1. Acceleration-induced spontaneous excitation of a ground state atom: Transition Rate A. Calogeracos (HAFA, Greece) with G. Barton (Sussex, UK) Leipzig, 17 – 21 September 2007

2. The model Relativistic scalar nucleon following a prescribed trajectory R(t) Spin 1/2 electron Scalar radiation field

3. Relativistic Hamiltonian/Routhian of atom + field with constrained nucleus Relativistic scalar nucleon following a prescribed trajectory R(t) Spin 1/2 electron Scalar radiation field

4. Canonical transformations.... lead to a unitarily equivalent Hamiltonian

5. If we start with a ground state atom.... the amplitude for ending up with an excited state | f > and one photon |k> is:

6. Prescribe the motion constant proper acceleration between –τ0 and +τ0, i.e. hyperbolic motion, B = B 0 tanh(ατ/c) asymptotically inertial (with velocity continuous at +/- τ 0 )

7. For accelerations of very long duration.... things become simple: Introduce scaled energy ω = ε fi /α. Use K iω : modified Bessel function of imaginary order

8. Transition rate

9. Observe.. the thermal factor the 1/ω^2 correction in the numerator

10. Conclusions We calculated the amplitude for the excitation of an atom + emission of a photon for a nucleus following a prescribed trajectory. The trajectory includes an interval of constant acceleration between asymptotically inertial initial and final stages. We use standard time – dependent perturbation theory. If the acceleration is constant and lasts for ever we verify the Unruh effect.