  We study the behavior of massless Dirac particles in the vacuum C-metric
spacetime, representing the nonlinear superposition of the Schwarzschild black
hole solution and the Rindler flat spacetime associated with uniformly
accelerated observers. Under certain conditions, the C-metric can be considered
as a unique laboratory to test the coupling between intrinsic properties of
particles and fields with the background acceleration in the full (exact)
strong-field regime. The Dirac equation is separable by using, e.g., a
spherical-like coordinate system, reducing the problem to one-dimensional
radial and angular parts. Both radial and angular equations can be solved
exactly in terms of general Heun functions. We also provide perturbative
solutions to first-order in a suitably defined acceleration parameter, and
compute the acceleration-induced corrections to the particle absorption rate as
well as to the angle-averaged cross section of the associated scattering
problem in the low-frequency limit. Furthermore, we show that the angular
eigenvalue problem can be put in one-to-one correspondence with the analogous
problem for a Kerr spacetime, by identifying a map between these "acceleration"
harmonics and Kerr spheroidal harmonics. Finally, in this respect we discuss
the nature of the coupling between intrinsic spin and spacetime acceleration in
comparison with the well known Kerr spin-rotation coupling.
