By Jerome I. Kaplan
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Example text
21, 961 (1971). A. Abragam , "Th e Principle s of Nuclea r Magnetism, " Chap . 8. Oxfor d Univ . Press , Londo n an d N e w York , 1961. N . C . Pyper , Mol. Phys. 21, 977 (1971). N . C . Pyper , Mol. Phys. 21, 1 (1971). N . C . Pyper , Mol. Phys. 22, 433 (1971). P. S. Hubbard , Rev. Mod. Phys. 33, 249 (1961). I. Solomon , Phys. Rev. 99, 559 (1955). N . Khazanovic h an d V. Y. Zitserman , Mol. Phys. 2 1 , 65 (1971). M . Alia an d E . Lippma , J. Magn. Reson. 4, 241 (1971). N . R . Krishn a an d S.
Now, (b\%b{t - r)\by = = e {b\e^-^%sbe-^-^\by ί ω / ! ( T ' - \b\%sb\b}e- = 0, as we have previously assumed (b\% \b) sb % b is diagonal. Thus (4-54) is proved. ω / ( ' ' '" τ) (4-56) = 0 in a representation in which 1. The Relaxation Operator 35 Equation (4-53) is our final formal result. The next step is to express 2 quite generally that ^* % = b 4>¸ (4-57) where i ' s are solely spin operators and *>'s solely lattice operators; spins are labeled /. The 5's are defined so that ω / ω/ e ' ' '
P o (4-73) In terms of ca(i (0 τ ) (4-72) can be rewritten as - *PS = ΣΣ " Σ Σ Car «(<, -") ^° c , (r)f^ e ( e^c_a(i, 0 0 , β - ' ( 5 . + ^ ί Γ - ρ ι β' ( ί Κ ; (-τ)Γ5? + T 5i + , e - ' ( ^ ^ ) p s5 - « e ' ( » ^ 1 + 3i T «) l. (4-74) IV . Relaxatio n 38 To motivate what we are going to d o next consider a simple two level nuclear spin system with populations nx a n d n2 a n d energies Ex a n d E2. The rate equations for this system are dn x/dt = wX2n x At equilibrium dn/dt + w2Xn 2 , dn 2)dt = w2Xn 2 + wX2n x .