Relaxation of spins due to a magnetic field gradient, revisited; Identity of the Redfield and Torrey theories

Abstract

There is an extensive literature on magnetic gradient induced spin relaxation. Cates, Schaefer and Happer (CSH) in a seminal paper, have solved the problem in the regime where diffusion theory (the Torrey equation is applicable using an expansion of the density matrix in diffusion equation eigenfunctions and angular momentum tensors. McGregor has solved the problem in the same regime using a slightly more general formulation using Redfield theory formulated in terms of the auto-correlation function of the fluctuating field seen by the spins and calculating the correlation functions using the diffusion theory Green's function. The results of both calculations were shown to agree for a special case. In the present work we show that the eigenfunction expansion of the Torrey equation yields the expansion of the Green's function for the diffusion equation thus showing the identity of this approach with that of Redfield theory. The general solution can also be obtained directly from the Torrey equation for the density matrix. Thus the physical content of the Redfield and Torrey approaches are identical. We then introduce a more general expression for the position autocorrelation function of particles moving in a closed cell, extending the range of applicability of the theory.

2 figures

References in corpus (2)

• Polarized 3He as a probe for short-range spin-dependent interactions
• Electric dipole moment searches: Effect of linear electric field frequency shifts induced in confined gases, II

Cited by in corpus (16)

• New classes of systematic effects in gas spin co-magnetometers
• Probe Spin-Velocity Dependent New Interactions by Spin Relaxation Times of Polarized ${}^{3}He$ Gas
• Magnetic field uniformity in neutron electric dipole moment experiments
• Observation of gravitationally induced vertical striation of polarized ultracold neutrons by spin-echo spectroscopy
• Frequency shifts and relaxation rates for spin 1/2 particles moving in electromagnetic fields
• General Solution to Gradient Induced Transverse and Longitudinal Relaxation of Spins Undergoing Restricted Diffusion
• Spin relaxation and linear-in-electric-field frequency shift in an arbitrary, time-independent magnetic field
• Gravitational Depolarization of Ultracold Neutrons: Comparison with Data
• Random walks with thermalizing collisions in bounded regions; physical applications valid from the ballistic to diffusive regimes
• Universality of spin-relaxation for spin 1/2 particles diffusing over magnetic field inhomogeneities in the adiabatic regime
• Comments on "Limits on possible new nucleon monopole-dipole interactions from the spin relaxation rate of polarized ${}^3$He gas"
• Frequency Shift Caused by Nonuniform Field and Boundary Relaxation in Magnetic Resonance and Comagnetometers
• The neutron electric dipole moment experiment at the Spallation Neutron Source
• Size-independence of statistics for boundary collisions of random walks and its implications for spin-polarized gases
• Determination of diffusion coefficients of mercury atoms in various gases from longitudinal spin relaxation in magnetic gradients
• Relaxation, frequency shifts and other phenomena at the transition between diffusion and ballistic motion