Resonance Frequencies and Lineshapes of a System of Nuclei Subject to a Random Two-Site Exchange

• Published in: Journal of magnetic resonance. Series A Vol. 103; no. 2; pp. 175 - 182
• Main Author: Seliger, J.
• Format: Journal Article
• Language: English
• Published: Orlando, FL Elsevier Inc 1993; Academic Press
• Subjects: Atomic and molecular physics; Exact sciences and technology; Molecular properties and interactions with photons; Nuclear resonance and relaxation; Physics; Perturbation theory; Spin system; Spectral line profile; Spin lattice relaxation; Nuclear quadrupole resonance; Theoretical study; Correlation time; Nuclear magnetic resonance; Energy level
• ISSN: 1064-1858; 1096-0864
• DOI: 10.1006/jmra.1993.1149

Resonance frequencies and lineshapes of a system of nuclei subject to a random two-site exchange are calculated by the second-order perturbation theory. It is assumed that the time-dependent perturbation which is the consequence of the random two-site exchange contains both diagonal and off-diagonal matrix elements in the representation of the eigenstates of the main Hamiltonian. The results show that the time-dependent perturbation averages out in two steps. A resonance line which is a doublet at very long correlation times of the random exchange changes into a singlet when τ −1 cexceeds the splitting of the doublet. The second-order shift of the resonance line caused by the off-diagonal matrix elements of the perturbation vanishes when τ −1 c exceeds the resonance frequencies of the main Hamiltonian. Two particular examples, NQR and quadrupole-perturbed NMR of a system of spin- 3 2 nuclei subject to a random two-site exchange, are discussed in detail.