Comparison of the structure of various KL⁰M¹and KL¹M⁰x-ray satellite lines of lead

Abstract

Multiconfiguration Dirac–Fock calculations (with the inclusion of the transverse Breit interaction and QED corrections) have been performed for various Pb K x-ray lines. The calculated positions and intensities of many electric dipole, electric quadrupole and magnetic dipole KL0M1 and KL1M0 x-ray satellite lines have been analysed. On the basis of theoretically constructed stick and synthesized (the sum of the Lorentzian natural line shapes) K x-ray spectra, the effect of the additional single ionization of different subshells of the M shell on the shapes and structure of Pb K x-ray spectra has been investigated and compared with the effect of the single L-shell ionization. It has been found that in the KL0M1 satellite spectra the sticks are less scattered and the shapes of the bands are narrower and smoother than in the KL1M0 spectra. The much weaker influence of an additional M-shell hole on the K x-ray spectra than of an L-shell hole is also reflected in very small values of the energy shifts (with respect to the corresponding diagram lines) of the KL0M1 satellite lines in comparison with those of the KL1M0 lines. This study provides an exhaustive set of data, enabling not only the correct quantitative analysis of many experimental Pb K x-ray spectra (induced in collisions with various projectiles), but also predictions concerning the K x-ray spectra of multiply ionized Pb or other heavy atoms, which can be helpful in designing new experiments.

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

“…The studied satellite K x-ray lines correspond to 12 (10 for Pd, because of the unoccupied 5p subshell) different K x-ray diagram lines (accompanying the transitions from the initial states with only a K-shell electron removed). 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 ).…”

“…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.…”

“…It can be noted that the higher the Z the more widely the sticks are scattered. In comparison with the KL 1 M 0 satellite line spectra, the distribution of the sticks in the KL 0 M 1 spectra is narrower and generally very different, but there are much more KL 0 M 1 lines than the corresponding KL 1 M 0 lines (see [1,57]).…”

“…We have used the MCDF method [58][59][60][61][62][63][64][65], with the inclusion of the transverse Breit interaction and two types of QED corrections (self-energy and vacuum polarization). The theoretical background of the present work is the same as in [57], thus here only essential points are presented. Within the MCDF scheme, the effective Hamiltonian for an N-electron system is expressed by…”

“…Those studies were performed with a view to preparing for future nuclear physics experiments in a similar energy range, involving the measurement of the fission time scale (see [56]). Finally, we have been encouraged by the promising results presented in [57], where we compared the structure and shapes of the KL 0 M 1 and KL 1 M 0 x-ray satellite lines of Pb and shown the importance of theoretical research in obtaining the data about the M-and L-shell ionization probability for this element. Here, we would like to make a detailed investigation of the predicted shapes of the K x-ray spectra of other (medium-Z and heavy) atoms from a wide range of Z, at the same time analysing the changes of the shapes with Z.…”