Nonexponential Decay Law of the 2P-1S Transition of the H Atom

We evaluate numerically the survival probability P(t) for the unstable 2P excited state of the hydrogen atom that decays into the ground-state 1S by emitting one photon (τ ≈ 1.595 ns), thus extending the analytic study of Facchi and Pascazio, Phys. Lett. A 241, 139 (1998). To this end, we first determine the analytic expression of the spectral function of the unstable state, which allows for an accurate evaluation of P(t). As expected, for short and long time scales, P(t) shows deviations from the exponential law: a 'Zeno' region occurs at extremely short times (up to ≈ 0.3 attosec), followed by a longer 'anti-Zeno' domain (up to ≈ 50 attosec); at long times above 125 τ the decay law scales as t-4.