Squared form factors of valence-shell excitations of atomic argon studied by high-resolution inelastic x-ray scattering

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

“…Furthermore, the ionization continuum also contributes to the elastic scattering in these experiments due to the same reason. So these previous elastic differential cross sections definitely have contributions from the inelastic scattering, which have been observed recently by inelastic x-ray-scattering experiments [8][9][10][11]. Because of the lack of experimental data, only Bentley et al [12,13] have calculated the elastic squared form factor of molecular hydrogen using ground wave functions prepared by different theoretical methods [14].…”

“…Then the squared form factor ζ (q) for the elastic scattering of hydrogen was absolutized by taking into account the different target densities (pressure) of hydrogen and helium. A similar normalization method was also used in our previous paper [11]. The resolution of momentum transfer is about 0.091 a.u., which is due to the finite size of the solid angle viewed by the analyzer.…”

“…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.…”

“…The experimental setup used in this work is shown in Fig. 1 and has been described in our previous works [8][9][10][11]. Briefly, a Si(333) monochromator was used to achieve a high-energy resolution of 70 meV.…”

Ab initio calculation of inelastic scattering

“…To evaluate the matrix elements, we note that L is the sum of one-electron operators, leading to three standard cases for the evaluation of the brackets on the right-hand side of eqn (9). 48 The first case occurs if the two Slater determinants are identical,…”