Exchange and spin relaxation in solid ³He

Abstract

Spin relaxation measurements in solid ³He in the temperature region where exchange dominates the behavior are reviewed and reanalyzed. A model which brings together the complex exchange modulation of the dipolar interaction into a single correlation time is adopted. This may be regarded as introducing an effective pairwise exchange Hamiltonian. On the basis of this model new procedures are proposed for obtaining mathematical expressions for the dipolar autocorrelation function and the spectral density functions, which determine the relaxation times. By the appropriate treatment of short-time and long-time asymptotic behavior, together with a method for taking into account the mid-range behavior, it is possible to fit the experimental data extremely well. The success of this procedure seems surprising in the light of multiple spin exchange in solid ³He. It is an indication that the dominant exchange processes scale with density in a similar way. This conclusion is supported by path-integral Monte Carlo calculations. Some consequences and implications of this conclusion are discussed.