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

Dewitt et al. 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 → ²D +ν _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 → ²D + e ⁺ + ν _e is enhanced. This effect may be measured in the near future.