Estimation of Relaxation Times During Free Evolution from the SECSY Signal of an Electron–Nuclear Spin-Coupled System in a γ-Irradiated Malonic Acid Single Crystal

The relaxation times \(T_2^{\prime}\), characterizing the allowed, and \(T_2^{^{\prime\prime}} ,\) characterizing the forbidden and coherence cross-resonances, during free evolutions over the coherent pathways p = ± 1 are estimated from the SECSY (spin echo correlation spectroscopy) signal of an electron–nuclear spin-coupled system in a γ-irradiated malonic acid single crystal. This is accomplished by fitting the intensities of the two main peaks in the Fourier transform of the SECSY signal reported by Lee et al. (J Chem Phys 98:3665, 1993) to \(T_2^{\prime}\) and \(T_2^{^{\prime\prime}}\). The values of the fitted relaxation times \(T_2^{\prime} = 500 {\text{ns}}, T_2^{^{\prime\prime}} = 50,000 {\text{ns}}\) reveal that the relaxation via the allowed resonance is two orders of magnitude faster than that via the forbidden and coherence cross-resonances. Full details of the calculation exploiting the Liouville–von Neumann equation are presented.