Magnetic resonance in systems with equivalent spin-1/2 nuclides. Part 3: Ket analysis and spectral intensities

In earlier papers (Parts 1 and 2), featuring group-theoretical analysis, it was shown that the isotropic EPR spectra of free radical (S=1/2) species XL(n), where the n equivalent nuclei also have spin 1/2, have a more complicated form than disclosed by the usual (first-order) oversimplified analysis. Explicit solutions for n=3 (analytic, as well as computational) of the spin-hamiltonian matrix H(s) for the energies and spin states were obtained and given in Part 2, but are amplified herein, and differences in several important representations of H(s) are discussed. In the present work, we focus also on details of relative spectral intensities, some of which are not straightforward. Subtle asymmetry effects in relevant EPR spectra are demonstrated. The crucial factor here turns out to reside in the difference between field-swept and frequency-swept spectra, and hinges on the fact that H(s) for the two states involved in any transition depends on Zeeman-field B as a variable in field-swept spectra, but B is a constant in frequency-swept spectra. An experimental spectrum of the free radical CF(3) is used as a quantitative example.