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A model cluster, with a resonant electron spin surrounded with identicalnuclear spins occupying the sites of a cubic lattice, and with dipolar couplingbetween the spins, is used for a theoretical investigation of the transientnutations induced by a strong oscillating field but disturbed by these localdipolar fields. An effective Hamiltonian valid at the time scale of thenutations is first established. An analytical expression for the DipolarCoherence time tDC is derived by adapting Van Vleck's perturbative approach tothe present situation, with weak rather than intermediate dipolar coupling. Itis found that the dipolar coupling does not affect tDC at exact ESR resonance(Delta=0), a result reminiscent of a behaviour found in transient NMR inliquids, in an inhomogeneous static field. The expression for tDC also presentsa qualitative similarity with a time introduced in that liquid-state NMRcontext. Introducing a collection of independent clusters, a bridge is builtbetween tDC and the half-width delta of the usual steady state unsaturated ESRline. Assuming a simple cubic lattice, numerical values for (tDC)Delta=deltaare given, for both undiluted and dilute samples. It is shown that the TN donot obey the Bloch equations. Precautions to be taken when trying a qualitativecomparison between the present results and existing experimental data, and somethermodynamic aspects, are discussed.

Transient nutations of an electron spin 1/2 with dipolar coupling to neighbouring nuclear spins