Magnetic Dipolar Broadening of Rigid Lattices

Abstract

A number of physical phenomena may contribute to the width of a resonance line. The most prosaic is the lack of homogeneity of the applied static magnetic field. By dint of hard work and clever techniques, this source can be reduced to a few milligauss out of 10⁴ Gauss, although more typically magnet homogeneities are a few tenths of a Gauss. The homogeneity depends on sample size. Typical samples have a volume between 0.1 cc to several cubic centimeters. Of course fields of ultrahigh homogeneity place severe requirements on the frequency stability of the oscillator used to generate the alternating fields. Although these matters are of great technical importance, we shall not discuss them here. If a nucleus possesses a nonvanishing electric quadrupole moment, the degeneracy of the resonance frequencies between different m-values may be lifted, giving rise to either resolved or unresolved splittings. The latter effectively broaden the resonance. The fact that T ₁ processes produce an equilibrium population by balancing rates of transitions puts a limit on the lifetime of the Zeeman states, which effectively broadens the resonance lines by an energy of the order of ℏ/T ₁.