Principle of Hartmann-Hahn Transfer

In this article, the basic principles of Hartmann-Hahn transfer in isotropic liquids will be revealed and the most important tricks of the trade will be disclosed. We hope that this will dispel the mystique surrounding Hartmann-Hahn experiments without reducing the fascination with this potent and multifaceted experimental technique. 

Suppose in the presence of (effective) fields that are oriented along the z axis, two spins have the (effective) resonance frequencies i, and Th strength of the scalar coupling between the two spins is quantified by the 

Suppose at time / = 0 the system is prepared sueh that the first spin is polarized in the z direetion, while the second spin is saturated. The corresponding density operator is 

What is the evolution of the density operator a t) under the constant Hamiltonian if no further perturbations are applied The calculation may be considerably simplified if is divided into the two parts 

The term cannot affect the evolution of the density operator because commutes with and with o-(O) = Hence, it may be ignored. As we shall see shortly, the evolution of the density operator cr(t) under the remaining term depends critically on the relative magnitudes of the coupling constant nd the difference frequency 

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