Elements of Modern Physics
114
Fig. 4.2 Schematic diagram of the fine structure of the hydrogen
levels (greatly exaggerated), showing some of the transitions
allowed by the selection rules in Eq. (4.63).
4. Not all the transitions between the different levels are allowed. As will be
seen later, there are selection rules for the allowed transitions. For the
most prominent transitions, called the electric dipole transitions, the allowed
transitions satisfy the selection rules
∆l = ± 1
∆j = ± 1, 0,
but not j = 0 → j = 0
∆m j = ± 1, 0
(4.63)
∆n = unrestricted
Thus, these transitions are allowed only between adjacent columns in
Fig. 4.2. For example, there are two lines (a doublet) corresponding to transitions
between 2P and 1S levels, two lines (a doublet) corresponding to transitions
between 3S and 2P levels and three lines (a triplet) corresponding to transitions
between 3D and 2P states.