Double-Quantum Transitions in a Three-Level Electronic Spin System

A general formula describing the relaxation by double-quantum transitions in a three-level electronic spin system is given. The results are interpreted in terms of a parameter $\alpha =\frac{{\ominus }_c}{{\ominus }_D}$, of contact between the excited spin energy level at temperature ${\ominus }_c$ and the phonon spectrum of Debye temperature ${\ominus }_D$. The usual Raman and Orbach processes for Kramers and non-Kramers salts are derived.