Low Energy Nuclear Reactions (LENR)
Reports of Prospective Reaction Equations and Energies
Based on the Deflation Fusion Model

Horace Heffner Jan, 2010

Report A - Energetically Feasible Aneutronic X + n D* -> Y + Z Reactions, for n=1 to 12
Creating Stable Isotopes Y and Z With No Weak Reactions

Report B - Energetically Feasible Aneutronic X + n p* --> Y + Z Reactions, n = 1 to 4
Creating Stable Isotopes Y and Z With No Weak Reactions

Report C - Energetically Feasible Aneutronic X + 2 D* -> X + Z Reactions
Creating Stable Isotope Z Via Nuclear Catalytic Action

Report D - Energetically Feasible Aneutronic X + n D* -> X + Z Reactions, n = 1 to 10
Creating Stable Isotope Z Via Nuclear Catalytic Action

Report E - Energetically Feasible Aneutronic X + n D* --> Y + Z Reactions, n = 1 to 1
Creating Stable Isotopes Y and Z With No Weak Reactions

Report F - Energetically Feasible Aneutronic X + n D* --> Y + Z Reactions, n = 1 to 2
Creating Stable Isotopes Y and Z With No Weak Reactions

Report G - Energetically Feasible Aneutronic X + n p* --> Y + Z Reactions, n = 1 to 1
Creating Stable Isotopes Y and Z With No Weak Reactions

Report H - Energetically Feasible Aneutronic X + n p* --> Y + Z Reactions, n = 1 to 2
Creating Stable Isotopes Y and Z With No Weak Reactions

Report i1 - Energetically Feasible Aneutronic X + n D* --> Y + Z + n e Reactions, n = 1 to 12
Where X = Ba56, Y=Sm62, (Potential reactions for Iwamura's Ba --> Sm transmutation)

Report i2 - Energetically Feasible Aneutronic X + n D* --> Y + Z + n e Reactions, n = 1to 12
Where X = Cs55, Y=Pr59, (Potential reactions for Iwamura's Cs --> Pr transmutation)

Report i3 - Energetically Feasible Aneutronic X + n D* --> Y + Z + n e Reactions, n = 1 to 12
Where X = Sr38, Y=Mo42, (Potential reactions for Iwamura's Sr --> Mo transmutation)

Report i4 - Energetically Feasible Aneutronic X + n D* --> Y + Z + n e Reactions, n = 1 to 12
Where X = Sr38, Y=Mo42, but rfact=0.85 (Iwamura's Sr --> Mo transmutation)

Report J - Evaluation Spreadsheet for Deflated Proton Fusion Candidates

Notes on Report Contents

Report A, including 48,031 reactions in 1093 pages, in 2 MB, is one of the most general types of report presented here. It is intended to identify every energetically feasible aneutronic deuterium LENR reaction that might be of any interest, whether likely to occur or even feasible within the confines of the deflation fusion theory. The only reaction conditions enforced in Report A aneutronic reactions are that proton and neutron counts are preserved, and that each reaction produces net energy. Isospin is conserved in these reactions. Note that in all reports summarized here that one or more of the fused entities is either p* or D*, deflated state hydrogen. The deflated state electrons are included in the equations even though their role is primarily catalytic, and the catalytic energy deficit effect, as described in “Cold Fusion Nuclear Reactions”, and as applied to the intermediate or compound nucleus, is included in the energy value in brackets for each reaction. It is also notable that the deflated state electrons reduce the kinetic energy of the heavy reaction products, because the bulk of the reaction energy, due to conservation of energy and momentum, goes to the electrons. This further means that there is never less than two nonzero rest mass products, so the reaction energy is not required to be carried off via one or two high energy photons, as it is in the D(D,g)4He hot fusion reaction.

What is important about some of the reports here, is not so much what kinds of reactions are in them but what is not in them across the domain of the report, e.g. across the domains of X + n D* or X + n p*. For example, what is not to be found in the reports are reactions which by conventional nuclear physics, i.e. without the nuclear electrons involved, can have no highly energetic signatures. For some reports, e.g. Reports E-H, what is important is also what is not there. Some isotopes have no immediate decay channels which are not blocked by the negative energy of the hypothesized nulear electrons. These isotopes should be the most effective at generating deflation fusion based LENR.

One of the mysteries of heavy element LENR is that large quantities of heavy transmuted material are in some experiments produced without other readily noticeable effect. This means the primary reaction types involved necessarily produce (a) no neutrons and (b) no high energy signature particles including energetic gammas. Conventional fusion reactions are thought to have insufficient time to involve a large portion of weak force reactions, so only strong force mediated reactions are included in Report A. One of the most useful aspects of Report A is that it clearly demonstrates one of the greatest mysteries of heavy element LENR, namely the mystery as to how such reactions can occur without high energy signatures, because, as can be seen in the report, nearly all such reactions yield MeV magnitude energies based on mass changes alone. This report also clearly demonstrates that even the negative energy due to catalytic electrons located at the nuclear radius, as predicted by the deflation fusion theory, is not enough to suppress the huge energies of some heavy element LENR. Therefore, the energy deficits created by the presence of deflated quarks is necessary to the explanation of heavy element transmutation LENR. It is notable that few theories that may account for deuterium fusion also account for all aspects observedin association with heavy element transmuation.

Given that no neutrons are created in the bulk of heavy element transmutation reactions, it appears likely that “excess neutrons” are given the time in the de-energized compound nucleus to decay by the catalytic electrons binding the compound nucleus. The primary weak reaction in heavy transmutation, especially for deuterium reactions, is thus likely beta decay. This momentarily increases the in-nucleus electron count and increases the Coulomb binding energy in the de-energized nucleus. It also increases the multiple low energy photon radiating ability of the compound nulceus, thus eliminating high energy signatures. The large numbers of low energy photons released from the nucleus remove constaints that might otherwise be imposed by spin or partity violations.

Report A may be of interest with regard to models other than deflation fusion. For example, it may of interest with regard to cluster fusion models. For this reason all

X + n D* --> Y + Z

reactions, for n=1 to 12 are included for all X, Y and Z isotopes with natural abundances. A smaller value of n is used for other reports here, such as the Report B

X + n p* --> Y + Z

reactions, for n = 1 to 4. Note, however, that branching ratios for deflation fusion are vastly different from other reaction types due to the presence of the electron(s) eliminating the Coulomb barrier and de-energizing the resulting nucleus. This means ordinary approaches to determining reaction outcome probabilities do not directly apply to the compound nucleus formation, because there is no Coulomb barrier to the formation of the compound nucleus by deflation fusion, nor do normal rules apply to reaction channel probabilities, because the compound nucleus is initially highly de-energized. The components of the compound nucleus are held together longer due to extra binding energy supplied by the electrons. In addition, a true compound nucleus may not actually form in all cases. The catalyzing nucleus may only provide a general vicinity for tunneling of a neutral deflated hydrogen pair from separate sites. Once in the general locus of the nucleus, a deflated hydrogen pair can jointly tunnel back out to a single adjacent lattice site. The tunneling probability out of the vicinity of the catalyzing lattice heavy nucleus is about the same to all empty adjacent sites of equal distance, but the probability of joint tunneling of a deflated hydrogen pair is increased due to their spin coupling, i.e. attracting magnetic fields. This catalytic effect is enabled energetically by the magnetic binding energy of the pair once jointly and briefly in the locale of the catalytic nucleus.

Report B, 564 kB, including 13,771 reactions in 280 pages, is similar in all ways to Report A, except it examines energetically feasible reactions of the form:

X + n p* --> Y + Z

for n = 1 to 4.

Report C, including 288 reactions in 20 pages, 44 kB, demonstrates 3-body nuclear catalytic LENR reactions, which can more simply just be be called “nuclear catalytic reactions”, or NCRs, a new class of LENR reaction proposed by this author. This class of reaction may provide a fundamental new understanding of how hydrogen fusion most often occurs in a lattice, by use of the lattice heavy element nuclei as catalysts. A given hydrogen atom is much closer to lattice element nuclei than to any other hydrogen atom in the lattice. If a hydrogen nucleus is in the deflated state, it is much more probable it will tunnel to a lattice nucleus than to the site of another hydrogen nucleus which is much further away. Tunneling distance is in an exponential term of the tunneling probability. The lattice nucleus can thus act as a catalyst for multiple simultaneous deuteron reactions which would otherwise not be feasible under less than extreme loading conditions. In that magnetic gradients are necessary to the tunneling of deflated state nuclei, and thus heavy element LENR, it is therefore also true that magnetic gradients are important to n-body heavy element catalytic LENR. High magnetic fields are also important todeflation fusion because it tends to spin align the deflated nucleus and thus improve spin coupling binding energy. While only 3-body reactions of the type:

X + 2 D* --> X + Y

were selected for Report C, it is also true that many more (n+1)-body catalytic reactions of the form:

X + n D* --> X + Y

can be found in Report A, and reactions solely of that type are in Report D. It is likely that 3-body catalytic reactions, rather than n-body reactions, n > 3, dominate heavy element catalyzed LENR, so Report C was created to show only those reactions, though it is very boring as they are all exactly of the form:

X + 2 D* --> X + 4He2 + 23.847 MeV

What notably changes is the energy deficit due to deflated electrons. It appears elements heavier than tin can be expected to be capable of weak reactions and heavy element transmutation LENR.
It is especially notable that no equivalent report is feasible for the strong force catalytic reactions:

X + 2 p* ---> X + Z

because no such reactions are feasible producing stable Z, because pp is not a stable particle. This makes for a significant difference between light water and heavy water experiments. Light water experiments are not capable of heavy element catalytic LENR unless weak reactions follow the creation of the compound nucleus. This makes such reactions rare. It is feasible for X + n p* --> X + Z heavy element transmutation reactions to occur via strong force reactions, but only in the cases n > 2, or the cases of reactions of the form X + 2 p* --> Y + H. It is important to note that

X + 2 p* --> Y + H

is energetically not the same as:

X + p* --> Y

because the negative energy due to the two catalytic electrons in the former greatly exceeds the negative energy provided by the single catalytic electron in the later reaction. Further, two additional bodies are available to carry off kinetic energy. For example, consider the two reactions:

26Mg12 + p* --> 27Al13 + 8.271 MeV [3.663 MeV]
26Mg12 + 2 p* --> 27Al13 + 1H1 + 8.271 MeV [-1.593 MeV]

The trapping energy of the extra deflated electron provides a strong catalytic influence due to the initial negative reaction energy, i.e. due to deflated electron binding energy immediaely post fusion.

Report D, 136 kB, including 2,016 reactions in 94 pages, provides all the energetically feasible X + n D* --> X + Z Reactions, for n = 1 to 4. These are in the set of all n-body heavy element nuclear catalytic LENR reactions, a new class of reaction. Note the preponderance of negative energies in brackets for the heaviest lattice elements. This indicates good prospects for subsequent weak reactions when these heavy elements are in the lattice. Such weak rections are covered in separate reports.

It is notable that the above reports merely examined energetically feasible final products, without regard to the nature of the compound nucleus. 
If lead can be used productively as a deuterium to helium nuclear catalyst effectively then lead is an interesting candidate because it is cheap and plentiful, and because its various naturally occurring stable isotopes are terminal isotopes in a number of decay chains.  Though lead does not make a useful CF lattice by itself, it might be co-deposited with deuterium and with Pd or Ni or other appropriate lattice forming element, including Ca.  Deuterium can be diffused through lead layers to enable the reactions, or possibly diffused through a medium with lead nanoparticles  or through a low conductivity lead alloy. Numerous lead alloys are commercially available, including lead-calcium alloys used commonly in battery electrodes.  See:


Key is utilization of a hydrogen permeable high lead content lattice.  Lead alloys have low melting points, which might be useful for helium removal. 
Of further interest is that the Pd + 2D* compound nuclei spontaneously alpha decay with practical half-lives, even if their source is not LENR. 
The lead isotopes and natural abundances are:

El.        Abundance
204Pb   1.4% (1.4x10^17 y half-life)
206Pb   24.1%
207Pb   22.1%
208Pb   52.4%

The primary lead nuclear catalytic reactions are:

208Pb82 + 2D* --> 212Po84 --> 4He2 + 208Pb82   (3x10^-7 s half life)
207Pb82 + 2D* --> 211Po84 --> 4He2 + 207Pb82   (56 ms half life)
206Pb82 + 2D* --> 210Po84 --> 4He2 + 206Pb82   (148.37 d half life)

with some much less common (and desirable) additional reactions:

204Pb82 + 2D* --> 208Po84 --> 4He2 + 204Pb82   (2.898 y half life)
204Pb82 + 2D* + e- --> 208Po84 + e- --> 208Bi83     (2.898 y half life)

The half lives given, though they apply to the compound nuclei, are only upper limits in these cases, because they only apply to nuclei without tightly bound free electrons in them. Such electrons generate much shorter half-lives and precipitate heavy fragment fissions.

Unfortunately, of the above isotopes of lead, only 207Pb has a nuclear moment, which is useful in increasing tunneling probability.  More interesting from the perspective of magnetic moment is 209Bi, which has a 100% abundance, and a large nuclear magnetic moment in comparison to 208Pb.  

Bismuth-209 appears to be an excellent CF nuclear catalysis agent when used with deuterium. It has 100% abundance. The bismuth nuclear catalysis LENR reaction is:

209Bi83 + 2 D* --> 213At85 --> 209Bi83 + 4He2 + 23.847 MeV [-8.560 MeV] (125 ns)

The major potential drawbacks are the presence of energetically feasible fission reaction channels not deflated electron confined:

209Bi83 + D* --> 198Pt78 + 13C6 + 21.660 MeV [5.599 MeV]

209Bi83 + 2 D* --> 198Pt78 + 15N7 + 37.819 MeV [5.412 MeV]

bismuth has a typically low melting point, even in many alloys, and bismuth does not sustain a viable CF lattice by itself, i.e. must be imbedded in a useful lattice. It has a lattice constant of 4.75 Å, as opposed to Pd at 3.89 Å, and iron at 2.87 Å. Interesting coincidence that the average of iron and bismuth lattice constants is within about 2% of that of Pd. A bismuth-iron alloy might provide a feasible CF lattice at high loading temperatures.

Bismuth has a spin of 9/2, a large value of mu = 4.5444 mu_N, and gyromagnetic ratio of 43.75 x 10^6 rad s^-1 T^-1. It has a nuclear magnetic resonance frequency of 6.963 MHz in a 1 T field.

Nuclear catalysis is carried out best in as large a magnetic field as possible, using as large a B field gradient as possible. Other considerations are documented here:



Report E, 168 kB, 109 pages, provides all 1,203 energetically feasible reactions of the form X + D* --> Y + Z, with the added information provided by the table “Electron constrained isotopes involving up to 1 D fusions”. This kind of table, and its supporting documentation in the form of the reaction equations, is the principle aim of Reports E-H. This kind of table is useful for designing deuterium based experiments because it identifies which isotopes and elements are effective at creating nuclei that are initially sufficiently de-energized such that no reaction channel is available until the electron wavelengths expand sufficiently to eliminate the energy deficit caused by deflation fusion. Reports E-H are also useful for designing experiments intended to produce kaons and strange matter. Ziconium should be very effective in this regard, due to its ability to sustain high voltage glow electrolysis.

One of the more notable features in reports E-H is the effectiveness of 16O in catalyzing deuterium reactions, and its ineffectiveness in catalyzing protium reactions.

For each source element in the Reports E-H, a “Fusion Product Chart” is produced at the end of the reaction equations for that source element. It is weighted by source isotope abundance, the square of the ratio of fusion energy to deflated hydrogen binding energy, and inversely as the square of the number of deuterons fused. This chart, which has the general appearance of an element spectrogram, is not yet a predictive spectrogram, but is provided at this point merely as a somewhat arbitrary visual representation of the equation data.

Report F, 201 Pages, 336 kB, examines the 4,500 X + n D* --> Y + Z, n = 1 to 2, reactions to look for elements and isotopes with good hydrogen fusion catalytic qualities. Tl, Pb, Th, Pa, and U stand out in the “Electron constrained isotopes involving up to 2 D fusions” Table, though the lattices for these appear to not be effective in producing cold fusion. These elements may be more effectively located in the electrolyte in HV glow experiments, or more effectively used as lattice dopants or co-deposited agents. The fact that 32% of Pt atoms are effective as X + 2 D* nuclear catalysts, while Pd and Ni are not, is also potentially useful information. This is a sparse and unexpected list.

Report G, 123 pages, 188 kB examines the 1,484 feasible reactions of the form X + p* --> Y + Z. The lack of effectiveness of Ni shown in the “Electron constrained isotopes involving up to 1 p fusions” Table, and the apparent effectiveness of Cu, are both notable, as these are unexpected. Ce, Ba, Y, Sr and U stand out as very effective. Br and Se stand out for use as an electrolyte ingredient in high voltage light water anode glow type electrolysis experiments.

Report H, 203 pages, 348 kB, examines the 5,025 energetically feasible reactions of the form X + n p* --> Y + Z, for n = 1 to 2. Of special interest here is the effectiveness of thorium in producing the reactions:

232Th90 + 2 p* --> 234U92 + 11.880 MeV [-22.144 MeV] (H_Th:1)

232Th90 + 2 D* --> 232Th90 + 4He2 + 23.847 MeV [-10.081 MeV] (F_Th:1)

as well as the lack of the presence of Th in Reports E and G. This may be an indication that Thorium “remediation” experiments, which expose Th to light water cavitation, may be producing some uranium. The half-life of 234U is 245,500 years. The deuterium reaction with thorium is nuclear catalytic in producing 4He, which might be useful, but does not provide remediation.

Also very notable is the high effectiveness of all the isotopes of Ni for X + 2 p* reactions, while only the 0.925% abundant 64Ni is effective at X + p* reactions. This is an indication that a light water experiment with 64Ni enriched nickel may be useful.

Report H indicates iron and various forms of steel are under explored for light water Fe + 2 p* reactions, especially for the apparent ability to produce Co and Ni.

Report i1 shows all feasible reactions, under the above stated assumptions, for the Ba --> Sm transmutations observed by Iwamura. Most interesting is the necessity of a minimum of 6 D fusions with the Ba. It is also notable that all combinations have negative energy due to the electrons, thus the reactions can occur without high energy signatures.

Report i2 shows all feasible reactions, under the above stated assumptions, for the Cs --> Pr transmutations observed by Iwamura. There is only a necessity of a minimum of 4 D fusions with the Ba. It is also notable that all combinations have negative energy due to the electrons, thus the reactions can occur without high energy signatures.

Report i3 shows all feasible reactions, under the above stated assumptions, for the Sr --> Mo transmutations observed by Iwamura. Only the reaction:

88Sr38 + 6 D* --> 97Mo42 + 3He2 + 63.502 MeV [-0.531 MeV]

has a prospect of ocurring without high energy signatures. However, the assumption in Report i3 is that the deflated electron negative energy is a result of being located at the mean radius of the compound nucleus. If the electrons are assumed to reside at an average of 0.9 times that radius, then many of the strontium reactions start looking like viable explanations. This was done in Report i4.

Report i4 is identical to Report i3 except the deflated electron post fusion mean orbital radius is reduced in size by 10%. Many of the strontium reactions now start looking like viable explanations. All this means is that the energy deficit based on electrons at the compound nucleus average radius is not enough to explain the experimental observations. It is necessary to use a smaller radius.  In fact, only when positive quarks are used as the nucleating point for deflation fusion does the situation begin to make sense when you look at the big picture.  A significant part of the de-energization comes from the de-energizing of the proton itself, as described in “Cold Fusion Nuclear Reactions”.