Spin Echo Decay in a Stochastic Field Environment

We derive a general formalism with which it is possible to obtain the time (τ) dependence of the echo size for a spin in a stochastic field environment. Our model is based on “strong collisions”. We examine in detail three cases where: (I) the local field is ±ω0, (II) the field distribution is continuous and has a finite second moment, and (III) the distribution is Lorentzian. The first two cases show a T2 minimum effect and are exponential in τ 3 as τ → 0. The last case can be approximated by the phenomenological expression exp(−[2τ/T2] ) with 1 < β < 2, where in the τ → 0 limit β = 2.