"When you change the way you look at things, the things you look at change."   —Max Planck


Analysis Of Miley Data
Consequences Of Partitioning The Photon Into Its Electrical And Magnetic Vectors Upon Absorption By An Electron
Nickel Transmutation and Excess Heat Model Using Reversible Thermodynamics - The Least Action Nuclear Process (LANP) Model
Re-thinking Cold Fusion Physics: An Essay
Cold Fusion and the First Law of Thermodynamics: An Essay
Can We Explain Excess Heat Uncertainty With a Law of Physics: An Essay
The Atom's Temperature
Cold Fusion and the Three Laws of Thermodynamics
Review Of Temperature Issue And My Calculations 12/8/15
Theory of Heat I - Non-equilibrium, Non-quantum, Blackbody Radiation Equation Reveals a Second Temperature Scale
Theory of Heat II - A Model of Cell Structure and Function
Theory of Heat III - Nickel Transmutation and Excess Heat Model Using Reversible Thermodynamics

Theory of Heat III
Nickel Transmutation and Excess Heat Model using Reversible Thermodynamics: The Least Action Nuclear Process (LANP) Model

Daniel S Szumski, Independent Scholar
Davis, California, USA
July 3, 2012

A. Introduction

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)

It is theorized that excess heat (3,4) and (5) are generated, and that the heat evolved is consistent with the mass difference (5,6) in the reaction:

(1)     (ignition requirement = 0.01MeV)

It is also becoming apparent that the reactions taking place are a near surface phenomenon (7) that is spatially clustered (7), occurs in bursts (7), and has a cyclic character within those bursts (8). Even more controversial than the contention that Reaction (1) occurs, is a growing body of data showing other nuclear transmutations in F-P cells(9,10,11,12,13), and still more alarming, in living cells (14).

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, perhaps in ways that we cannot immediately imagine.

This research endeavors to provide insight into three theoretical issues. First, recognizing that the fusion reaction's energy has its origin within the experimental apparatus, we explore a mechanism for accumulating the energy required by Reaction (1) or other fusion/fission reactions. Second, there has to be a way of storing that energy within the apparatus, and in some way, disguising it until the moment of ignition. And the third is the elusive coherence principle that focuses the accumulated energy on 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. Its description was first formalized by Maxwell(15), and then by Boltzman(16). Their theory represents the molecular velocity distribution of an ideal gas as a function of the system's temperature and the gas molecules' mass. It is an equilibrium theory stating the functional dependence of temperature and thermal motion. It was Helmholtz who had first shown that molecular motion is equivalent to heat; an observation that is central to what follows. Max Planck, in his 1909 lectures at Columbia University(17), elevates this insight to an equal footing with Maxwell's treatment of light as electromagnetic waves.

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 (18) 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. A discussion of this principle and the thermodynamics of reversible processes are presented by Planck (17).

In a previous paper (19), I proposed a mathematical form for the blackbody spectral distribution that permits a glimpse into its non-equilibrium, and far-from-equilibrium characteristics. The theory treats light absorption as a two step process: the first (and this will be the important one to what follows) being wholly reversible, the second irreversible and entropic. In special cases only the first step occurs, and the energy absorption is adiabatic, that is, without loss of Joule heat. The functional form of the non-equilibrium blackbody spectra is given by:


Blackbody = Emittance / Absorptance

Spectra (Rayleigh Law) (This study)


(4) (Wien frequency), and

exists where the number of quanta is equal to or greater than 1.

Planck's equation for the equilibrium case is given by:


The non-equilibrium form of the equation is close to, but not exactly Planck's at equilibrium.

Secondly, the theory suggests that independent temperature scales might represent the mass and radiation domains. Figure 1 illustrates the principle characteristics of the non-equilibrium, or more accurately, the far-from-equilibrium, blackbody radiation spectra. Two equilibrium cases are shown: 300°K and 100,000°K.

Curve A, labeled Mass Domain Heating, refers to the transient initial condition where heating is initiated by increasing molecular motion, for example, by frictional input of heat. The Wein Frequency remains constant momentarily, and there is a logarithmic increase in the spectral energy at all frequencies.

If an identical amount of heat is instantaneously added via the radiation domain alone (by introducing higher energy radiation), the thermodynamic temperature, Tm, is initially constant, and the Wein frequency increase, shifts the emittance spectra to higher frequencies as shown in curve B.

Figure 1. Illustration of non-equilibrium changes in the heat radiation spectra (Equation 2). 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.

Both of these cases decay to an equilibrium spectrum 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 its far-from-equilibrium condition, and in this way store vast amounts of energy in a nickel or palladium cathode that is apparently at about 60°C.

This paper attempts to reconcile this non-equilibrium theory of heat with experimental observations from cold fusion experiments, and show how the energy stored at room temperature can be made accessible to fusion reactions.

C. Consider A Thermodynamically Reversible Process

In thermodynamically reversible chemical processes all of the available energy, including that of thermal motion, is utilized, and none of the energy in the post-reaction space is lost to random thermal motion. I have found that the easiest way to understand the principles involved in what is to follow, is by considering the reaction occurring at the active site of a biological enzyme. The reactants and enzyme have fundamentally different thermodynamic properties. The former are relatively small molecular forms having both chemical potential and thermal motion. The enzyme, on the other hand, is a large molecule, that in its globular active form, has very little or no thermal motion, and no apparent chemical potential.

The enzyme mediated biological reaction brings reactant molecules into conformational position, generally by electrostatic attraction, and in so doing, makes improbable reactions, probable. The secret lies in transformations to the energy states of both the reactants and the enzyme. In particular, cleavage at the active site eliminates thermal motion in the reactants; it quiets them. The First Law tells us that the 'lost' thermal energy must be conserved, and in its limit, the Second Law tells us under what conditions the reaction can proceed. In essence, the reactants' thermal motion has become part of the reactant-enzyme complex, elevating its overall free energy content.

If the thermodynamics of the enzyme/reactant complex are truly reversible, the total energy is passed on to the reaction products, and there is no energy residual that contributes to thermal motion in the reaction space. As long as these conditions are met, the reaction proceeds in accordance with the Principle of Least Action. Then conformational changes occur, and the product becomes subject to the slightly altered thermal state of its environment. In essence, the enzyme has harvested random heat motion from the environment, converted it to useful work, and in so doing increased the radiation domain's heat content. What at first appears to be a violation of the Second Law, is simply its limiting case, a zero net energy reaction that produces a more negentropic state.

It was Szilard's argument (20) concerning Maxwell's sorting demon (15) that correctly showed how the negentropy stored by the demon as molecular organization and intellect, sponsors his trick, in apparent violation of the Entropy Principle. In the case considered here, it is the massive information content in the globular enzyme form that allows the demon to operate. In a related theoretical context, Prigogine (21) would label the enzyme/reactant complex a dissipative structure: a far-from-equilibrium thermodynamic state, which once formed, allows no recourse to the previous state, and in so doing, lowers the local entropy.

D. Consequences of Deuterium Absorption into a Metallic Lattice

Consider a deuterium ion, (21H+), in Fleischmann and Ponn's original experiment(1). Its total energy is the sum of its chemical potential and its kinetic energy, , that associated with temperature-dependent random motion. The kinetic energy is given by the product of the deuteron's mass, md, and its temperature dependent velocity squared:


Where: , and is the velocity of an individual deuteron, or in our simplified treatment, the average velocity of an ensemble of deuterons at F-P cell temperature, Tm. We will assume an average velocity of 0.2m/sec, a simplification that ignores for the moment the system's actual velocity distribution, but facilitates illustrative calculations.

The average kinetic energy of the deuterons in their F-P cell can be calculated as

(7) .

When a deuteron first encounters the nickel matrix, it is absorbed into it in a process that we will assume to be thermodynamically reversible, and similar to the enzyme process described above. The deuteron is 'quieted' to zero velocity, and zero kinetic energy. The First Law requires that the kinetic energy be conserved in the metal hydride lattice. And because the loading process is thermodynamically reversible, the energy storage is adiabatic, with no losses to Joule heat.

To place an order of magnitude estimate on this energy storage, we will use the 0.2cm diameter x 10cm electrode from Fleischmann and Pons 1989 experiments(1). The surface area of the cathode is 6.28 x 10-6 meters. Assuming -phase absorption approximating , and having a lattice parameter of 0.405nm, the number of filled sites at the surface of the cathode, , is approximated as:

(8) surface sites

The 85% load factor yields: 3.26x1013 [21H+] sites on a single atomic layer at the cathode surface. We assume that the total cathode is immersed in heavy water.

The energy storage capacity, E, of only the surface layer of atoms in this cathode is:

(9) ,

which is consistent with the energy required to ignite the fusion reaction:

(10) (ignition requirement = 0.01MeV)

Absorption of deuterons into the second, third, and deeper atomic layers in the cathode, increase the total energy availability proportionally. If the average deuteron velocity in the cell is taken as 20 cm/sec, 2 cm/sec and 0.2cm/sec, the ignition requirement is achieved in approximately 80 (10-6%), 6,200 (10-4%), and 7.4x105 (0.5%) atomic layers. The calculated percentage of the cathode's total lattice volume is indicated in parentheses. Energy accumulation increases at higher temperatures, and doubles again if 21H2 molecules form within the interstitial space (22). Thus, deuterium's sequestered thermal motion appears to be more than sufficient for ignition.

E. Possible Modes of Energy Storage within a Metallic Ni Lattice

The mechanism presented thus far has the advantage of providing qualitative insights into several theoretical issues. First, it provides a simple explanation of how the ignition energy is first acquired in the Ni cathode. All that might be required is a reversible thermodynamic process that harvests kinetic energy from the F-P cell environment. Secondly, it provides a basis for understanding the 'breathing' mechanism in the SRI experiments (8). Stored thermal energy and deuterium are expended and need to be replaced on a periodic basis. This manifests as a harmonic superimposed on the excess heat output. Third, it offers an explanation of the apparent surface nature of the effect. This is where the energy accumulation occurs, and where it must be renewed. And, finally, it provides a plausible explanation of why loading rates increase at higher current density/temperature. The total energy storage per mole of 21H+ is increased as the square of the average deuteron velocity.

For this transfer to be a thermodynamically reversible one, the lattice energy has to increase sequentially, in discrete amounts, exactly equal to each sequestered deuteron's total kinetic energy. Then it must be held there in opposition to all entropic tendencies until ignition.

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. The energy is not dissipated in incremental amounts, as it was in the enzyme example. Instead, the Ni lattice has massive numbers of active sites that must be filled before the reversible process can proceed to its fusion step. During this 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.

This constraint, that the energy storage be in a thermodynamically reversible state, allows us to further limit the possibilities. The mode of energy storage could be:

  1. electro-magnetic, in which case the energy of, for example, discrete metallic bonds might be increased by quantum amounts forming covalent bonds or excited electronic states; or
  2. it could be magnetic energy storage in paramagnetic Pd's electron spin re-orientation, or it could be (and probably is) energy stored as excited nuclear states.

It is not stored as elastic stress, electric charge, or atomic vibration, all of which are entropic processes. In addition, the energy storage mechanism must make allowances for energy storage that spans a continuous range from the ambient temperature of the experimental apparatus, through thermonuclear temperatures.

It appears to me that the best explanation for the lower bound might be found in energy storage within discrete covalent bonds; each covalent electron pair alternately absorbing and emitting electro-magnetic energy that remains in a wholly reversible state, i.e. the first step of the two step absorption process. Here the energy storage is in a stable far-from-equilibrium state (upon which excited electron states might be superimposed) that manifests as an increase in the cathode's redox potential. As the total energy storage increases further excited nuclear states become active, ultimately bringing the reversibly stored cathode energy to gamma levels, where Mossbauer resonance, a reversible process, prevails, and energy storage occurs as resonant gamma exchange.

If we now look more closely at the consequences of energy storage in excited nuclear states, we find that this energy is stored entirely within the atomic structure of the lattice, and without any external manifestation. No heat energy is emitted. The thermodynamic temperature remains unaffected by the deuterium loading, and in this way, the process' energy storage is masked from observation. The observer witnesses a very typical electrolysis apparatus, and has no hint of the continually increasing radiation temperature within the lattice's atomic structure.

The spectra labeled B in Figure 1 represents the distribution of energy levels corresponding to this storage of heat energy. These are filled sequentially at each Wein frequency. Then the Wein frequency increases one unit, and another layer is added to the spectral structure. Eventually, the Wein Frequency reaches gamma intensities, and the radiation temperature approximates that in the solar core, about 107°K 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 includes both the indicated radiation domain energy and also the mass domain kinetic energy, and is about four orders of magnitude higher than that operative in the F&P cell. The total energy requirement is many orders of magnitude greater. 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 cold fusion process is actually quite hot.

Figure 2. Comparison of theoretical radiation temperature structure in the F&P electrode, with the solar core temperature. Both exhibit the same radiation temperature, but at very different thermodynamic temperatures.

Let us, for the moment, assume that fusion and/or fission events occur in our electrode as TR approaches 107°K. Where are the Gamma emissions?

We can answer this question by recalling that we are dealing here with an extension of blackbody theory wherein electromagnetic energy of all wavelengths is emitted and fully absorbed within the lattice. The mass quantities involved in this absorbtion and emission are electrons at the low energy end of the spectrum, and atomic nuclei as the energies increase through gamma intensities. This is an absorption/emission process wherein electro-magnetic energy is shared between identical mass quantities. In effect, gamma emission occurs as part of the normal blackbody dynamic, and within that context, participates in nuclear fusion or fission events. Gamma absorption and emission adds and subtracts energy quanta to/from the spectrum. Because this is a metal lattice, the emission/absorption occurs in accordance with Mossbauer kinetics, without recoil or heat loss, or more precisely in a completely thermodynamically reversible manner. And, as long as there is room in the spectra, the gamma energy released by fusion and fission events is fully absorbed elsewhere in the lattice by a nucleus having exactly the same ground/excited state as the emitting nucleus.

This is simple blackbody behavior, occurring now, at a very far-from-equilibrium state. One might rightfully ask: is it the mere fact that the gamma portion of the blackbody spectra is being filled, that causes the nuclear reactions? Or, is it the radiation temperature that sponsors fusion/fission events?

One consequence of associating the energy requirement for the nuclear reactions with the blackbody spectra is that all reactions that can occur, do. This is because the entire continuum of spectral energies are available in the far-from-equilibrium blackbody spectra.

F. Experimental

Now let's return to the mechanisms of thermonuclear fusion/fission under these conditions. Miley's data from electrolysis of nickel coated micro-spheres(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 micro-spheres, which I will refer to as the electrode. Those reactions that consistently produced observed transmutation products without producing extraneous isotopes are presented in Tables 1 through 8. I have used 'isotope of (element)' data extracted from Wikipedia (23).

Nickel-deuterium fusion reactions are presented in Table 1. The second and third columns are the initial isotope formed, and the final stable product of its decay. I initially thought that the reversible portion of the nuclear reaction would extend only to column 2, and that the heat evolved from the experimental apparatus would be that from beta-decay of the initial fusion product to stable isotopes. I also suspected that the isotopes observed in the electrode 'post-experiment' would be all of the decay products of the initial fusion/fission reaction. This worked fairly well as long as I made some other assumptions.

First, I had to allow gaseous products to 'gas out' of the apparatus. This seemed reasonable, but then I had to look at the half lives of gaseous intermediaries, to make the judgment call – is it reasonable to assume that this gaseous product had enough time to 'gas out'? Wherever unstable gaseous products were formed in the initial fusion/fission reaction, the half-life of the isotope is provided in the table so that the reader can assess the opportunity for gassing that product out of the electrode before it reacts further. Stable gaseous products were assumed to gas out of the electrode.

Another source of concern at this point was the feasibility of fusion reactions involving 5, 6, …10 deuteron. Having completed hundreds of decay sequences for all types of possible nuclear reaction, it had become apparent that multiple deuteron reactions were the only way to produce most of the low atomic weight products in Miley’s Table. But there were practical problems here. Did the multiple deuteron reactions occur all at one time? Or, did they occur sequentially. There seemed to be a proximity issue in a face centered cubic lattice if the reaction involved, for example, 10 deuterons. Yet this still seemed a preferred route, because sequential deuteron addition produced many short half-life, radioactive isotopes that probably were not available for further deuteron addition.

Another concern about multiple deuteron reactions is apparent in the reaction involving5828Niplus six deuterons, yielding . But,7032Geis not measured in the post-experiment electrode. Is it because the addition of six deuterons to5828Ninever occurs, or occurs only after the first five additions (which occur during this experiment's duration), and is not occurring in sufficient amounts to be measured yet in the experiment. Or perhaps,7032Geundergoes fission to as shown in the Table. This result is ambiguous. There are many reactions involving 6 or more deuterons that yield stable terminal isotopes that Miley did measure. I also saw that although the final fission product, chlorine gas, is a plausible fate for the unwanted7032Ge, why doesn't every other final, stable isotope undergo fission.

There are also questions regarding the initial amounts of specific isotopes available for reaction. For example the nickel isotopes in the initial electrode are probably present in the normal isotopic composition5828Ni(68%),6028Ni(26%),6128Ni(1.1%),6228Ni(3.6%), and6428Ni(0.9%), indicating that reactions involving5828Niare far more likely to produce measurable quantities of fission/fusion products as those involving6128Nior6428Ni.Electrode impurities should react according to this same concentration dependance.

Another issue that crops up in the data analysis presented here is illustrated in the fusion of6428Niwith 3, 5, and 7 deuterons. In each case, there are multiple reaction pathways. Is one path preferred over the other? Why is one of the product isotopes absent (7032Ge,7834Se) even though it occurs along an overwhelmingly preferred pathway?

I have also looked at the range of fusion reactions between the initial electrode isotopes ( i.e.5828Ni+6028Ni,5828Ni+10747Ag+ or10747Ag+6830Zn) and also that full range of those fusion reactions, but incorporating one or more deuterons (i.e.5828Ni+10747Agn(21H+)). These pathways produce large numbers of stable isotope products that Miley did not observe, as well as some that were observed.

These are the kind of questions that have kept me up at night.

Overall the tables show that the reactions producing the lower atomic weight portion of the final electrode composition are: 1) fusion reactions of initial electrode isotopes with one or more deuterons, 2) fission reactions of initial electrode isotopes or absent isotopes, or 3) alpha decays. I have also looked at the same three types of reactions, but involving the products of the initial reactions. This was less productive.

The first three columns in Tables 1 through 8 summarize my initial analysis of Miley's data. It shows that my methods to this point account for all of the Miley isotopes through 75As, about half of those in the atomic mass range of 76 through 125, and none of the higher mass isotopes 126Te through 208Pb. I had originally suspected that I would find pairs of reactions that produced a net zero mass change. That is, that there would be no net change in energy content in the initial reaction of the reaction sequences when two or more coupled reactions occurred simultaneously. This would satisfy the reversibility constraint. However, I now realize that net zero energy changes are not required for the reactions to satisfy the reversibility requirement. All that is required is that the blackbody spectra has an absorption and emitance quantum of exactly the same energy as the difference between the initial nuclear reaction in the overall reaction sequence, and the final stable products of that reaction. The blackbody form accomplishes this implicitly. The entire continuum of spectral energies are present by definition. Thus, all reactions that can occur, do occur.

The absence of atomic masses above 20882Pband the mass accumulation in 206Pb, 207Pb and 208Pb is informative in several respects. These three isotopes are the radioactive decay end products of the uranium, actinium, and thorium series respectively. These are the most likely, if not the only, paths to them. Thus, it is reasonable to conclude that nuclei having mass greater than Pb-208 are produced in the electrode. There is no other plausible explanation of how such neutron heavy, lead products could form in the electrode given the composition of the initial nickel electrode and its impurities. More important is my estimation that there simply aren't enough neutrons in the initial system. Neutron formation appears to be one of the fundamental processes taking place in the cold fusion electrode.

The only way that heavy, trans-lead isotopes can form is by rapid neutron capture in the kind of nucleosynthesis that occurs in supernovae. I am out of my element here. But, if the radiation temperature hypothesis can be given any weight, it is not a great leap to the conclusion that the radiation temperature, TR of our far-from-equilibrium blackbody spectra could also approach stellar supernovae temperatures.

Following this argument further, it is particularly noteworthy that no intermediate, radioactive isotopes of the uranium, actinium, and thorium series are present. Decay along these routes produce unstable intermediates that should be detected in cold fusion experiments. Is it possible that the theorized reversible reaction process short circuits the decay steps to a stable end product, producing only a mass/energy change for the overall reaction. In this way none of the radioactive intermediates or time delays associated with long half-lives occur, and cold fusion proceeds without the messy radioactive signatures of other nuclear processes.

At this point, I was out of ideas and assumptions for explaining reaction products that are absent in Miley's data. Still there were outliers. And the one thing that I known with absolute certainty, is that a law of physics cannot have outliers.

As it turns out, the solution to this dilemma lay in this study's initial premise: the reactions involved in cold fusion processes are thermodynamically reversible. The one thing that all reversible reactions have in common is that their evolution is completely described by the Principle of Least Action. Thus, the rule governing the selection of specific nuclear isotope products, and the exclusion of others can be summarized:

Rule 1 – 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.

The result of applying this rule to the reactions in Web Site Tables 1 through 10 is shown in column 4. I have calculated the mass of the reactants in column 1, subtracted from it the mass in the final stable product(s) (column 3), and shown that difference in column 4. Bold type is used to highlight the product selected for by the least action principle. In several cases, I have also shown other possible reaction paths to illustrate that the selected one does indeed have the least energy change. In nearly all cases (one exceptions in Table 7), where absent products formed, or where there were several stable isotope choices, the Least Action Principle selects for an isotope in Miley's Table 3. This is true regardless of the sign associated with the overall energy change. I call this model the Least Action Nuclear Process (LANP) Model.

I have tested this model with an independent set of data that was more challenging than the data set used in its development. In particular, I had already drawn about 20 more complex decay diagrams for fusion reactions involving silver and nickel, and also multiple nickel reactants. These produced initial isotopes in the 120-205amu range. In many cases there were more than 10 intermediate decay products, some with extremely long half-lives, and others having low probability decay paths that would normally produce a small fractional of a percent of the total decay product. In all of these cases, the LANP model selects for isotopes in Miley's table, without false positives.

Figure 3. Comparison of the known decay sequence resulting from the nuclear reaction: 16776Os,with the LANP decay path. The Least Action decay is to16768Er,with subsequent alpha decay to16366Dy.However, the decay to16366Dyoccurs as a single step without any radioactive intermediates, and without any of the normal half-life decays.

Consider the reaction illustrated in Figure 3 where the nuclear reaction: produces 45 intermediate radioactive isotopes and 9 stable isotope products, three of which are in Miley's Table 3:15163Eu,15564Gd,and16366Dy.The results obtained from this reaction sequence are shown in Table 10 where the Principle of Least Action correctly selects for16366Dy,but not along the normal decay pathway shown in the Figure. Instead the Principle of Least Action selects for16768Erwith a mass change of +0.0775065amu. This is an end product of the normal decay path. It is followed by alpha decay to16366Dy,still within the domain of reversible thermodynamics. The energy change drops accordingly to +0.0767937amu. Helium is produced in this final step, but without generating excess heat via the expected pathway (Equation 1). I call this mode of nuclear decay where no radioactive intermediates are formed, and where there are no half-life time delays, -decay.

We are finally ready to look at the issue of excess heat generated in Miley's experiment. The reversibility constraint requires that the overall process be adiabatic. Therefore, we need to explore the limits of that process to identify the step at which it departs from the limiting case of the Second Law where no entropy is produced, and crosses into the domain of irreversibility, First, we note that the mass change appears as Mossbauer resonance within the far-from-equilibrium blackbody spectra. Negative mass changes increase the total energy within the spectra. Positive changes do the opposite. It seems possible that the summation of these mass changes over all reactions occurring from the point of ignition to the end of the experiment, in some way determines the time history of total excess energy production, or possibly even energy consumption.

If this energy were to enter the radiation domain at its gamma frequency, but where the number of quanta at that frequency is already saturated, the resulting imbalance necessitates re-distribution into the mass domain. Such an exchange might occur through the Wein frequency channel, where Equation 3 is the transfer function describing the re-distribution of Wein frequency energy into the domain of molecular motion. This increases the thermodynamic temperature, Tm, of the experimental device, producing excess heat. Similar thought experiments describe the evolution of endothermic LANP events, and situations in which the blackbody spectra does, or does not, have vacancies at the gamma frequency.

I believe that such a model will ultimately be capable of not only predicting the amount of excess heat produced, but also predicting the sequencing of nuclear reactions and their time history of endo- and exothermic contributions to the heat reservoir. I say this because there are only a finite number of possible nuclear reactions for a given initial isotope mix, and if the reaction progression proceeds first with an increment in the Wein frequency, and then energy storage in the radiation domain, or energy re-distribution into the mass domain, it should be possible to very precisely map this process because at each step, its continued evolution is limited to the one remaining nuclear event that satisfies the Least Action Principle. This is a very ordered and precise process.

What then is the end point where excess heat production terminates? To place a perspective on this issue, it is necessary to return to the sorting demon discussion in section C. LANP energy is achieved by harvesting random heat of21H+molecular motion, accumulating it in excited nuclear states, and then transforming it into thermo-nuclear work. The demon assumes the form of a Ni lattice structure with an affinity for deuterons. By capturing deuterons, and their kinetic energy, he traps heat energy within the lattice, and transforms that random heat of motion into excited electronic and nuclear states, and in this way, decreases the electrode's entropy. But, here is a dilemma. What trick has the demon played on us to first cause deuterons to cascade into the palladium lattice? It is this organizing principle that is his real presence, and the secret of this type of neg-entropic process.

Returning now to the cessation of excess heat production, I can only speculate that isotope transformations distort the ability of the near surface lattice to absorb deuterons. In other words, as the near-surface lattice becomes fouled with atoms that no longer participate in the demons trick, the absorption rate decreases. Nevertheless, deuterons continue to occupy deeper sites, albeit at a slower rate, and nuclear reactions continue until the rate of kinetic energy capture becomes rate limiting.

G. Some Final Thoughts

The LANP theory is not nickel specific. It can probably be applied equally well to other metal hydrides, and either hydrogen or deuterium absorption. Reactions that can be achieved within the context of reversible thermodynamics occur. Those that do not meet this standard, do not. In fact, there is no reason to limit consideration to metal hydrides. Other processes that are thermodynamically reversible could be subject to a similar theoretical treatment. I would suggest that a good case can also be made that the processes within a living cell might fit into this theoretical framework equally well (24).

The 1-D to 3-D transform function given by Equation 3 appears to be a mathematical statement of the Second Law at the boundary between electrodynamics and mechanics. In its temporal form (19) the equation represents the relative dominance of the forward(entropic) and backward (negentropic) reaction directions. As an example of this function's utility, consider its application to the phenomenon of sono-luminescence wherein mechanical energy is converted to electro-magnetic energy. In this case, mechanical energy increases Tm instantaneously without a corresponding increase in TR (Case A in Figure 3). Lacking any mechanism to maintain this far-from-equilibrium condition, the system spontaneously moves toward equilibrium by channeling the stored mechanical energy through the Wein frequency channel, and thence, into the radiation domain. If the energy flux's frequency is high enough, visible light is observed.

H. Discussion

LANP theory is unique in its ability to describe many of the unexplained phenomena occurring in a Fleischmann-Pons electrolytic cell. These include:

  1. A mechanism for loading energy into the metal hydride lattice,
  2. A mechanism for storing that energy until ignition,
  3. A theoretical basis for the fusion temperature requirement and how it is masked,
  4. A mechanism for selecting reactions and products that do and do not occur,
  5. 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 to occur requires a detailed methodology for sequencing endo- and exothermic reactions, and more discussion of Equation (2), including a 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 can be bypassed by LANP's sigma decay process. 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.

I. References

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