By Charles P. Slichter
This is a textbook meant for graduate scholars who plan to paintings in nuclear magnetic resonance or electron spin resonance. The textual content describes the fundamental rules of magnetic resonance, steady-state and pulse tools, the speculation of the width, form and place of spectral absorption strains in addition to the idea of leisure occasions. It additionally introduces the density matrix. This 3rd version provides new fabric to many elements, plus new sections on one- and two-dimensional Fourier remodel tools, a number of quantum coherence and magnetic resonance imaging.
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We recall that such a pulse causes the expectation value of the magnetization vector to undergo a rotation about HI which returns it to its initial value. 78) These relationships show that after a 271' rotation the wave function has not returned to its original value but has instead changed sign. For the wave function to return to its initial value, the pulse length, t w , must lead to a 471' rotation. Thus, if WI tw =471' a(tw) = a(O) , b(tw) = b(O) . 79) The general property that a 271' rotation produces a sign reversal of "p and that a 471' rotation is needed to get "p back to its initial value is referred to as the "spinor" property of "p.
13d. Noting the orientation of 6M, we immediately see that during a second time interval T, 6M will again advance through the same angle e, which will bring it exactly along the positive y-axis at t =2T. The argument applies to all spins, no matter what 6H they experience, because the result does not depend on the angle of advance. Though all the spins are in phase at t = 2T, they get out of phase again owing to the field inhomogeneity, so the free induction signal decays. Note that its form as a function of time during the dephasing from t = 2T onward must be identical to the form of the decay following the initial1r/2 pulse (see Fig.
Note that the buildup before t 2r is the mirror image in time of the decay after 2r. Note further that no free induction signal is produced immediately following the 11" pulse = = develop exponentially with Tl. The 11" pulse will invert the z-component which has developed, so that it does not contribute to the component of 6M in the x-y plane existing at t = T+. During the next interval T, the component 6M in the x-y plane will continue to decay via the T2 tenns in the Bloch equations. 110) If the second pulse is a 11"/2 pulse, as in Hahn's original experiment, the pulse at t = T will put some of the z-component of 6M into the x-y plane.