Speaker
Description
In the theory of characteristic X-ray radiation, there remain several discrepancies with the experimental observations, including astrophysical ones. One of the reasons for them may be the simplified treatment of the inner atomic shell wave functions. Even in Hartree-Fock methods, inner shell trial functions are often chosen in a relatively simple form, structurally close to that for hydrogen, with an adjustable effective charge. Whereas that should be relatively harmless for K shell, for L shell, whose radius is larger, that may be questionable. At the same time, the sensitivity to the shape of wave functions is high for the X ray fluorescence yield.
In the present work, it is demonstrated that energies of inner-shell atomic electrons are accurately described by including a perturbative correction due to the difference between the self-consistent potential of the entire atom and the pure Coulomb potential, along with a relativistic perturbative correction. This implies that electrons of all the atomic shells contribute to screening of the inner shells collectively. By using the Thomas-Fermi model, the screening correction for the K shell may further be simplified to a form of an expansion in noninteger powers of $1/Z$, which refines Moseley’s law. For L shell, this does not prove to be possible.
Within this framework, screening corrections to the hydrogenic wave functions of K- and L-shells are also evaluated. The corresponding corrections to the dipole matrix elements are computed. For K shell, the correction is moderate, whereas for L shell it is sizable. For the matrix element of the K-L transition, the correction is sizable, as well.