  We compute the corrections to the transition amplitudes of an accelerated
Unruh ``box'' that arise when the accelerated box is replaced by a ``two level
ion'' immersed in a constant electric field and treated in second quantization.
There are two kinds of corrections, those due to recoil effects induced by the
momentum transfers and those due to pair creation. Taken together, these
corrections show that there is a direct relationship between pair creation
amplitudes described by the Heisenberg-Euler-Schwinger mechanism and the Unruh
effect, i.e. the thermalisation of accelerated systems at temperature $a/ 2
\pi$ where $a$ is the acceleration. In particular, there is a thermodynamical
consistency between both effects whose origin is that the euclidean action
governing pair creation rates acts as an entropy in delivering the Unruh
temperature. Upon considering pair creation of charged black holes in an
electric field, these relationships explain why black holes are created from
vacuum in thermal equilibrium, i.e. with their Hawking temperature equal to
their Unruh temperature.
