Theoretical study of the X-ray Kβ emission spectrum of an argon atom

The influence of many-particle effects on absolute values and the shape of the doubly differential cross section of resonant inelastic scattering of a linearly polarized X-ray photon by a free Ar atom close to the K- and KM ₂₃-ionization thresholds is studied theoretically. The evolution of the spatially extended profile of the scattering cross section to the principal Kβ_1,3 and satellite Kβ₅ structures of the Ar X-ray Kβ emission spectrum is demonstrated. The calculations are performed in the nonrelativistic Hartree-Fock approximation for the wave functions of one-electron states and in the dipole approximation for the anomalous-dispersion amplitude of the scattering probability. The effects of the radial relaxation of electron shells, the correlation loosening, vacuum correlations, the spin-orbit and multiplet splitting, as well as the Auger and radiative decays of the vacancies produced are taken into account. The calculation results have a predictive character and, for the case of the incident photon energies of 3199.2 and 3245.9 eV, they are in good agreement with the results of the synchrotron experiment on measuring the X-ray Kβ emission spectrum of a free Ar atom.