Exact selection rules for electronic transitions

K itself the quantum numbers, then in a single-configuration approach they may be treated as exact quantum numbers as well. 

However, due to the admixture of weak interactions it may occur that the parity is no longer a completely exact quantum number. The same is true for J if we account for hyperfine interactions. Fortunately, due to the weakness of the above-mentioned interactions, the parity and total momentum are the most accurate quantum numbers. In many cases a single-configuration approximation describes fairly accurately atomic characteristics, then the configuration may also be treated as an exact quantum number. However, quite often one has to account for the admixtures (superposition) of other configurations. 

In order to establish more detailed selection rules, we have to examine the tensorial structure of the respective operators. Let us start with selection rules for orbital momentum L. The operator of Ek-radiation (4.12) contains the tensor C k whereas that of M/c-radiation (4.16) contains 

In the particular case of electric dipole radiation A/ = 1, i.e. El-transitions are permitted between configurations of opposite parity. For 2-transitions Al = 0, 2 (excluding transitions ns — n s), i.e. they are allowed between levels of one and the same configuration or between configurations of the same parity. M 1-transitions may take place only between levels of one and the same configuration. There are no restrictions on An for /c-transitions. Selection rules for J and M follow from the Clebsch-Gordan coefficient 

Let us notice that selection rules for M, q and M are important only if we are interested in the polarization of the radiation, otherwise they may be neglected, because the other radiation characteristics do not depend on these parameters. 

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