Selection rules for atomic spectra

In many-electron atoms, states can have different S quantum numbers. For light elements, where the spin-orbit coupling is weak, the selection rules for atomic spectra are... 

The selection rules for atomic spectra are determined in the same way as it was done previously for vibration-rotation spectroscopy (see Section 6.7). For a hydrogen atom, the dipole moment operator of the incoming photon, H, is operated on and integrated over all space between the initial state n, /, m, with the final state n , m/ . Allowed transitions occur when the integral... 

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