Theory of the multiphoton cascade transitions with two photon links: comparison of Quantum Electrodynamical and Quantum Mechanical approaches

QED theory of multiphoton cascade transitions in atoms and ions is developed. In particular the $3s\rightarrow1s+2γ$, $4s\rightarrow1s+2γ$ and $3p\rightarrow1s+3γ$ processes are considered. Two different approaches (Quantum Electrodynamical and phenomenological Quantum Mechanical) are applied.

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