Nuclear Induction in Inhomogeneous Fields

Abstract

The mathematical methods developed by Jaynes are applied to the study of nuclear resonance in inhomogeneous magnetic fields. It is shown that a description of delayed-signal phenomena such as spin echoes is greatly simplified by the use of the spinor representation involving 2\ifmmode\times\else\texttimes\fi{}2 transformation matrices. The original results of Hahn on spin echoes are rederived in simplified fashion and more complicated situations are discussed, including large numbers of pulses, exact time dependence in extremely inhomogeneous fields, and continuous pulse trains. Several previously unreported types of delayed-signal phenomena are discussed and illustrated experimentally by oscilloscope traces. The apparatus used to study nuclear induction in very inhomogeneous fields is briefly discussed.