New method for the determination of the sign and magnitude of electric quadrupole splittings. I. Theoretical considerations

For systems with a small electric quadrupole interaction ${\nu }_Q=\frac{e^2\mathrm{qQ}}{h}$ besides a large magnetic hyperfine splitting ${\nu }_M=\left|\frac{g{\mu }_N{B}_{\mathrm{hf}}}{h}\right|$ the centers of the NMR-ON (oriented nuclei) resonances are displaced by $\Delta \nu =c{\nu }_Q$. It is shown that $c$ is different for $\theta =0\mathrm{}° \mathrm{and} 90°$, $\theta$ being the angle of observation with respect to the quantization axis. This implies that the magnitude and sign of ${\nu }_Q$ can be determined from the differential resonance displacement $\overline{\Delta \nu }=\overline{\nu \mathrm{}\left(0\right)\mathrm{}}-\overline{\nu \mathrm{}\left(90\right)\mathrm{}}$. Model calculations are performed and the applicability of the method is discussed.