# Can we have molecular transitions that change multiplicity?

• A
• BillKet

#### BillKet

Hello! Can we have molecular transitions (not restricted to electric dipole) that change the multiplicity of the electronic level i.e. ##2S+1##. For electric dipole that is strictly forbidden. For magnetic dipole, we have a term in the operator of the form ##S\cdot B## and assuming the B is along the z-axis of the lab frame and after a bit of math we get a matrix element for this of the form:

$$<S' \Sigma'|T_q^1(S)|S \Sigma>$$
where I assumed Hund case a, and ##T_q^1(S)## is the spherical tensor representation of the operator S in the molecule frame. However this operator seem to act only on ##\Sigma##, while leaving S unchanged, which would imply that we can't change S by a dipole transition either. Is this the case? How can we change S? Thank you!

$$\langle S' \Sigma'| \text{T}^{(1)}_{q}(\mathbf{S})|S \Sigma \rangle = (-1)^{S'-\Sigma'} \begin{pmatrix} S' & 1 & S\\ -\Sigma' & q & \Sigma \end{pmatrix} \langle S'|| \text{T}^{(1)}(\mathbf{S})||S \rangle \rm{,}$$
$$\Delta S \equiv S - S' = \pm 1 \rm{,}$$