INVERSION OF THE BLOCH EQUATIONS WITH T-2 RELAXATION - AN APPLICATIONOF THE DRESSING METHOD

The Bloch equations, with time-varying driving field, and T-2 relaxati on, are expressed as a scattering problem, with Gamma(2 )= 1/T-2 as th e scattering parameter, or eigenvalue. When the rf pulse, describing t he driving field, is real, this system is equivalent to the 2x2 Zakhar ov-Shabat eigenvalue problem. In general, for complex rf pulses, the s ystem is a third-order scattering problem. These systems can be invert ed, to provide the rf pulse needed to obtain a given magnetization res ponse as a function of Gamma(2) In particular, the class of ''soliton pulses'' are described, which have utility as T-2-selective pulses. Fo r the third-order case, the dressing method is used to calculate these pulses. Constraints on the dressing data used in this method are deri ved, as a consequence of the structure of the Bloch equations. Nonline ar superposition formulas are obtained, which enable soliton pulses to be calculated efficiently. Examples of one-soliton and three-soliton pulses are given. A closed-form expression for the effect of T-1 relax ation for the one-soliton pulse is obtained. The pulses are tested num erically and experimentally, and found to work as predicted.