Magnetic resonance in a cubic Γ3(E) doublet system I. Theory

For an ion of the 4f group in a crystal field of cubic symmetry, the splitting of a doublet Γ3 level by the quadratic Zeeman effect may be appreciable. The energy of this splitting is calculated for a general direction of the applied field B, together with the effects of magnetic dipole and electric quadrupole hyperfine interactions. E. s. r. transitions are allowed except when B = 0 or B is along a fourfold cubic axis; formulae are given for their intensity and the nature of the spectrum. The n. m. r. spectrum in a strong field is discussed, and the electric quadrupole splitting when B = 0 is evaluated for integral and half-integral values of I between ½ and 7/2. The problem of linewidth arising from magnetic interactions with ions in Γ3 doublet states is discussed briefly.