Why there are good theoretical reasons for attempting to modify nuclear reaction parameters

In a recent online discussion on the topic of nuclear fusion in the solid state, the question was raised how there could be any hope to “overcome the Coulomb barrier” — the repulsive potential barrier between nuclei, which is on the order of MeV — in a solid-state environment where kinetic energies between nuclei are on the order of eV. This is a very reasonable question to ask, and here is a response that seeks to address it.

Electron screening: a well-understood modification of the Coulomb potential shape

For starters, there is an effect known as electron screening which is pretty well understood and can cause fusion rate enhancement of up to 20 orders of magnitude when calculating fusion rates between nuclei at eV level energies. See the PRC paper by Huke et al. 2008 (references below) for theoretical details and experimental support. The idea here is simple: In a metal lattice, you get some level of background electron density associated with free electrons. The negative charge of the metal electrons partially neutralizes the repulsion between positively charged nuclei (such as between a deuteron pair that sits in a metal lattice vacancy). Effectively, this represents a modification of the shape of the Coulomb potential V(r) which then enters into the Gamow model calculation of the fusion rate, yielding a higher rate. This is a welcome effect but it is not causing enough enhancement to lead to observable fusion rates at ambient temperatures.

Enter Dicke enhancement

But there is another effect offering the potential for further enhancement. This is a well-known collective quantum effect that goes — depending on the context — under the name of superradiance, superabsorption, supertransfer, or simply Dicke enhancement. The principle in a nutshell is that the dynamics of certain quantum state transitions can get accelerated when many equivalent quantum systems are coherently coupled (see Dicke 1954; Lloyd & Mohseni 2010; Ferioli et al. 2021; Papatryfonos et al. 2022 as a selection of relevant papers — also check this 11 min video explanation by Susanne Yelin of Harvard).

Assumptions underlying the established Gamow model are violated if more than two nuclei interact

Dicke enhancement is a kind of many-body process, which — if it were to apply to fusion reactions, as argued below — is in conflict with a basic assumption that underlies the Gamow model. The Gamow model, which is typically used for estimating fusion rates (and typically the origin of concerns about low fusion rates in the solid state), assumes that the fusion rate between two nuclei depends on the characteristics of the two reactant nuclei and of those two nuclei only. In other words, the Gamow model does not care (i.e. it yields the same results) if a deuteron pair is isolated in a vacuum or if it is embedded in a metal lattice along with many other nuclei. It also has no way to account for (i.e. it ignores by assumption) any interactions that the nuclei in question might be affected by. That such assumptions can be highly problematic and that they can lead to erroneous predictions, e.g. of rates, was already pointed out in a 1965 PRL by Terhune and Baldwin:

“The solid, characterized by internal energy states of the nuclei, by the lattice vibrations, and by the electromagnetic field, is treated [in this paper for the first time] as an integrated quantized system rather than as a number of noninteracting nuclei. [..] In a solid composed of N identical two-level nuclei in a perfect crystal lattice at a uniform and low temperature, correlations in the internal motions of the radiators are more probable than in the case of a gas. Furthermore, the interactions among members of the solid system are much stronger than in the gas, because of the coupling between neighbors in the lattice. The usual assumption that each nucleus radiates independently of the states of other nuclei in the system is incompatible with the coupling of the nuclei through the common electromagnetic and phonon fields. Calculations of the spontaneous radiation rate for a solid system in which the nuclei are a priori assumed independent preclude the possibility of coherent spontaneous gamma emission by assumption. The present analysis is free from this inconsistency.”

Ever since that recognition, suggestions of changing nuclear reaction parameters (such as fusion rates) in a coherently stimulated lattice appear conceivable in principle — and may be better met with humble curiosity rather than with immediate insistence on the impossibility of such a thing based on the highly reductionist Gamow model of 1928.

This way of thinking is in line with Nobel laureate Julian Schwinger’s position on the subject:

“It is not my intent [..] to declare the reality of the evidence offered for what has been called cold fusion. Rather, I only point out that the argument that has produced contemptuous dismissal of the possibility could be based on a false premise. The subject requires research, not fiat.” Elsewhere Schwinger states: “Whether or not the reality of cold fusion has been demonstrated experimentally, one must ask if any conceivable mechanism now exists, or might be devised, whereby nuclear energy could be extracted by manipulations at the atomic level.” (Schwinger 1991; 1994)

Note that as fundamental research questions such considerations have been direly neglected, which is surprising given both their potential impact and the theoretical motivation through principles such as Dicke enhancement. Independent of Fleischmann & Pons and any other experimental claims, one could ask why there has been such a lack of imagination and boldness in recent decades to take on the tough challenge of externally manipulating and modifying nuclear reaction parameters (short of high-energy particle bombardment).

Interactions between nuclei

In addition to Schwinger, Edward Teller was also supportive of such investigations. Here is a quote from him from 1989:

“Some of the good [PdD] experiments show that something is really wrong with the branching of D+D to T+H and D+D to He3+n  [..] What if we are presented with the fact that the results are correct? [..] Then you must assume that nucleons can interact not just when they touch. [..] I think it would help if we postulated that the nuclei can interact at 10 000 nuclear radii [..] The probability that this could result in cold fusion is possible. [..] If there is such an effect, we will then learn something very important. This would be a scientific discovery of the first order.”

Were one to follow Teller’s argumentation, the question reduces down to: How could nuclei interact with each other across distances on the order of picometer or nanometer? There is wide consensus that the nuclear strong force is much shorter range than that and thus no direct strong force interactions are likely to be possible across distant nuclei. However, nuclei can directly interact with oscillator modes that they participate in (see, for instance, Bocklage et al. 2021 for a demonstration of magnon-nuclear interactions), and different quantum systems that interact with the same oscillator modes can interact with each other indirectly (i.e. as a second order or higher order effect, see Hagelstein & Chaudhary 2008 for the theoretical argument and simulations; Bienfait et al. 2019 provide an exemplary experimental demonstration of such indirect coupling between remote qubits). While such indirect coupling between nuclei would be expected to be weak, it would be subject to the type of Dicke enhancement discussed above, as long as many nuclei participated in the process. 

Experimental confirmation of accelerated nuclear transitions via many-body Dicke enhancement

Terhune & Baldwin’s 1965 prediction that nuclear reaction parameters can be accelerated through Dicke enhancement has been experimentally confirmed, at the very latest through research published in a 2018 Nature Physics paper (Chumakov et al. 2018). In that paper, the authors present experimental data that shows the acceleration, by a factor of 15, of the 14.4 keV-to-ground transition in Fe-57 nuclei. Note what this means: What has been treated for decades as a “decay constant” has now become a “decay parameter” that is subject to change based on external manipulations of the environment of the nuclei in question.

Note that a nuclear quantum state transition is a kind of nuclear reaction and, vice versa, that a fusion reaction is a kind of nuclear quantum state transition — both are effectively reorganizations of nucleons from one temporarily stable configuration to another. In each case, the transition is hindered but probabilistically possible. In this context, the Coulomb barrier is not qualitatively different from other hindrance factors, or “barriers” if you like, that prevent one metastable nucleon configuration from instantaneously transitioning to another, more energetically favorable nucleon configuration.

Let me stop here and refer to our paper manuscript (Metzler et al. 2022) for more details on how such considerations may apply to nuclear fusion. I hope this provides interested observers with enough conceptual motivation why changing fusion rates is not such an insurmountable problem after all and worthy of continued investigation.

References:

• Huke et al. (2008). Enhancement of deuteron-fusion reactions in metals and experimental implications. Physical Review C, 78(1), 015803.
• Lloyd, S., & Mohseni, M. (2010). Symmetry-enhanced supertransfer of delocalized quantum states. New Journal of Physics, 12(7), 075020.
• Schwinger (1991). Nuclear Energy in an Atomic Lattice—Causal Order. Progress of Theoretical Physics, 85.
• Schwinger (1994). Cold Fusion Theory–A Brief History of Mine. Fusion Technology, 26(4), XIII.
• Teller (1989). NSF/EPRI workshop on anomalous effects in deuterated materials; Washington, DC (USA); 16-18 Oct 1989.
• Terhune & Baldwin (1965). Nuclear Superradiance in Solids. Physical Review Letters, 14(15), 589–591.
• Chumakov et al. (2018). Superradiance of an ensemble of nuclei excited by a free electron laser. Nature Physics, 14(3), 261–264. 
• Metzler, F., Hunt, C., & Galvanetto, N. (2022). Known mechanisms that increase nuclear fusion rates in the solid-state (arXiv:2208.07245). arXiv. https://doi.org/10.48550/arXiv.2208.07245 
• Papatryfonos et al. (2022). Hydrodynamic superradiance in wave-mediated cooperative tunneling. Communications Physics, 5(1), 1–7.
• Dicke, R. H. (1954). Theory of superradiance. Physical Review, 93(1), 99–110.
• Ferioli, G. et al. (2021). Laser-Driven Superradiant Ensembles of Two-Level Atoms near Dicke Regime. Physical Review Letters, 127(24), 243602.
• Hagelstein & Chaudhary (2008). Excitation transfer in two two-level systems coupled to an oscillator. Journal of Physics B: Atomic, Molecular and Optical Physics, 41(13), 135501.
• Bocklage et al. (2021). Coherent control of collective nuclear quantum states via transient magnons. Science Advances, 7(5), eabc3991.
• Bienfait et al. (2019). Phonon-mediated quantum state transfer and remote qubit entanglement. Science, 364(6438), 368–371.