Revision of spin echoes in pure nuclear quadrupole resonance

Goldman's spin-1/2 formalism has been used for describing the response of an I=3/2 spin system to a two-pulse sequence in a pure nuclear quadrupole resonance experiment. A detailed analysis of the polarization evolution and quadrupolar echo generation is carried out through the use of explicit expressions for secular homo- and heteronuclear dipolar interactions. In striking contrast with previous studies, it is predicted that Van Vleck's second moments governing a classical solid-echo or Hahn sequence differ from those obtained by equivalent means in magnetic resonance. In fact, it is shown that, although measured moments still complement each other, the combined use of standard sequences does not allow the separate determination of homo- and heteronuclear dipolar contributions to the linewidth, not even in an indirect manner. In this context, the importance and potential usefulness of a crossed coil probe are also briefly discussed.