Heavy Electron Catalysis of Nuclear Reactions

Keywords: Band structure, Catalysis, Heavy electron, Muon, Transmutation, Tunneling

∗Corresponding author. Address for correspondence: 211 North Citrus STN 27, Escondido, CA 92037, USA, Tel.: +1-858-753-8964,

†Address for correspondence: 1061 210th Street, Ionia, Iowa, 50646, USA, Tel.: +1-217-369-0489, E-mail:dolantj@illinois.edu.

A.C. Zuppero and T.J. Dolan / Journal of Condensed Matter Nuclear Science 31 (2020) 62–90 63

Our proposed three-body model attempts to understand the transmutations that have been observed in many experiments. The model combines several phenomena to derive the conditions where a binding potential energy and an electron’s Coulomb bond can combine to attract the ions together to form a new nucleus.

We hypothesize that heavy electron quasiparticles are created by placing electrons near inflection points of a lattice band diagram and last about one collision time (∼10 fs). They are placed near the inflection point by injection of phonons carrying crystal momentum, which last picoseconds, long enough to create many generations of transient heavy electron quasiparticles.

We consider the interaction of two ions, such as a nickel nucleus and a proton, separated by a distance x with an electron of mass m trapped between them. The increase in energy needed to confine the electron (Kinetic Energy of Confinement, KEC) ∝ 1/(mx2 ) from the Heisenberg Uncertainty Principle acts like a repulsive potential.

The KEC keeps the ions separated by many picometers, but with a heavy electron that distance can be reduced to tens of femtometers, from where the heavy electron tunnels through the region between reactant ions. The transient shielding by the evanescent electron wavefunction at the nucleus permits the f and R nuclear bond to form, and scatters the electron.

The electron may be ejected with much or all of the nuclear binding energy, or the excited compound nucleus may break into stable fragments. The Hamiltonian is

where Te is the kinetic energy of the electrons, Ti the kinetic energy of the nuclei, Ve the net Coulomb potential, and Vb is the independent binding energy (other than Ve). For example,Vb may be a nuclear binding potential Vnuc, which is zero except at very small x ∼ several fm.

We approximate these potentials using a one-dimensional analysis, calculate the approach distances, calculate the threshold electron mass for tunneling to occur, and estimate the tunneling probability for many possible reactions.

We compare the 1D model predictions with data from experiments, such as transmutation of Ni into Fe, Cu, and Zn.

If we can create many heavy electron quasiparticles, then our model predictions are consistent with transmutation data from many experiments, showing which isotopes are probable and which are improbable.

• Kinetic Energy of Confinement (KEC), due to the Heisenberg Uncertainty Principle.

We will discuss each phenomenon, and then combine them to model nuclear transmutations that have been reported experimentally.

Consider a three-body reaction where two reactants R and f can bond together by the Coulomb attraction of an electron bond between them, and also by an independent binding mechanism (chemical or nuclear), as in Fig. 1.

There are two separate potentials: a three-body Coulomb potential of R + e + f; and an independent, two-body potential binding only the reactant R and fuel f. Chemists have discovered that when the R and f merge into a new entity, Rf, the bonding electron between ions R and f can be ejected with most of the binding energy, and the new molecule Rf is left in a lower energy vibration state.

The other electrons are responsible for the independent chemical binding mechanism. That a single electron captures the binding energy instead of a thermal bath was an unexpected discovery.

The binding reaction of R and f with an ejection of a single electron was discovered in chemical physics during the 2000s. The principle of operation for the chemical physics case had a a potential energy diagram the same as a hydrogen

Figure 1. The reaction includes a three-body electron σg (“sigma gerade”) bond plus an independent binding potential between a reactant R and a fuel f that does not require the σg electron.

Figure 2. H gives up electron at Ag surface. Principle of chemicurrent detection.

H atoms react and bond with the metal surface creating e–h pairs. The hot electrons travel ballistically through the film into the semiconductor where they are detected.

Right-hand side: Schematic cut view through the H sensing Schottky diode. The ultrathin metal film is connected to the Ag pad during evaporation [1].

and nickel nuclear reaction. Understanding the chemical physics case would mean that we could understand the H–Ni reaction.

Before 2000, a common assumption for chemists and physicists was that a vibrating molecule would lose 1, or at most 2, vibrational quanta during a chemical reaction. The energy released would either be radiated or given to a sea of thermal electrons at the Fermi level of a conducting wall where the vibrating molecule collided or was attached.

The “molecule” in the first observation comprised a free radical bonded to a conductor surface. Nienhaus et al. at UC Santa Barbara provided the first observations in April 1999, Fig. 2.

During 1999, Nienhaus provided free radicals such as H, OH, CH2, and O to a 6 nm thin silver conducting nanolayer sheet [2]. The nanolayer on top of n-silicon made a Schottky diode that put a voltage barrier preventing any electron with energy less than the barrier from going over the barrier.

Nienhaus was one of the few who knew a higher energy electron would be emitted. He measured electron current which had to have higher energy than the barrier. The barrier was about 700 mV, and the electrons with only thermal energy, according to dogma, only had about 20 mV.

Immediately upon his April 1999 publication colleagues in the field proclaimed the discovery of a rule-breaking observation. The electron had more energy than expected. Figure 2 shows the schematic and the diode configuration.

In October 2000 Huang et al. published the observation that a highly stretched gaseous NO molecule would collide with a conductor surface and suddenly have many vibration levels less energy (Fig. 3 [3]). A laser excited the NO molecule to a high vibration state, between 12 and 15. The NO attracted an electron from the metal chamber wall.

The vibration spectrum after the wall collision showed final vibration levels as low as the ground state, and peaked at levels between 5 and 8. An electron emission experiment showed a corresponding emitted electron energy with as much as all the binding energy, e.g. a ground state final product.

In 2005 Xiao, Ji and Somorjai (University of California – Berkeley) deposited thin films (<10 nm) of Pt or Pd on TiO2 or GaN to form Schottky diodes. They monitored the continuous electron flow across the metal–oxide interfaces during the catalytic oxidation of carbon monoxide, due to conversion of energy released by the oxidation of carbon monoxide into the kinetic energy of free electrons in platinum and palladium (Fig. 4).

Zuppero and Dolan considered electrical power generation by the ejected electron [5]. That a single electron would get all the energy was still controversial.

But in 2011 LaRue, of the same UC Santa Barbara Chemistry department as Huang, published the observation of the partition of energy between a single electron and the vibrational energy remaining in the NO molecule [6]. However, Ji, Zuppero et al. suspecting that the Nienhaus and Huang observations were correct, reacted carbon monoxide with oxygen on a 3 nm conducting catalyst.

Figure 3. Left-hand side, NO molecule energized to a highly vibrationally excited state by lasers come close to a metal substrate, attracting an electron to form NO. Right-hand side upper, the NO immediately ejected the electron, leaving the NO molecule in a much lower vibration state than it originally started with. Right side lower, the same excited state NO ejected the electron into a multichannel plate detector (MCP) in a vacuum, overcoming the work function of the contacted surface, proving that a single electron can carry off the entire binding energy in a single reaction.

One experiment developed a forward voltage of about 0.68 V, far above thermal [7]. This meant the CO2 gas leaving the surface would have almost no internal vibration energy, because adsorbing on the catalyst took most of it. The process was apparently like that reported by Huang and LaRue, called “Vibrationally Promoted Electron Emission.”

During 2015 Zuppero realized that the first muon catalyzed fusion experiment by Alvarez at UC Berkeley in 1957 had the same potential energy diagram and had the same result: the entire binding energy went into the heavy electron (a muon) and the resulting fusion nucleus, helium-3, was in the ground state [8,9].

The reactants attracted each other with 5.3 MeV of binding energy. The model provided by muon catalyzed fusion had two reactants, R and f, attracted together by a nuclear binding potential totally independent of the electron. The muon provided an electron with enough effective mass to create a new, electron bond at the nucleus and with a bonding, sigma gerade σg wave function.

This model had the same properties as the chemical physics discovery. We refer to this as a “tri-body attraction reaction.”

• quantum kinetic energy of electrons squeezed between two positive particles,

to explain transmutations observed in many experiments The potential energy diagram (energy vs. separation distance x) of an electron trapped between a proton and a heavy nucleus has a function similar to the case of an electron trapped between two atoms of a vibrating molecule, such as NO. The vibrational energy of a molecule can be transferred to a single electron, which ejects, leaving the molecule in a lower energy state [72,73].

The validity of our model depends on our ability to create heavy electrons by Eq. (32) that exceed the threshold mass of Eq. (25). If the electron is not heavy enough, the repulsive pressure due to the kinetic energy of confinement (KEC) prevents a nuclear reaction entirely. We can generate the transient heavy electron quasiparticles (lifetime ∼10 fs) by injection of energy E and phonons with crystal momentum k (lifetime ~0.3–30 ps) into a lattice, such that some electrons are energized to become close to an inflection point of the band diagram (E vs.k).

The KEC potential barrier is proportional to 1/mx2 , making it a higher barrier, but much narrower barrier than the usual high-energy ions Coulomb barrier, which is proportional to 1/x. The electron is never confined at nuclear dimensions, but part of its evanescent wave function tunneling to nuclear dimensions can overcome the repulsion due to KEC that holds R and f apart, facilitating a reaction.

The theoretical probability of electron tunneling through the barrier is several percent for favorable cases. The reaction can apparently transiently place or confine a heavy electron quasiparticle inside the compound nucleus

An electron inside the nucleus allows re-use of the binding energy directly inside the compound nucleus to fracture the nucleus into stable fragments that would be ejected. We have not explored possible electron spin interactions inside the nucleus.

Our model predictions appear to be consistent with transmutation data from many experiments. For example, the secondary product nuclides observed in a Ni+H catalyzed transmutation are consistent with our model (Table 5).

Transmutation reactions might have a variety of applications, including neutralization of radioactive isotopes (such as Cs-137 and Sr-90), industrial heat, electricity generation, and possibly using the ejected isotopes in rockets having a high specific impulse.

These estimates are based on a simplified one-dimensional particle model. We will need to

• compare the theoretical reaction rates with the experimentally achieved reaction rates, estimated from the number of transmutations measured and from the heat generated,

• design experiments to test the hypothesis described here (e.g., our model predicts that heavy elements could quench some otherwise-abundant reactions).

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