Theory of the Nuclear Magnetic Resonance Chemical Shift of Xe in Xenon Gas

Abstract

A theoretical study is made of the density-proportional paramagnetic shift of the resonant magnetic field observed in nuclear magnetic resonance studies of ${\mathrm{Xe}}^{129}$ in pure xenon gas by Streever and Carr. The theory is based on a computation of the chemical shift in "diatomic molecules" formed by colliding Xe atoms, including the effects of van der Waals and exchange interactions on the wave function of the colliding atoms. The results of this calculation show that only the exchange interactions between the colliding atoms make a significant contribution to the chemical shift. When averaged over the various types of collisions, the following value is obtained for the shift in the resonant field: $\ensuremath{\Delta}H=\ensuremath{-}2.85{(10)}^{\ensuremath{-}7}H\ensuremath{\rho}$, where $H$ is the field strength and $\ensuremath{\rho}$ is the density in amagats. This is in order-of-magnitude agreement with the observed result: $\ensuremath{\Delta}H=\ensuremath{-}4.3{(10)}^{\ensuremath{-}7}\ensuremath{\rho}H$.