Spin relaxation and linear-in-electric-field frequency shift in an arbitrary, time-independent magnetic field

Abstract

A method is presented to calculate the spin relaxation times T(1), T(2) due to a non-uniform magnetic field, and the linear-in-electric-field precession frequency shift δω(E) when an electric field is present, in the diffusion approximation for spins confined to a rectangular cell. It is found that the rectangular cell geometry admits of a general result for T(1), T(2), and δω(E) in terms of the spatial cosine-transform components of the magnetic field. The result is applied to the case of a permanently-magnetized dipole impurity near the cell.

Universality of spin relaxation for spin-1/2 particles diffusing over magnetic-field inhomogeneities in the adiabatic regime

“…The solution of the problem for k = 1 is well known and will be given here for completeness. A general expression for longitudinal relaxation Γ 1 due to 1D diffusive motion reads [3,25,26]:…”

Frequency shifts and relaxation rates for spin-1/2 particles moving in electromagnetic fields

“…[16] gave analytic expressions for the relevant correlation functions for a gas of particles moving in a cylindrical vessel exposed to a magnetic field with a linear gradient along with an electric field. Petukhov et al [17] and Clayton [18] showed how to determine the correlation functions for arbitrary geometries and spatial field dependence for cases where the diffusion theory applies, while Swank et. al.…”

A Three-step Model for Optimizing Coil Spacings Inside Cuboid-shaped Magnetic Shields

“…Extremely uniform magnetic fields with a high temporal stability are essential to various precision measurements, such as electric dipole moment (EDM) measurements [1][2][3][4] or magnetic field detector calibration [5][6][7] . For the challenging EDM measurements a nonzero magnetic field gradient enhances vibration noise seen by magnetometers 8,9 and shortens the possible measurement time for a single experiment, thus deteriorating its statistical sensitivity [10][11][12] . The final unavoidable field gradient also causes systematic uncertainties like geometric phase shift 13,14 , which is the dominant error contribution to the present neutron EDM upper limit 15 .…”