transition amplitudes between hyperfine levels

wdlang

i am working with cold atoms, alkali atoms specifically

Is there any book on the calculation of the transition matrix elements between different hyperfine levels?

I know the wigner-eckart theorem is central to this problem, but there are still a lot of stuffs to deal with.

For example, are the transition to the D1 and D2 lines share the same reduced matrix element? or almost the same?

all books i can find only treat trivial problems.