Operators for calculating the intensities of the allowed and forbidden hyperfine lines in electron paramagnetic resonance spectra

Abstract

Expressions in the form of operators that enable one to calculate the intensity of allowed ( Delta M=1, Delta m=0) and 'forbidden' ( Delta M=1, delta m=+or-1) hyperfine EPR lines have been derived (M and m denote, respectively, the electron and nuclear magnetic quantum numbers). The spin Hamiltonian considered consists of the electron Zeeman, zero-field and hyperfine terms. The axis of quantization for the nuclear spin is assumed to be along the direction of the effective magnetic field at the nucleus. The various spin Hamiltonian 'tensors' are considered to be anisotropic, having non-coincident principal axes. These operators depend only on the components of the spin operators S and I along their respective axes of quantization. To calculate the intensity, it is sufficient to determine the square of the matrix elements of these operators between the zero-order states that take part in resonance. The present results are compared with those published previously. The angular variation in the intensity calculated using the present expressions compares favourably with experimental values.