Cross-Relaxation in Spin Systems

TLDR

Energy transfer between adjacent resonances in nuclear and electron spin systems is governed by overlap of line‑shape functions, with implications for solid‑state maser operation. The method extends Kronig and Bouwkamp’s proposal by partially including off‑diagonal spin‑spin interaction terms omitted in Van Vleck’s Hamiltonian, with special attention to magnetically dilute substances and inhomogeneously broadened lines. Small‑frequency off‑diagonal spin‑spin interactions produce an additional relaxation channel, explain cross‑saturation in paramagnetic salts, account for a key experiment that cannot be explained by hot‑phonon assumptions, and yet inhomogeneously broadened lines still reach homogeneous steady‑state saturation.

Abstract

The energy transfer between adjacent resonances in nuclear and electron spin systems is analyzed in terms of the overlap of line-shape functions. The procedure is an enlargement on the original proposal of Kronig and Bouwkamp, and consists of taking partial account of off-diagonal elements in the spin-spin interaction, which are omitted in Van Vleck's truncated Hamiltonian. If the frequency of these off-diagonal elements is sufficiently small, they give rise to an additional kind of spin-spin relaxation, observed by Gorter and co-workers. They are also responsible for cross-saturation effects in paramagnetic salts of the type observed by Townes and co-workers. A crucial experiment is described which can be explained by spin-spin interactions, but not by the assumption of a hot-phonon region. Implications of the cross-relaxation for the operation of solid state masers are discussed. Special consideration is given to magnetically dilute substances and inhomogeneously broadened lines. Paradoxically, the latter will usually still undergo a homogeneous steady-state saturation.