Decay of nuclear magnetization by diffusion in a parabolic magnetic field: An exactly solvable model.

An exact expression for the decay of the transverse magnetization of spins diffusing in a field (B 0 +g 1 z+g 2 z 2 )z reveals that a natural length scale l c =(8D/γg 2 ) 1/4 , and a frequency associated with it Ω=4D/l c govern the problem. Here D is the difusion constant and γ is the gyromagnetic ratio. l c is the size of the packet of magnetization at long times, i.e., Ω o t>>1