  We study the spontaneous excitation of a uniformly accelerated two-level atom
non-linearly coupled with vacuum Dirac field fluctuations using the formalism
proposed by Dalibard, Dupont-Roc and Cohen-Tannoudji (DDC) and generalized to
the present case in the current paper. We find that a cross term involving both
vacuum fluctuations and radiation reaction appears, which is absent in the
linear coupling cases such as an atom interacting with vacuum scalar or
electromagnetic fluctuations. Furthermore, the contribution of this term
actually dominates over that of radiation reaction. Thus, the mean rate of
change of the atomic energy can no longer be distinctively separated into only
the contributions of vacuum fluctuations and radiation reaction as in the
scalar and electromagnetic cases where the coupling is linear. Our result shows
that a uniformly accelerated atom interacting with vacuum Dirac fluctuations
would spontaneously excite and a unique feature in sharp contrast to the scalar
and electromagnetic cases is the appearance of a term in the excitation rate
which is proportional to the quartic acceleration.
