Reexamining the Lyman-Birge-Hopfield band of N2

Abstract

Motivated by fundamental molecular physics and by atmospheric and planetary sciences, the valence excitations of N 2 gas have seen several decades of intensive study, especially by electron energy loss spectroscopy (EELS). It was consequently surprising when a comparison of nonresonant inelastic x-ray scattering (NIXS) and nonresonant EELS found strong evidence for violations of the first Born approximation for EELS when leaving the dipole scattering limit. Here we reassess the relative strengths of the constituent resonances of the lowest energy excitations of N 2 , encompassed by the socalled Lyman-Birge-Hopfield (LBH) band, by expanding on the prior, qualitative, interpretation of the NIXS results for N 2 by both quantifying the GOS of the lowestenergy excitations and also presenting a new time-dependent density functional theory calculation of the q-dependence of the entire low-energy electronic excitation spectrum.At high q, we find that the LBH band has an unexpectedly large contribution from the octupolar w 1 Δ u resonance exactly in the regime where theory and EELS experiment for the presumed-dominant a 1 Π g resonance have previously had substantial disagreement, and also where the EELS results must now be expected to show violations of the first Born approximation. After correcting for this contamination, the a 1 Π g GOS from the NIXS results is in good agreement with prior theory. The NIXS spectra, over their entire q range, also find satisfactory agreement with the new TDDFT calculations for both bound and continuum excitations.

Determination of the electronic structure of atoms and molecules in the ground state: Measurement of molecular hydrogen by high-resolution x-ray scattering

“…With the dramatic development of third-generation synchrotron radiation and the crystal spectrometer, the brightness and the energy resolution of the x-ray-scattering technique have been greatly improved, which provides the possibility for high-precision measurements of the elastic differential cross section of x-ray scattering by atoms and molecules. Recently, the dynamic parameters of the valence shell excitations of some atoms and molecules have been measured by the x-ray-scattering technique with high-energy resolution in our group [8][9][10][11] and with moderateenergy resolution in Seidler's group [15,16], and some interesting excitation mechanisms have been revealed. In this Brief Report, we extend this experimental technique to study the elastic scattering of the x ray by a free molecule, and pure electronic structure information about the ground state is determined.…”

Ab initio calculation of inelastic scattering

“…The first multi-electron atom that we consider is the closed-shell rare-gas atom Ne, where we investigate inelastic excitations from the outer subshell np 6 electrons. These have been studied before, theoretically 46,59 and experimentally using both EELS 60 and IXS.…”

Core and shallow-cored- tof-shell excitations in rare-earth metals

“…To do this with the Bethe sum rule, the instrumental response must be characterized over a large energy range (~3 keV) and the normalization integral, which is formally taken over an infinite region, must be handled appropriately. A detailed discussion of this procedure is included elsewhere [53], and the normalization for Ce was done along these lines. Relative normalization uncertainty for Ce is 10-20% for most q values, but is worse at lowest q because of lowered signal due to details of the particular experimental geometry.…”

“…Spectra for Ce were brought into absolute units of eV -1 using the Bethe sum rule, as described elsewhere [53], and a linear background was subtracted before fitting to the calculated multipole spectra to account for Compton scattering from the valence electrons over the ~10 eV pre-threshold region that was fitted.…”