Spin Absorption Spectra

Spin systems exhibit a whole spectrum of absorption lines when in small constant external magnetic fields giving Zeeman energies comparable to internal interaction energies. With such small constant magnetic fields, power is absorbed from an alternating magnetic field at zero frequency, at the Larmor frequency, and at harmonics of the Larmor frequency, both for perpendicular- and parallel-field configurations. The calculation of this spectrum for spin systems in powdered materials is the main purpose of this paper. Both magnetic dipole-dipole and electric quadrupole internal interactions are considered and treated as second-order perturbations on the Zeeman interaction. The intensities of the two absorption lines that occur at the Larmor frequency and double the Larmor frequency are obtained for the parallel-field case. The intensity, frequency shift, and second moment of the Larmor line, and the intensities of the lines that occur at zero frequency and double the Larmor frequency, are obtained for the perpendicular-field case. The second-order calculation for powdered materials gives results which are identical within a constant factor for both dipole-dipole and quadrupole interactions.