Transverse relaxation of spin-polarizedHe3gas due to a magnetic field gradient

The presence of a magnetic field gradient in a sample cell containing spin-polarized ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ gas will cause an increased transverse relaxation rate. The origin of this relaxation mechanism is the loss of phase coherence of the atoms due to the fluctuating magnetic field seen by the atoms as they diffuse throughout the cell. The Redfield theory of relaxation due to randomly fluctuating magnetic fields is applied to yield expressions for the transverse relaxation rate for spherical and cylindrical sample cells. Experiments performed with an experimental ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ free-precession magnetometer give results in agreement with the theory.