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Relaxation Times (T1, T2)

T1 represents the time constant for longitudinal relaxation, while T2 represents the time constant for transverse relaxation, both crucial for spectral quality.
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The statement of the theorem

Define the longitudinal magnetization Mz(t)M_z(t) and transverse magnetization Mxy(t)M_{xy}(t) as functions of time tt. The relaxation processes are governed by the following differential equations: \n\n1. Longitudinal Relaxation (T1T_1): The recovery of Mz(t)M_z(t) towards its equilibrium value M0M_0 is described by: Mz(t)=M0(1−e−t/T1)M_z(t) = M_0 \left(1 - e^{-t/T_1}\right) where T1T_1 is the longitudinal relaxation time constant.\n2. Transverse Relaxation (T2T_2): The decay of Mxy(t)M_{xy}(t) is described by: Mxy(t)=Mxy(0)e−t/T2M_{xy}(t) = M_{xy}(0) e^{-t/T_2} where T2T_2 is the transverse relaxation time constant. It is mathematically constrained that T2≤T1T_2 \le T_1.