Electron-Nuclear Double Resonance Spectrum of anF-Center Electron in Alkali Halides (with NaCl Structure)

Abstract

From the de Boer model of the $F$ center, one can calculate a spin Hamiltonian to describe the hyperfine interaction of the $F$-center electron with an arbitrary nucleus in the lattice. This Hamiltonian was discussed in the preceding paper. In this paper we shall use this Hamiltonian to construct a spin Hamiltonian describing the hyperfine interaction of the $F$ electron with all nuclei in the lattice in the presence of a constant and uniform magnetic field. From this we shall deduce the electron-nuclear double resonance spectrum for the $F$ electron. The negative-ion vacancy (in a cubic lattice) is an inversion center, and the magnetic field is a pseudovector. Consequently, nuclei at sites which are mapped into each other by an inversion in the vacancy are physically equivalent. If this fact is accounted for, then the entire electron-nuclear double resonance spectrum may be viewed as a set of spectra, each one of which is associated with the interaction of the $F$ electron with a particular pair of physically equivalent nuclei. This contrasts with the present theory which assumes that the $F$ electron interacts with individual nuclei. The new theory leads to a marked improvement in the agreement between the calculated and observed spectra. An even more interesting result is that the calculated spectrum is now sensitive to the relative sign of the nuclear $g$ factor and the electric quadrupole coupling constant. Thus the experimental data can be used to determine not only the magnitude but also the sign of the electric field gradient at lattice sites close to the $F$ center.