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The central challenge that needs to be overcome to make nuclear fusion work is the electrostatic repulsion between nuclei. Because of the protons contained inside, nuclei are positively charged and therefore they experience a (Coulomb) force when approaching one another. This electrostatic force gets all the larger, the closer on gets. Consider the example of hydrogen nuclei in a hydrogen gas: increasing the gas pressure will force the nuclei closer together but only by so and so much. Pretty soon one will hit highly diminishing returns i.e. by increasing the gas pressure by a lot, the distance will be reduced only a little more.
However, the picture above is an overtly simple one. In reality, nuclei are not by themselves in many situations. In a gas or in a solid, they are accompanied by negatively charged electrons. The negatively charged electrons will then to some extent “neutralize” the positively charged field that causes the internuclear repulsion.
With this background, Assenbaum et al. argue that — in first approximation — one ought to consider the position of the innermost electron of a nucleus (in the classical electron radius picture). One can then effectively ignore the Coulomb force from this radius into infinity, as it is neutralized by the surrounding electrons. The authors also make the argument that this adjustment corresponds to an effective down-shifting of the Coulomb potential. As a result, the position of the electron vis-a-vis the nucleus (which in a lattice can be somewhat related to the electron density) determines a so-called screening length, which in turn corresponds to a so-called screening potential. The screening potential is simply the amount of energy by which the Coulomb barrier is reduced.
The authors show some experimental data that support these conjectures and call for more experiments (which have since been conducted and will be discussed in other posts). With respect to theoretical considerations, the picture laid out in this paper relies on a number of simplifications. There are many ways this proposed picture can be refined. This is especially important when it comes to making quantitative estimates. We will discuss some of those refinements — as developed in other papers — in future posts. We will also discuss more concretely how estimates can be obtained for the extent of fusion rate enhancement resulting from electron screening under different circumstances.
The effects of electron screening on the low-energy cross sections of nuclear fusion reactions of astrophysical interest have been studied within the Born-Oppenheimer approximation using a simplified model. These studies indicate that a significant enhancement of the cross sections can occur already at beam energies, which are about a factor 100 higher than the electron binding energies. Cross sections near such energies can now be measured, in some cases, and several examples are discussed. For an understanding of the low-energy data as well as for a reliable extrapolation of the cross sections (for bare nuclei) to lower energies, the effects of electron screening must be well understood.