Relaxation. Can T₂, be longer than T₁?

The basic equations describing the decay of the magnetization vector in the transverse plane and its growth along the longitudinal axis, after a pulse, are briefly examined for very simple systems that obey the extreme narrowing condition, and relax in the absence of radiation damping. It is shown that in these cases, the vector does not simply tip backwards with a constant magnitude, retracing the path it followed during the pulse. It is mathematically proven that if T 2 is equal to or less than twice T 1 , then immediately after a pulse, the vector first shrinks and then grows back to its initial magnitude while it tips back toward the longitudinal axis, instead of simply retracing its path. It is also shown that if T 2 is greater than this threshold value, then at some point during the relaxation, the magnitude of the resultant will exceed its starting value, a situation apparently not consistent with our present understanding of the laws of physics.