Distinguishing single photonic transitions from the multiphotonic cases for (ns2S1/2) → (np2P3/2) → (n's2S1/2) photonic transitions in hydrogen-like atoms

We calculate the selection rules for (ns2S1/2) → (np2P3/2) → (n's2S1/2) single photonic transitions in hydrogen-like atoms. We show that for the first part the reduced selection rules read: [Δj = ±1 while Δmj = 0,±2]. For the second part the reduced selection rules read: [Δj = ±1 while Δmj = 0,±1,±2].