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SpinLatticeRelaxation< Radio Frequency enhancement | Index | NMR.ThermalNoise > Saturation recovery for spin {$I=5/2$} (Mn in La1-xSrxMnO3), when the aperiodic train is longer than {$W=1/T_1$}, the full saturation condition, the theory predicts the following recovery law {$M(t)=M_\infty[1-(\frac 9 {35} e^{-Wt} + \frac 4 {15} e^{-6Wt} + \frac {10}{21} e^{-15Wt})]$} If instead the train is longer than {$T_2$} but shorter that {$T_$}, the fast saturation condition, and one gets {$M(t)=M_\infty[1-(\frac 1 {35} e^{-Wt} + \frac 8 {45} e^{-6Wt} + \frac {50}{63} e^{-15Wt})]$} A description of this theory is in A. Narath, Phys. Rev. 162, 320 (1967). In short: The approach to thermodynamic equilibrium of the ensemble of nuclear spins {$I$} is governed by a closed set of rate equations for the population Nm (m = I, . . . , - I ) of the mth level . When the relaxation is due to fluctuations of a local magnetic field transitions are allowed only if they connect two nearby levels, i.e. {$\Delta m=\pm 1$}. It this case the set of equations has the form {$N_m = W \left[(I + m + 1)(I - m) \left(N_{m+1} - N^0_{m+1}\right) +(I - m + 1)(I + m)\left(N_{m-1} - N^0_{m-1}\right) - 2(I^2 - m^2 + I)\left(N_m - N^0_m\right)\right] $} where {$N^0_m$} are the equilibrium populations of each level and W is the transition probability between two adjacent Zeeman levels {$ m \leftrightarrow m - 1$}. When a strong internal magnetic field is present, with a much smaller quadrupolar interaction, a single transition {$m\leftrightarrow m - 1$} may be selectively excited. The NMR signal intensity {$M$} is proportional to the population difference {$M\propto N_m-N_{m-1}$} of the two levels and the equations above yield a solution for this quantity that is in general the superposition of {$2I$} exponential components. Their relative weights depend on the initial conditions (e.g. the saturation or inversion method). The fast saturation guarantees that the population is initially redistributed only among the two levels m and m-1, with equal populations (hence M=0). The full saturation condition guarantees that all levels are equally populated and again M=0. |