Abstract
The line shapes of ENDOR spin-echoes of free radicals in liquid solution are calculated by exact solution of the equation of motion of the density matrix including relaxation and coherence effects. It is found that the duration of the r.f. pulse is very important in determining the ENDOR line width. The strength of the r.f. field, the various relaxation times, and the inclusion of r.f. coherence effects also contribute to the line shape in a complicated way. Although the theory is presented for free radicals in the motionally narrowed regime, it is expected that the calculated line shapes demonstrate the gross features of relaxation and coherence effects in rigid limit ENDOR spin-echo spectra.