Determination of the Spectral Density FunctionJ1(ω)in SolidHe3from Nuclear-Relaxation Measurements

Abstract

The transverse and longitudinal relaxation times are studied theoretically in a system of nuclear spins where the modulation of the dipolar Hamiltonian by an exchange interaction is the dominant relaxation mechanism. If the sample is a powder, it is shown that the nuclear-magnetic-resonance properties are entirely governed by the knowledge of one single spectral density function $J_1\left(\omega \right)$, which is determined experimentally for solid ${\mathrm{He}}^3$, for both bcc and hcp phases. The shape of $J_1\left(\omega \right)$ depends strongly on the lattice structure and, in the case of a bcc lattice, does not have the Gaussian shape proposed in the existing literature. Attempts were made to measure the second order frequency shift associated with the nonadiabatic broadening ($\frac{10}{3}$ effect); however, the experimental error was too large for the predicted shift to be measured.