Magnetic resonance in systems with equivalent spin-1/2 nuclides. Part 1

Electron paramagnetic resonance (EPR) spectra of S=1/2 systems XL(n) with n equivalent nuclei having spin I=1/2 have been simulated for microwave frequencies in the L-, X-, and W-bands. It has been shown that for n>2 nuclei, the EPR spectra have a more complicated form than anticipated from the usual oversimplified analysis, which predicts n+1 lines with intensity ratios given by the coefficients of the binomial expansion. For the XL(n) system with n=3, the EPR spectra in fact consist of six lines. The exact solution of the spin-hamiltonian for this case has been obtained, which gives four levels in zero magnetic field. For n>2 systems, the degeneracy of the energy levels cannot be completely removed by the Zeeman electronic and nuclear interactions. For n>4, certain spin states cannot occur, consistent with the (generalized) Pauli exclusion principle. Discussion of the underlying theory, invoking exchange degeneracy and the appropriate permutation group theory, is included in some detail. Analogous considerations hold for NMR spectroscopy of non-radicals.