Spontaneous excitation of an accelerated atom: (i) Acceleration of infinite duration (the Unruh effect), (ii) acceleration of finite duration

We consider a proton and an electron bound by scalar electrodynamics with the proton forced by an external agency to move along an asymptotically inertial trajectory. We apply previously developed methods for atoms constrained to move relativistically (Barton and Calogeracos, 2005) to examine spontaneous excitation of the atom accompanied by photon emission. In the limit where the asymptotically inertial trajectory tends to the well-known hyperbolic trajectory we do recover the constant transition rate first obtained by Unruh a long time ago: the atom radiates as if it is found in a bath of photons at the Unruh temperature (Barton and Calogeracos, 2008 [7]). In the case of a truncated hyperbolic trajectory and for small accelerations we obtain a transition probability proportional to the square of the acceleration scaled by the acceleration at the Bohr orbit. On the other hand it is to be noted that the Unruh transition rate is exponentially small for small accelerations. Hence accelerations of finite duration provide a more promising context for the observation of spontaneous excitation.