Structure of variousKL1x-ray satellite lines of heavy atoms

Abstract

Multiconfiguration Dirac-Fock calculations with the inclusion of the transverse (Breit) interaction and QED corrections have been carried out for Pd, Sn, Tb, Ta, Pb, and Th in order to obtain positions and intensities of various electric dipole, electric quadrupole, and magnetic dipole K x-ray diagram lines and of their KL 1 satellites. Theoretically constructed stick spectra have been presented together with synthesized spectra (the sum of the Lorentzian natural line shapes) for each studied element. Taking into account the existence of an L-shell hole in the 2s or 2p subshell, the effect of additional L-shell ionization on the shapes and structure of the K x-ray spectra has been examined. It has been observed that generally with increasing atomic number Z the shapes of particular satellite line groups tend to become smoother and to differ less from the shapes of appropriate diagram lines. Relations between the values of energy shifts of various satellite lines for each element and the changes of these relations with Z have also been studied. Additionally, the relations between the intensities of different diagram lines for each element have been systematically analyzed, likewise the changes with Z of the role of particular diagram lines. This study can be helpful in reliable and quantitative interpretation of many experimental K x-ray spectra of Pd, Sn, Tb, Ta, Pb, and Th induced in collisions with various projectiles.

Possibility of extraction of various KL0M1and KL1M0satellite lines in the x-ray spectra of medium-Zand heavy atoms

“…Among these diagram lines (see figure 2 in [57]), there are eight electric dipole, E1, x-ray transitions: Kα 2 and Kα 1 (both from the initial states of the ion with one hole in the 1s subshell to the final state where an electron from the 2p subshell has filled that hole, denoted thus (1s −1 → 2p −1 ), Kβ 3 and Kβ 1 (1s −1 → 3p −1 ), Kβ II 2 and Kβ I 2 (1s −1 → 4p −1 ), and KO 2 and KO 3 (1s −1 → 5p −1 ). There are also four so-called forbidden transitions (see [1] for details) of the electric quadrupole, E2, type, i.e., Kβ II 5 and Kβ I 5 (1s −1 → 3d −1 ), and Kβ II 4 and Kβ I 4 (1s −1 → 4d −1 ). The number of the investigated KL 0 M 1 lines was 380 for Pd and about 450 for the other elements.…”

“…The present work, focusing mainly on the KL 0 M 1 x-ray satellite lines of Pd, Tb, Ta and Th, has been the continuation of the studies presented in [1], containing a detailed analysis of various KL 1 M 0 x-ray satellite lines of Pd, Sn, Tb, Ta, Pb and Th. It has also been partly inspired by [55], where extensive MCDF calculations for various KL 1 M 0 satellite lines of heavy atoms (Ta, Pb and Th) enabled otherwise impossible correct interpretation of the measured K x-ray spectra induced during near-central collisions with light (He), as well as heavy (C, O and Ne) projectiles.…”

“…Test calculations have shown that the optimum values [45] of λ (which could be regarded as obtained by approximate adjustment to the empirical diagram spectra) depend strongly on the kind of spectral line but are rather weakly dependent on the atom. In [1,57], we have discussed the good agreement of the theoretical results with available experimental data [40,46,47,[66][67][68] and the successful application of the presented energy functional to the study on various K x-ray lines induced by different projectiles.…”

“…where H ii and H ff are the diagonal contributions to the Hamiltonian matrix, the first sum runs over all the initial CSFs (n i ), the second sum runs over all the final CSFs (n f ). The presence of a factor λ in formula (4) in the simplest way enables the compensation of the difference in the quality of description of initial and final states (see [1] for details), which is the main problem in the reliable theoretical (MCDF) analysis of the structure of the satellite lines in the K x-ray spectra. Test calculations have shown that the optimum values [45] of λ (which could be regarded as obtained by approximate adjustment to the empirical diagram spectra) depend strongly on the kind of spectral line but are rather weakly dependent on the atom.…”

“…To the best of our knowledge, the study presented in this paper is the first systematic study on the structure and shapes of so many KL 0 M 1 satellite lines for elements from such a wide range of Z (from Z = 46 to Z = 90), analysing in detail the effect of removing a 3s, 3p and 3d electrons on the K x-ray spectra. Owing to the fact that in our research we have also used theoretical results obtained previously for the KL 1 M 0 satellite lines (an additional L-shell electron removed) for the studied elements [1], we could provide help in getting information about the M-and L-shell ionization probability in near-central collisions, which is often very complicated, especially that for heavy atoms there is little hope for clear visibility of most kinds of the KL 0 M 1 satellite lines and some kinds of the KL 1 M 0 satellite lines.…”