Small-angle elastic electron scattering and moments of the molecular electronic charge density

The first-Born-approximation expression for elastic scattering by molecules in the gas phase is expanded in a power series in the momentum transfer. It is shown that this expansion can be fitted to high-energy electron scattering measurements to obtain accurate estimates of the mean-square radius of molecules. In addition, by use of information on the molecular quadrupole moment and the molecular structure, the electronic moments 〈$x^2$〉 and 〈$z^2$〉, and the diamagnetic susceptibility may be calculated. It also appears possible to obtain information on some of the higher electronic moments such as 〈$r^4$〉. Results are given for ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and ${\mathrm{O}}_2$.