Screening of fusion reactions from the principle of detailed balance and application to the $pep$ reaction

TL;DR

This paper simplifies the derivation of plasma screening factors for fusion reactions using detailed balance, extends the method to reactions with multiple ions, and applies it to the solar $pep$ reaction, predicting measurable effects.

Contribution

It introduces a simpler derivation of plasma screening factors via detailed balance and generalizes it to reactions with multiple fusing ions, demonstrating its application to the solar $pep$ reaction.

Findings

The screening factor for the $pep$ reaction is roughly equal to the enhancement of the $p+p$ reaction.

The $pep$ reaction is suppressed by plasma screening near the Sun's center.

The effects predicted could be measured in future experiments.

Abstract

Dewitt et al. (1973) derived a useful relation between the plasma screening factor for a reaction of two fusing ions and their chemical potentials, based on the plasma pair distribution functions. We show that their result can be derived in a simpler, more straightforward way, by applying the principle of detailed balance, which also enables us to generalize the relation to reactions involving $N$ fusing ions. In order to demonstrate the usefulness of applying the principle of detailed balance, we calculate the screening factor for the $pep$ reaction, $p+e+p\rightarrow ^{2}$D $+\nu_{e}$. For the plasma conditions near the centre of the Sun, the reaction is suppressed by roughly the same amount by which the reaction $p+p\rightarrow ^{2}$D $+$ $e^{+}+\nu_{e}$ is enhanced. This effect may be measured in the near future.