Theory of Nuclear Hyperfine Broadening of ESR Lines in Liquids

Abstract

The theory of the broadening of ESR spectral lines arising from fluctuations in the isotropic and anisotropic g factors and hyperfine tensors is discussed. Particular attention is paid to the case where the molecule has several equivalent nuclei and the spectrum, therefore, has degenerate lines, i.e., several transitions of the same frequency corresponding to different nuclear states. A mean linewidth T_2γ^—1 is calculated for each degenerate set, and the significance of this quantity is discussed. Certain special cases where the relaxation matrix is diagonal in a spin‐state basis are discussed, and the linewidths for each component line of the degenerate set is obtained. The Redfield and the Kubo and Tomita theories are compared, and the limitations of the latter in dealing with degenerate lines is analyzed.