It is also possible to generate a spin echo with the same rotational axis for the...

   

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It is also possible to generate a spin echo with the same rotational axis for the π/2 and T-pulses. Consider, for example, the case where the 7/2 and 7-pulses are both applied along the r'-axis (so the spins are always rotated clockwise about the x'-axis). Write the equations for the phase during the experiment in analogy with (8.11) (8.12), using the convention that the phase is zero when Mis parallel to y'. Show that an echo is produced along the direction opposite to that which the magnetization had immediately after the π/2 excitation (i.e., a negative-echo along ). Signal plots would therefore display a 'negative' peak at the echo. The entire second step, for present purposes, is considered to be instantaneous. Another rf pulse with twice the amplitude, but otherwise identical to the first, is then applied. The second pulse is along y', rotating the spins about the y'-axis through the angle 7, at time 7. The spins which had previously accumulated extra positive phase now have, at the instant after the 7-pulse,³ the negative of that phase, and vice versa,¹ O(FT) = 0(FT) AB(T) T (8.11) ³We shall use the notation f(t) to refer to the limits limf(t +le). The action of the -pulse, o-o, would be changed to o--o, for example, if the p=0 line were redefined to lie along the r'-axis. 8.2. The Spin Echo and T₂ Measurements In the third step, the spins continue, after time 7, to accumulate phase according to (8.10) o(F,t) = with the echo time defined by = (7.7) - YAB(r)(t-T) -YAB (F) (t-27) -7AB(r)(t-TE), TR = 2T t>r 121 (8.12) (8.13) It is also possible to generate a spin echo with the same rotational axis for the π/2 and T-pulses. Consider, for example, the case where the 7/2 and 7-pulses are both applied along the r'-axis (so the spins are always rotated clockwise about the x'-axis). Write the equations for the phase during the experiment in analogy with (8.11) (8.12), using the convention that the phase is zero when Mis parallel to y'. Show that an echo is produced along the direction opposite to that which the magnetization had immediately after the π/2 excitation (i.e., a negative-echo along ). Signal plots would therefore display a 'negative' peak at the echo. The entire second step, for present purposes, is considered to be instantaneous. Another rf pulse with twice the amplitude, but otherwise identical to the first, is then applied. The second pulse is along y', rotating the spins about the y'-axis through the angle 7, at time 7. The spins which had previously accumulated extra positive phase now have, at the instant after the 7-pulse,³ the negative of that phase, and vice versa,¹ O(FT) = 0(FT) AB(T) T (8.11) ³We shall use the notation f(t) to refer to the limits limf(t +le). The action of the -pulse, o-o, would be changed to o--o, for example, if the p=0 line were redefined to lie along the r'-axis. 8.2. The Spin Echo and T₂ Measurements In the third step, the spins continue, after time 7, to accumulate phase according to (8.10) o(F,t) = with the echo time defined by = (7.7) - YAB(r)(t-T) -YAB (F) (t-27) -7AB(r)(t-TE), TR = 2T t>r 121 (8.12) (8.13)

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