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Yet Another LENR Theory:
Electron Mediated Nuclear Reactions (EMNR)
1
#Andrea Calaon 1
Independent Researcher, Monza, Italy, a.calaon@libero.it
An attempt is made to build an LENR theory that does not contradict the basic principles of physics and gives a
relatively simple explanation to the plethora of experimental results.
The theory is based on two assumptions. The first is that nuclei are kept together by the magnetic attraction
proposed by Valerio Dallacasa and Norman Cook ([1] and [2]). The second assumption is that the Zitterbewegung
of the electron ([3]) can generate the same magnetic attractive force between the electron and a nucleon/nucleus.
This force can couple the electron to any of the three isotopes of hydrogen and lead to the formation of an almost
neutral pseudo-particle, named here Hydronion. This particle can then couple with (almost) any other nucleus and
lead to a soft nuclear fusion reaction with very low excess kinetic energy. So the Coulomb barrier is not overcome
kinetically, but through what could be interpreted as a range extension of the nuclear force itself, done by the
electron when a series of conditions are satisfied.
The large quanta of nuclear energy fractionate into photons thanks to the accelerations of the charges during the
formation of the Hydronions, during the coupling of Hydronions to other nuclei and during the approach of two
nuclei “inside” the Hydronions.
The formation of Hydronions requires the very special conditions that make LENR so rare and difficult to
reproduce: The so called Nuclear Active Environment (NAE). It is proposed that the NAE is formed when vacancy
hopping (between two adjacent positions) becomes part of a “phonon resonance” of very small domains, which
have almost no other defects (dislocations, cracks or voids) and are highly loaded with hydrogen nuclei.
Background
The fact that the LENR phenomenon has been discussed for 26 years and no widely accepted explanation has
emerged, suggests that the phenomenon in based on some new or not commonly accepted fact of physics.
Uncommon Assumptions
The theory proposed here is based on the following uncommon assumptions:
• Nuclei are kept together by the electromagnetic interaction through the magnetic attraction mechanism
proposed by Dallacasa and Cook ([1]). The approach assumes that the magnetic moment of nucleons comes
from the rotation of charges (quarks), and not from gluons or intrinsic properties of the quarks.
• The electron Zitterbewegung (ZB) is not different from the internal charge rotation of the nucleons. So
electrons can be attracted to nucleons by the same magnetic force that keeps nucleons together in nuclei.
Magnetic Attraction Mechanism
The description of the attraction mechanism done by Dallacasa and Cook in [1] is repeated here with some changes
to the original proposal.
If a particle has a magnetic moment it must generate a magnetic field that oscillates. Here it is assumed that the
magnetic moment of particles comes from the rotation of a single charge travelling along a circular orbit at the
speed of light (c). Whereas this assumption is essentially in accordance with what we know about the electron, it is
not for the nucleons, which have three fractional charges of opposite sign. However, for this simple case, one gets:
• Rotation radius:
• Rotation Frequency:
r=2
mmag
gqc
ω=
c
2π r
Where mmag is the magnetic moment, g the gyromagnetic ratio and q the particle charge.
Let us now evaluate the oscillating magnetic field. Since non-accelerated particles do not emit electromagnetic
radiation, the associated magnetic field can not have the radiative component, and can only correspond to the so
called “static” part of the Liénard–Wiechert potential. Moreover, since the speed of the charge is assumed to be
equal to c, the only expression for B that makes sense is the very well known non-elativistic expression:
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μ 0 q1 v 1∧|R12|
4π
R 212
where the subscript 1 stands for the emitting charge, and 2 for the place where the magnetic field is evaluated. μ0 is
the vacuum permeability, v1 is the particle speed (in modulus equal to c), R12 is the radius at which the magnetic
field has to be evaluated and |R12| is the unit vector in the direction of the vector R12.
When another massive particle with a magnetic moment is immersed into this magnetic field, the magnetic part of
the Lorentz force (F2=qv2B1) generates a “strong” (oscillating) attractive force that can overcome the electrostatic
repulsion. The formula is:
μ m
m
|v |∧|v 2|∧|R 12|
[2]
,
F 2= π0 mag 2 mag1 1
g2 r2 g 1 r 1
R 212
where the mmag are the magnetic moments of the two particles, v the charge speeds, r the charge rotation radius and
the notation |.| means a unit vector.
The attractive force reaches high values only if some necessary conditions are satisfied:
• Alignment of the two magnetic moments (i.e. spin): parallel or anti-parallel, apart from precession.
• Frequency: Synchronous rotation.
• Phase: zero for parallel spins and half-cycle for anti-parallel spins.
In the case of the proton:
• rp = 0.105 [fm] (much smaller than its charge radius, which is around … 0.8775 [fm])
• ωp = 4.54∙1023 [Hz]
At typical nucleon separation distances (~2 [fm]), the potential of the attractive force obtained with these data is of
the same order of magnitude of the nuclear force, i.e. a few [MeV].
So, if both nucleons have the same internal charge rotation frequency this force could well be responsible for the so
called “nuclear force”. This is what Cook and Dallacasa suggest ([1]). The short range of the nuclear force would
be due the fact that the necessary phasing is reached only at very short distances.
Many more considerations could be done regarding this attraction mechanism.
[1]
B 1=
Electron Zitterbewegung
The electron manifests as a point charge with an intrinsic and very rapid rotation at 2.47·10 20 [Hz], the so called
Zitterbewegung (ZB). The commonly defined “speed” of the electron combines with the rapid ZB giving a
“variable pitch” helical motion. The apparent radius, as seen by an external (inertial) observer shrinks as the speed
of the “speed” of the electron approaches c. The “static” radius is about 193 [fm], much larger than the nucleons.
The only value that makes sense for the module of the charge speed along the ZB trajectory is the speed of light.
The spin, the magnetic dipole moment and the nature of the electron orbitals are consequences of this very rapid
rotation.
Coupling Between Electron and Hydrogen Nucleus
One necessary condition for the manifestation of a net attraction is a synchronous charge rotation. Electron and
nucleon intrinsic frequencies (calculated as explained before) are not equal, in fact their ratio is ω p/ωe =
1,836.152…, which corresponds to their mass ratio (m proton/melectron). So the only way to have an attraction between
the electron and a hydrogen nucleus is having the electron rotate around the proton (spins aligned) at about 2 [kHz].
This frequency is clearly extremely low and appears to have nothing to share with orbital and electron properties in
any condensed matter state. At any given temperature the average speed of electrons is much higher than that of
hydrogen nuclei because of the mass ratio. Electrons bound to light nuclei have “average speeds” approximately
equal to the atomic number multiplied by the ratio between c and the (reciprocal of the) fine structure constant a
(about 137): Zc/a. In the hydrogen atom for example the electron “speed” is about 2.200 [km/s]. In solids instead
the nuclei vibrate at a few [km/s].
So normally the electron wave function does not allow it to “rotate” around the proton at the very low frequency
necessary for the magnetic attraction, and no net force manifests between these two particles.
It must be said that in the case of electron and hydrogen nucleus there is no electrostatic repulsion and the magnetic
attraction can be effective at larger distances if compared to the case of two nucleons/nuclei.
The NAE should therefore host a mechanism that somehow “slows down” the electron despite being at low
distances from the proton. This will be discussed later.
Now let us imagine that all the necessary conditions are satisfied and a hydrogen nucleus and an electron accelerate
towards each other radiating photons (possibly through different energy levels). They pass from a free to a bound
state. In fact when the hydrogen nucleus crosses the ZB radius the attractive magnetic force becomes repulsive, so
that the hydrogen nucleus is captured inside the ZB trajectory, as schematically shown in Fig. 1.
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Fig. 1. Schematic view of a Hydronion with the p/d/t bound to move along the ZB trajectory.
Actually, due to the mass ratio, it will be the electron that moves towards the proton.
A possibly stable pseudo-particle forms. This particle will be called here Hydronion (Hyd).
As the stable isotopes of hydrogen are three, there are three possible reactions that generate three different
Hydronions:
0p: p+e -> pe (Hydronius) +
0d: d+e -> de (Deuteronius)+
0t: t+e -> te (Tritionius) +
Gp [MeV]
Gd [MeV]
Gt [MeV]
Gp, Gd and Gt are the binding energies of the Hydronions.
Since the mass of the hydrogen nucleus is much larger than the mass of the electron, the electron trajectory would
look more like a circle fixed at the hydrogen nucleus location and turning around it at about 2 [kHz].
Randell L. Mills called the same object Hydrino, describing it as a “compact hydrogen”. The present theory
suggests however that this particle has little to share with the hydrogen atom.
The LENR Take Place in Two Stages
Hydronions have a maximum charge displacement vector of 386 [fm] and a pulsation frequency around 10 20 [Hz]
(essentially this is the electron Compton frequency), therefore they should travel much more freely than electrons
and nuclei inside matter.
Hydronions can attract other nuclei towards the ZB trajectory though the magnetic attraction. Once two nuclei are
both moving along the ZB, they will attract each other because now their magnetic moments are aligned and
probably will phase. Fig. 2 tries to depict this.
Fig. 2. A Hyd has “captured” a nucleus and the two nuclei attract each other emitting photons.
The nuclear fusion between the two nuclei happens only when their distance is down to a few femtometres. The
electron provides very special conditions for the fusion reaction, which si probably the reason why the LENR do no
generate the same products of hot fusion.
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Depending on the hydrogen isotope of the Hyd, there are a series of possibilities for the fusion reaction:
With Hydronius (ep):
(p1) Nu(Z,A) + ep -> Nu(Z,A+1)
+ neutrino
(p2) Nu(Z,A) + ep -> Nu(Z+1,A+1) + e
+ photons
+ photons
With Deuteronius (ed):
(d1) Nu(Z,A) +
(d2) Nu(Z,A) +
(d3) Nu(Z,A) +
?(d4) Nu(Z,A) +
ed
ed
ed
ed
->
->
->
->
Nu(Z,A+2)
Nu(Z+1,A+2)
Nu(Z,A+1)
Nu(Z+1,A+1)
+
+
+
+
neutrino
e
ep
e + n
+
+
+
+
photons
photons
photons
photons
With Tritionius (et):
(t1) Nu(Z,A)
(t2) Nu(Z,A)
(t3) Nu(Z,A)
(t4) Nu(Z,A)
?(t5) Nu(Z,A)
et
et
et
et
et
->
->
->
->
->
Nu(Z,A+3)
Nu(Z+1,A+2)
Nu(Z,A+2)
Nu(Z,A+1)
Nu(Z+1,A+1)
+
+
+
+
+
neutrino
e
ep
ed
e + 2n
+
+
+
+
+
photons
photons
photons
photons
photons
+
+
+
+
+
The reactions with the question mark probably are impossible, because they would liberate two neutrons.
The nuclear reaction could even be delayed until a stable nucleus can form (multiple couplings), as the results of
Iwamura seem to suggest ([7]).
So the LENR take place in two stages:
• First Stage: Generation of Hydronions (this stage needs a NAE),
• Second Stage: The Hyd are captured by other nuclei and host nuclear reactions at very low excess kinetic
energy.
The flow of Hyd should be the “strange radiation” detected in many LENR experiments.
The Second Stage is responsible for the metachronous thermal effects and the double optimal operating power
measured by Mitchell Swartz (see ref. [4]).
Second Stage Reactions with Hydrogen Nuclei
When Hyd react with hydrogen nuclei the possible reactions are these:
1e :
2e :
3e :
3 :
4e:
4.1:
4.2:
5e :
5 :
6e :
6.1:
6.2:
7
:
p+ep
->d
p+ed
->t
d+ep
->t
d+ep
->He3
d+ed+0.141[MeV]+Gd->H4
H4 ->t
d+ed
->He4
d+ed
->t
t+ep+4.174[MeV]+Gp->H4
H4 ->t
t+ep
->He4
t+ed+5.318[MeV]+Gd->H5
H5 ->t
t+ed
->He5
He5 ->He4
t+ed+5.616[MeV]+Gd->H4
H4 ->t
t(beta decay)
->He3
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
neutrino + (max)
1.442[MeV] - Gp
neutrino + (max)
5.475[MeV] - Gd
neutrino + (max)
5.475[MeV] - Gp
e +
4.472[MeV] - Gp
neutrino +
0.00 [MeV]
n +
3.391[MeV]
e +
22.825[MeV] - Gd
ep +
4.033[MeV] - Gd + Gp
neutrino +
0.00 [MeV]
n +
3.391[MeV]
e +
18.792[MeV] - Gp
neutrino +
0.00 [MeV]
2n +
2.311[MeV]
e +
15.832[MeV] - Gd
n +
0.735[MeV]
ep
0.00 [MeV] + Gp
n +
3.391[MeV]
e + antineut. + (aver) 5.7 [KeV]
He3 can turn into He4 in presence of Hydronius or Deuteronius with these reactions:
8e : He3+ep
9 : He3+ed
->He4 + neutrino + (max)
->He4 + ep
+ (max)
19.80 [MeV]
20.58 [MeV]
Remarks:
• The reactions producing neutrons are all endothermic, apart form reaction 6.1, which requires tritium.
• If Gp > 1.442 [MeV] reaction 1e is endothermic and no deuterium is produced without stimulation (this is
supported by Iwamura's results ([7]) as discussed later).
• When He4 is produced there is a large energy release.
• The minimum energy contribution for producing neutrons is 0.141[MeV] + Gd (raction 4e).
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• Tritium is generated without the production of free neutrons: this explains the so called “branching ratio
anomaly”.
• When tritium is destroyed in presence of Deuteronius (reaction 6.1), neutrons are produced.
• If Hydronius (ep) decomposes, reaction 4.2 is the source of protons/molecular hydrogen in cases of deuterium
loading.
• When tritium is destroyed, a large quantity of energy is released.
• These reaction resemble in some the isotopic ladder that Brillouin Energy Corp. proposes.
It is guessed that titanium emits more neutrons than other materials because the Hyd formation in its structure
generates photons that stimulate reaction 4e.
Some General Remarks
Susceptibility to a Magnetic Field
Since the proposed LENR mechanism is essentially magnetic, it should be susceptible to the presence of a magnetic
field. In fact this has been confirmed by many experiments.
Some Nuclei Do Not React
As the Hot-Cat measurement shows ([6]), some nuclei do not react at all. The magnetic coupling in fact has a
chance to take place only if a nucleus has a magnetic moment of first or higher order. Probably Ni62 does not have
magnetic moments, due to symmetry.
Preference for Stable Nuclei
Inside the ZB the two reacting nuclei approach at a very low excess kinetic energy. This could be the reason why
unstable and more massive isotopes are somehow avoided. Anyway the mediation of the electron offers to the
fusion reaction an unusual setting.
No Tritium Accumulation
The magnetic moments of protium and tritium are higher than the magnetic moment of deuterium, in fact m d/mp =
0.31, mt/mp = 1.07. So the reactions with deuterium should be kinetically slower than those with protium and
tritium.
Here are summarized the exothermic reactions that generate tritium and that destroy it:
Sources of tritium
2e : p+ed
3e : d+ep
4.2: d+ed
->t
->t
->t
+ neutrino + (max)
+ neutrino + (max)
+ ep +
5.475[MeV] - Gd
5.475[MeV] - Gp
4.033[MeV] - Gd + Gp
Tritium Sink
5
: t+ep
->He4 + e +
18.792[MeV] - Gp
Since all reactions producing tritium involve deuterium (slower reaction), while the elimination of tritium involves
protium (faster reaction), tritium should not accumulate.
This should be the basic reason for the lack of accumulation of tritium and for its reported elimination.
The Nuclear Active Environment (NAE)
The most important bit of any LENR theory, necessary for any industrial application, is the NAE.
The two necessary conditions for the formation of a Hydronion are:
• electron and proton must rotate one around the other at such a low speed that it almost corresponds to rest,
• at the same time the distance between them must be very short, whereas normally the bound electron has
“higher speeds” when it travels nearer to the positive charge.
Normally electrons turn too fast around nuclei, and inside a solid it is not possible to accelerate the hydrogen nuclei.
It is however possible to imagine a mechanism that “moves around” an electron orbital at low radio frequencies.
The guess is that there could be a coupling mechanism between phonons and an alternate vacancy hopping.
The equilibrium density of vacancies is very low in a regular lattice, and can increase significantly only at
temperatures near to the melting point. However near to the surface of nanometre sized grains the lattice is so
distorted that the density of vacancies can be high enough.
Generally the energy of phonons is too low for a coupling with a vacancy hopping. But the distance between the
energies of the two mechanisms can be reduced. In fact the energy of the vacancy hopping can be lowered near to
the surface of metal grains where the metal lattice distortion is increased by the contribution of non-metallic
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superficial compounds ([7]) or by the presence of (almost) interstitial elements like lithium ([6]). Moreover inside
nanometre sized grains the phonons are non-linear and the vibrational energy can concentrate greatly near to the
surface.
Once the alternated vacancy hopping becomes part of the steady lattice oscillations the electron orbital can
effectively acquire a low frequency angular momentum component and couple with the hydrogen nuclei. In other
words the solid state is guaranteeing that the orbital will be regularly dragged along the alternate vacancy hopping.
For the analysis or the simulation of such a phenomenon, the Born Oppenheimer approximation has to be
abandoned in favour of a full coupling between electron orbital and the nucleus movement.
Why Vacancies Movement?
There are a number of experimental evidences suggesting the implication of vacancy movement in the NAE:
• Requirement of an irregular surface with non-metallic structures. As already mentioned, this deforms the
metallic lattice near to the surface, allowing more vacancies than those due to the pure “superficial tension”.
• Requirement of careful annealing after plastic deformation of Pd foils ([5]). This eliminates dislocations after
plastic deformation, but not the superficial vacancies. Dislocations would in fact absorb and scatter energy
from the phonon bath and prevent an effective coupling between phonons and vacancy hopping.
• Requirement of very small grains (under the “Hall Petch” limit), which have almost no dislocations,
• At least part of the RF emission measured by ENEA ([5]) could be due to a vacancy hopping resonance
mechanism.
Possible Formation Energies of ep and ed form Iwamura's Measured Radiation
In [7] Iwamura et al. measured the emission of several unknown gamma peaks. The highest peaks are at 1.445 and
1.745 [MeV]. In light of the present theory they should correspond to the energies released at the formation of
Deuteronius and Hydronius respectively. This would mean that reaction 1e is endothermic and requires at least 303
[keV] of stimulation.
This should be the reason for the lack of deuterium in the ash of the Lugano test in ref. [6]. The absence of
deuterium prevents the development of all reactions from 2 to 7 and so the generation of “classical” LENR products
like tritium, He3 and He4.
Summary of Relevant Features of the Proposed EMNR Theory
This proposed EMNR theory has a series of fundamental features that are summarized here:
• The Coulomb barrier is not overcome kinetically.
• The nuclear binding energy is electromagnetic and, thanks to the mediation of the electron, the LENR can
release at least part of it as photons during the formation of the Hyd and during the nuclear approach that
takes place inside the electron “race track”.
• The LENR take place in two stages:
– First Stage: Formation of the Hydronions,
– Second Stage: the “neutral” Hyd travel capture other nuclei which then fuse “inside the electron”.
• The NAE is proposed to be a coupling between the phonons and an alternate vacancy hopping that gives an
electron orbital a very low frequency angular momentum component, necessary for the coupling.
References
[1] Dallacasa V., Cook N. D., Models of the Atomic Nucleus, ISBN-10: 3540285695
[2] Cook Norman D., Dallacasa V., LENR and Nuclear Structure Theory for ICCF-17.
[3] Hestenes D., “Zitterbewegung in Quantum Mechanics – a research program”, on arXiv.org:
http://arxiv.org/abs/0802.2728v1
[4] Swartz Mitchell, “Amplification and Restoration of Energy Gain Using Fractionated Magnetic Fields on
ZrO2-PdD Nanostructured CF/LANR Quantum Electronic Component ”, ICCF 18, 2013
[5] Violante V., Castagna E., Lecci S., Pagano G., Sansovini M., Sarto F., “RF detection and anomalous heat
production during electrochemical loading of deuterium in palladium”, DOI 10.12910/EAI2014-6, 2014
[6] Giuseppe Levi, Evelyn Foschi, Bo Höistad, Roland Pettersson, Lars Tegnér, Hanno Essén, Observation of
abundant heat production from a reactor device and of isotopic changes in the fuel.
[7] Iwamura Y.,Tsuruga S. and Itoh T., Recent Advances in Deuterium Permeation Induced Transmutation
Experiments using Nano - Structured Pd / CaO / Pd Multilayer Thin Film, presented in 2013 at ICCF 18.
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