Molecular x-ray- and electron-scattering intensities

Various results concerning molecular x-ray- and electron-scattering intensities are presented. (i) Directional elastic intensities for ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$ are calculated and a qualitative explanation for the results is given. (ii) The differences between the usual elastic intensities for x-ray and electron scattering from nonvibrating but freely rotating diatomic molecules, and the fully elastic intensities for scattering from the $J=0\mathrm{}$ state are examined for ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$. The usual elastic intensities are rigorously shown to be greater than the fully elastic ones and the differences are correctly mimicked by the independent-atom model. (iii) Polarization functions are found to be important in the restricted-Hartree-Fock description of the total and elastic intensities. A counterintuitive ordering of basis-set effects on one- and two-electron properties is found and explained in the case of ${\mathrm{H}}_2$. (iv) It is shown that, in two-electron systems, a quantity closely related to the Coulson-Neilson Coulomb hole function can be extracted from experimental x-ray-scattering intensities. Both these quantities are displayed for ${\mathrm{H}}_2$. (v) An analogous procedure in the many-electron case is shown to yield the intracular projection of the statistical pair-correlation density.