Effect of Nonhomogeneous Broadening on the Free Induction Signal for a Double-Level Spin System

Abstract

An investigation of the evolution of the free induction signal as a function of σ/ω₁ is made, where σ is the nonhomogeneous width of the magnetic resonance line of a double-level spin system and ω₁ = γB ₁, where γ is the gyromagnetic ratio and B ₁ is the amplitude of a radio-frequency field. It is shown that two stages can be distinguished in the evolution of the free induction signal on excitation of the spin system by a large-area pulse (ω₁ t ₁ >> 1) of length t ₁. In the first stage (t ≤ t ₁), reversible relaxation leads to an oscillatory and exponential dip. With a fixed ω₁, an increase in σ practically does not change the frequency of oscillations and the signal amplitude decreases. In the second stage (t > t ₁), there is only an exponential decay of the signal at a rate equal to σ. It is demonstrated that, with nonresonant excitation, the coherent properties of the free induction signal manifest themselves in the formation of a single-pulse echo. The theoretical results are in good agreement with the experimental data obtained in nuclear magnetic resonance for protons in glycerin. The conclusion is drawn that the theorem of coherent transients in double-level systems with a finite nonhomogeneous width of the line is valid.