Selection rules for radiation

Conditions of non-zero values of the submatrix elements of the electron transition operators define the selection rules for radiation. The latter coincide with those non-zero conditions for the quantity Q. On the other hand, the selection rules for Q are defined by the conditions of polygons for 3nj-coefficients, in terms of which they are expressed. The requirement (24.21) must also be kept in mind. The selection rules for transitions (25.8)-(25.17) are summarized in Table 25.1. In all cases the selection rules JJ k, hhk and l2 +12 + k is even number are valid. The table contains only those polygons which have the quantum numbers of both configurations, because only in such a case do these conditions serve as the selection rules for radiation. If a certain quantum number has no restrictions from this point of view, this means that it does not form a polygon with quantum numbers of the other configuration. Such quantities are placed in curly brackets. 

---