  We consider ionized hydrogen-like atoms accelerated by an external electric
field to detect Unruh radiation. By applying quantum field theory in the
Rindler spacetime, we show that the first-quantized description for
hydrogen-like atoms cannot always be adopted. This is due to the
frame-dependent definition of particles as positive and negative frequency
field modes. We show how to suppress such a frame-dependent effect by
constraining the atomic ionization and the electric field. We identify the
physical regimes with nonvanishing atomic excitation probability due to the
Unruh electromagnetic background. We recognize the observational limits for the
Unruh effect via first-quantized atomic detectors, which appear to be
compatible with current technology. Notably, the non-relativistic energy
spectrum of the atom cannot induce coupling with the thermal radiation, even
when special relativistic and general relativistic corrections are considered.
On the contrary, the coupling with the Unruh radiation arises because of
relativistic hyperfine splitting.
