Definitions for "Relaxation time"
In general, the time interval required for a system exposed to some discontinuous change of environment to undergo the fraction (1 − −1), or about 63%, of the total change of state that it would exhibit after an infinitely long time. For example, a thermometer initially at equilibrium in a bath at temperature 1 will exhibit an exponential change of temperature with time after being suddenly plunged into a bath at temperature 2, theoretically assuming the new temperature 2 only after an infinitely long time. The finite time interval required for the thermometer to undergo a change of amount ( 2)(1 − −1) is called the thermal relaxation time of the thermometer. Occasionally, the fraction 9/10 is used in place of (1 − −1), so contexts must always be checked to be certain of the definition employed in a given case. The definition may also change for an underdamped device. The change of state of such a device may oscillate several times while approaching its final value.
after excitation the spins will tend to return to their equilibrium distribution in which there is no transverse magnetization and the longitudinal magnetization is at its maximum value and oriented in the direction of the static magnetic field. After excitation the transverse magnetization decays toward zero with a characteristic time constant T2, and the longitudinal magnetization returns toward equilibrium with a characteristic time constant T1.
the time constant of an exponential return of a system to equilibrium after a disturbance