Determination of the Sternheimer Antishielding Factor ofLi7in Lithium Fluoride by Acoustic Nuclear Magnetic Resonance

Abstract

An experimental determination of the magnitude of the Sternheimer antishielding factor $1-{\gamma }_{\infty }$ for the ${\mathrm{Li}}^{+}$ ion by means of acoustic nuclear magnetic resonance (acoustic NMR) of ${\mathrm{Li}}^7$ in single-crystal LiF is presented. It was found that $|1-{\gamma }_{\infty }|=3.4\mathrm{}\pm 13\%$, corresponding to an antishielding effect. This may be compared with theoretical calculations by other investigators which give $1-{\gamma }_{\infty }=0.75\mathrm{}$, a small shielding effect. The shape of the acoustic NMR line for $H$ parallel to the [001] direction was found to be approximately Gaussian with a second moment $\Delta H^2={(5.1\mathrm{}\pm 0.8)}^2$ ${\mathrm{G}}^2$. A theoretical calculation of that second moment was carried out, assuming only magnetic dipole-dipole interactions between nuclei, and yielding $\Delta H^2=5.9\mathrm{}$ ${\mathrm{G}}^2$ in good agreement with this experiment. Experimentally, the LiF crystal was cooled in liquid helium to 4.2°K and placed in a steady magnetic field $H$. Acoustic waves at twice the ${\mathrm{Li}}^7$ Lamor frequency were introduced into the crystal by means of a piezoelectric transducer. The resulting periodic distortions of the crystal modulated the interaction $\stackrel{}{\mathrm{Q}}:\nabla \overrightarrow{\mathrm{E}}$ between the nuclear electric quadrupole moment $\stackrel{}{\mathrm{Q}}$ and the electric-field gradient $\nabla \overrightarrow{\mathrm{E}}$ generated transitions among the Zeeman energy levels. These transition rates were measured by observing the rate of change of the amplitude of an ordinary (nonacoustic) NMR signal. The transition rate expected for a point-charge model of the crystal was calculated to be proportional to ${(\stackrel{}{\mathrm{Q}}:\nabla \overrightarrow{\mathrm{E}})}^2$, and, using the known value $Q=0.043\mathrm{}$ barn, was smaller than the experimental transition rate by a factor of 11.8. Additional calculations were made which showed that covalency and overlap should have a negligible effect on $\nabla E$, making it possible to ascribe this factor of 11.8 solely to antishielding. The ratio of the actual transition rate to that calculated is equal to the square of the anti-shielding factor: ${(1-{\gamma }_{\infty })}^2=11.8\mathrm{}$ so that $|1-{\gamma }_{\infty }|=3.4\mathrm{}$, with an estimated probable error of 13%.