Theory of electron spin-echoes in non-viscous liquids

Abstract

A theory which describes the electron spin-echo for free radicals in non-viscous solution whose steady-state E.S.R. linewidth is inhomogeneously broadened by unresolved intramolecular hyperfine structure is presented. It is found that the two-pulse electron spin-echo for such systems decays at a rate approximately proportional to exp [- tT ₂ ^-1], where T ₂ ^-1 is the ‘intrinsic linewidth’ of an individual spin-packet. The presence of Heisenberg exchange is shown to a good approximation to add to the decay constant so that T ₂ ^-1(ex) ≈ T ₂ ^-1 (0) + ω_ex, where T ₂(ex) is the phase memory time in the presence of exchange, T ₂(0) is the phase memory time in the absence of exchange, and where ω_ex is the Heisenberg exchange frequency. This work indicates that the electron spin-echo technique may be a very important investigative tool for relaxation studies of spin labels in solution.