i.e., the state labels O, N, M indicate which states are in the ket of the three matrix elements (keeping the order of the Hamiltonian derivatives, first l, then k, then j, fixed). Furthermore, the prime on the sum in Eq. (97) indicates that there is also a summation over degenerate states belonging to each energy level. Now, one can first solve the integration over ω 2 and then the remaining integration over ω 1 using Eq. ( ) and a new type of integral that is