Flip-flop term

For the dilute aH spins surrounded by a large number of the 2H spins, the heteronuclear aH-H dipolar interaction is dominant, lifting the spectral overlap between the 1H packets. H spin diffusion is driven by the flip-flop term of the 1H-1H dipolar interaction, which becomes secular in the presence of spectral overlap. Thus, spin diffusion would be accelerated if it had not been for the 1H-2H dipolar interaction. In order to confirm this prediction, they used another RF channel of the OPENCORE... 

Each of the terms A — F in Eq. 7.5 converts one of the basis functions— aa, a(3, (3a, (3(3—to the same or another function and is often said to link such pairs of functions. For example, A converts aa to aa because a is an eigenfunction of Iz. (a) Use the information in Section 2.3 to show the linkages for all four basis functions, (b) Convert the spin operators in term B to raising and lowering operators to demonstrate why this term is often called the flip-flop term. 

Because the raising and lowering operators change spin quantum number by one, the first two terms on the right account for double quantum coherence, and the last two flip-flop terms give zero quantum coherence. Clearly, cross products of any two transverse spin components lead to the same result. Moreover, we can represent two orthogonal forms of pure zero quantum and double quantum coherences by combinations of product operators ... 

When this term is present the dipole flip-flop terms (e.g. I+S-) are energy conserving so that order can be transferred between the I and the S spins. Thermodynamics means that the transfer of order occurs, tending to give the two systems a common spin temperature. Magnetic energy is conserved, given by... 

Conservation of total energy amongst the spin system from these flip-flop terms can be invoked on a timescale that is less than the spin-lattice relaxation times so that... 

In Equation (2.2), Ii and I2 are the like spins. yi is the gyromagnetic ratio of I nuclei, h is the Plank s constant and r denotes the length of the I1-I2 intemuclear vector. 6 is the angle between the static magnetic field and r. The B-term is called the flip-flop term and causes mutual spin-exchange when the energy levels of the states are very close to each other. Two dipolar precession frequencies in the rotating frame can be obtained from Equation... 

The secular contributions for these interactions are valid for heteronuclear spin systems. For homonuclear spin systems, the flip-flop term containing (/+S- + /-S+) is also secular. 

Here, 7+ and 7 are the raising and lowering operators and 9 is the angle between the applied magnetic field and the internuclear vector, r 2- The factor containing the raising and lowering operators is sometimes referred to as the flip-flop term. 

Note, the secular part of the IS dipolar Hamiltonian (Eq. 4c) contains no flip-flop term, as appears in Eqs. 4b and 4d, due to the frequency mis-match of I-and S-spin systems in Hq thus, the effect of the Hartmann-Hahn experiment is to make the IS flip-flop term secular. 

The last term represents the flip-flop terms causing polarization transfer. Here, S = S i iSyi and 7 = ily are the step operators, and A =A iA ... 

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