By Dr. N. Bloembergen (auth.)
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4) We are allowed to consider the nuclei as a voltage generator re~ presented in fig. 3. 10. The diagram holds also for the bridge of fig. 3. 3. The bridge of fig. 3. 4 behaves as a volta ge gene~ rator 6. Vj2 with an internal resistance R o/2. By virtue of its dependance on the susceptibility is 6. V R0 a function of the Larmor frequency and so of the magnetic field Ho. One canplot 6. V in the complex plane. · 65) with a factor 1/2for the li~ near X' and X". one finds that the locus of 6. V is a circ1e 1.
From (2. 65) we see that saturation occurs if y2 H l 2 Tl T 2 ~ 1. Assuming T 2 = 10- 5 sec, corresponding to a width of the proton line of about 3 oersted, we find that the relaxation time could be about four hours without saturating the spin system. An upper limit for the relaxation time in paraffin of 60 sec was established by observing the resonance as quickly as possible after the magnetic field Ho is applied. Immediately after the field is switched on, the relative population of the protons in the upper and lower level will be given by the a-priori probabilities of these levels, which are equal.
The proper factor has been calculated by Va n V I eck (V 3) in a rigorous manner with the diagonal sum method, using formula (2. 32). For Hop we take the terms of type A ami B of the perturbation =+ I I V ij • The component of the magnetic moment, rotating with the j>i applied radio frequency Seld, is proportional to I j Ix. ' J We can evaluate the commutator by making use of the commutation rules which exist for the components of the angular momentum operator I. Va n VI e ck's (V 3) result is This formula.