbers of conduction electrons which effectively masked the coulomb barrier. Subsequent investigators have proposed
refinements to this resonant tunneling model, incorporating enhanced electron mass , resonant nuclear states , and calculated
tunneling enhancements . None of the tunneling theories put forward to date has proven sufficient to explain cold fusion
This issue is magnified in the current research because fusion reactions beyond the elementary four nucleon model are not only
proposed, but presented without reference to the enormous coulomb barriers that they imply. For example, the H + Ni and Ni + Ni
(Z1 = 1, Z2 = 28) Coulomb barriers are approximately 25 and 750 times greater, staggering energy barriers
relative to the simple four nucleon problem. And yet, if the experimental results of Miley  and Mizuno  are to be believed,
nature overcomes these incredible coulomb barriers in room temperature experiments every day.
The one remarkable characteristic of the reversible thermodynamic, framework employed by the LANP model, is the way that the time
differentials, regardless of their mechanism, become identically zero. This occurs regardless of the order of the derivative (second
order in the case of coulomb barrier repulsive force). Therefore, it is entirely possible that when we treat the cold fusion
process as a reversible thermodynamic system, all of the repulsive coulomb barrier acceleration terms disappear from our model,
and reactions that are possible at the operative radiation temperature, all become candidates for the reactor's next step. Possible
reactions do not cascade randomly, but proceed stepwise in a systemized manner described entirely by the Principle of Least Action.
One occurs. Then the next step occurs, and the next, and so on. This is the Least Action Nuclear Process. I discuss some of the
fundamentals involved in , where I have included a calibration of my Theory of Heat; the larger research project that this paper
is derived from. The LANP theory does not require tunneling. The coulomb repulsion terms a in fCoulomb =
ma have all gone to zero.
Appendix B - The Gamma Conundrum
The LANP model differs from all other nuclear models in two important ways. First, it produces only stable nucleotides, and in fact,
expected unstable isotopes and excited nuclear states never occur within the process. These are entropic quantities that are foreign
to the reversible thermodynamic state, and cannot be produced within it. The only relevant quantities are the initial and final (Least
Gamma energies are produced. For example, in Section D, I refer to a fusion reaction: .16266Dy,which
normally results from 6 discrete beta decays and an alpha decay. Yet, no beta or alpha decay products are measured, nor are any of the
intermediate unstable isotopes detected. The reversible thermodynamic process began with the three reactants, and produced one stable
isotope and consumed a gamma photon (0.07607937amu = 70.86489MeV).
Secondly, although the LANP model produces these gamma energies, it liberates no gamma photons. Instead gamma quanta are theorized
to be absorbed and emitted within the far-from-equilibrium blackbody spectra where these quanta are Mossbauer resonant between
identical nuclei, and thus masked from observation beyond the limits of that absorption/emission process. In the circumstance where the
far-from-equilibrium blackbody spectra has no vacancies to accommodate the gamma photon, its energy dissipates into the low energy
spectra where it deteriorates to heat of motion, i.e. 'excess heat.'
Section C describes how Mossbauer resonant gamma energy alone defines the effective temperature within the LANP's metal lattice.
For this model to evolve, it is a sufficient condition, that the lattice's radiation temperature, TR,
described by the Mossbauer resonant gamma field, achieve solar core temperatures.
We might ask the question: Is this temperature real? I am not questioning the heat content of the system. The gamma energies place
the intra-nuclear temperature at solar core conditions. But at the boundary of this nuclei pair there exists no heat flux, a zero
derivative, and all appearances of room temperature conditions. In other words, the gamma energy exists, but not in a form that can be
observed. It seems only accessible through theory.
This is a radically different view than is found in the high energy physics literature. There, the fusion temperature condition is
the sum of enormous kinetic energy, and the same high, gamma dominated, radiation conditions employed here. The difference is in the
way that this theory finds radiation temperatures in the solar core range entirely sufficient to carry forward nuclear transmutations
in the absence of the equilibrium blackbody's kinetic energy pool.
Finally, I note the extraordinary amount of misinformation regarding reversible thermodynamic processes in the literature and in
physics textbooks. If we are going to have this discussion, we need to go back to the one reliable source, Planck's 1909 Lectures at
Columbia University(4 above). I believe that this paper's interpretation is entirely consistent with Planck's presentation in
Lectures 1 and 7. The only place where we differ is on pages 19 and 20, where he makes this often quoted statement regarding
"Reversible processes have, however, the disadvantage that singly and collectively they are only ideal: in actual nature there
is no such thing as a reversible process...."
Nevertheless, Planck cites several reversible processes elsewhere in the Lectures, and speaks of the ultimate division of all
physical processes into two categories: reversible and irreversible.
It is my carefully considered opinion that the common belief, quoted above, is at the very heart of our inability to understand
the cold fusion process, and possibly, the process that gives rise to matter's living state.
- Parmenter, R.H., and W.E. Lamb, Proc. Natl. Acad. Sci USA, 86,8614,1989, 87,3177, 8652, 1990.
- Widom, A., Larsen, L. "Ultra Low Momentum Neutron Catalyzed Nuclear Reactions on Metalic Hydride Surfaces", Euro Phys J., vol
- Hagelstein, P. L., "Resonant Tunneling and Resonant Excitation Transfer", Proc. 10th Intl Conf Cold Fusion, Cambridge, MA,
- Kim, Y, et al, "Reaction Barrier Transparency for Cold Fusion with Deuterium and Hydrogen", Fourth Intl Conf Cold Fusion,
Lahina,Maui, USA, 1994.
- Miley, G., J Patterson, "Nuclear Transmutations in Thin-Film Nickel Coatings Undergoing Electrolysis", J. New Energy, vol. 1,
no. 3, pp. 5-38, 1996.
- Mizuno, T., et al, Nuclear Transmutation: The Reality of Cold Fusion, Infinite Energy Press, Concord NH, 1998.
- Szumski, D. S., Introduction to Theoretical Biology- A Theory of Heat, Amazon.com, 2013.