Quadrupole Moment of the Electron Distribution in Hydrogen Molecules

Abstract

In molecular beam experiments on hydrogen molecules, measurements have been made in the past both of the rotational magnetic moment and of the dependence of the diamagnetic susceptibility on the orientation of the molecules' rotational angular momentum. It is shown in this paper that these two experimental results can be combined to give an experimental determination of the quadrupole moment of the electron distribution in hydrogen molecules. The results of this analysis are that the mean value of $\Sigma j^{}(3\mathrm{}z_j^{}{}_{}{}^2-r_j^{}{}_{}{}^2)$ with $z$ taken along the internuclear axis of the molecule is (0.38±0.15)×${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$. Alternatively, if the $z$ axis is the axis of quantization, the mean value of $\Sigma j^{}(3\mathrm{}z_j^{}{}_{}{}^2-r_j^{}{}_{}{}^2)$ in the rotational state $M_J=J=1\mathrm{}$ is (0.076±0.030)×${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$. The first figure can be compared to the value 0.31×${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ calculated from the hydrogen molecular wave function by James and Coolidge. Although the precision of the past measurements is small, a gain of a factor of about a hundred in the precision of this measurement should be possible with some experiments now in progress.