Separation of Transitions with Two Quantum Jumps from Cascades

Abstract

We consider the general scenario of an excited level |i> of a quantum system that can decay via two channels: (i) via a single-quantum jump to an intermediate, resonant level |bar m>, followed by a second single-quantum jump to a final level |f>, and (ii) via a two-quantum transition to a final level |f>. Cascade processes |i> -> |bar m> -> | f> and two-quantum transitions |i> -> |m> -> |f> compete (in the latter case, |m> can be both a nonresonant as well as a resonant level). General expressions are derived within second-order time-dependent perturbation theory, and the cascade contribution is identified. When the one-quantum decay rates of the virtual states are included into the complex resonance energies that enter the propagator denominator, it is found that the second-order decay rate contains the one-quantum decay rate of the initial state as a lower-order term. For atomic transitions, this implies that the differential-in-energy two-photon transition rate with complex resonance energies in the propagator denominators can be used to good accuracy even in the vicinity of resonance poles.

9 pages; RevTeX

References in corpus (6)

• Primordial helium recombination I: feedback, line transfer, and continuum opacity
• Two-photon transitions in hydrogen and cosmological recombination
• Relativistic calculation of the two-photon decay rate of highly-excited ionic states
• Self-Energy Correction to the Two-Photon Decay Width in Hydrogenlike Atoms
• Virtual Resonant States in Two-Photon Decay Processes: Lower-Order Terms, Subtractions, and Physical Interpretations
• Two-Photon Decays Reexamined: Cascade Contributions and Gauge Invariance