On the decay width of multiply measured unstable state

Abstract

In the case of multiple measurements we have found that there is nonzero decay width Γ (Δ) (even for bound states) and that, for relatively long time intervals Δ separating successive measurements, Γ (Δ) tends like Δ^−k (k ≥ 1 according to the investigated model) to the asymptotic value Γ_o for unstable states and to zero for bound states. We have shown that the detector efficiencyZ ≠ 1 is responsible for this effect and that the evolution operator acting in the considered subspace of states should be renormalized to avoid this effect. As an illustration we have considered electromagnetic levels in the Coulomb field as an example of unstable states.