Experimental Verification of the Individual Energy Dependencies of the Partial $L$-Shell Photoionization Cross Sections of Pd and Mo

An experimental method for the verification of the individually different energy dependencies of $L_1-$, $L_2-$, and $L_3-$ subshell photoionization cross sections is described. The results obtained for Pd and Mo are well in line with theory regarding both energy dependency and absolute values, and confirm the theoretically calculated cross sections by Scofield from the early 1970 s and, partially, more recent data by Trzhaskovskaya, Nefedov, and Yarzhemsky. The data also demonstrate the questionability of quantitative x-ray spectroscopical results based on the widely used fixed jump ratio approximated cross sections with energy independent ratios. The experiments are carried out by employing the radiometrically calibrated instrumentation of the Physikalisch-Technische Bundesanstalt at the electron storage ring BESSY II in Berlin; the obtained fluorescent intensities are thereby calibrated at an absolute level in reference to the International System of Units. Experimentally determined fixed fluorescence line ratios for each subshell are used for a reliable deconvolution of overlapping fluorescence lines. The relevant fundamental parameters of Mo and Pd are also determined experimentally in order to calculate the subshell photoionization cross sections independently of any database.

Figure 1

Comparison of subshell PCSs (${\tau }_{\mathrm{Li}}$) for molybdenum from different sources. The dotted lines correspond to total PCSs multiplied with energy independent jump ratios (Elam et al. [9]), the diamonds correspond to Scofield’s calculations [3], and the triangles show the calculations by Trzhaskovskaya et al. [7, 8]. The dashed lines are fits to Scofield’s data.

Figure 2

Spectrum of Mo recorded at an incident photon energy of 2.95 keV and its fit employing fixed linesets (LS) of fluorescence lines for the $L_3$ and the $L_2$ subshells, the single fluorescence lines of the $L_1$ subshell and a bremsstrahlung background originating from $\mathrm{Mo}\text{−}M$ photoelectrons. Si-K fluorescence radiation emitted from the membrane at 1.74 keV and scattered incident radiation at 2.95 keV are visible as well.

Figure 3

Experimentally determined PCSs for the $\mathrm{Mo}\text{−}L$ subshells and fifth order polynomial fits (solid lines) as well as the relative uncertainties in the inset. The right figure shows comparisons to Scofield’s data [3] (solid lines) and Trzhaskovskaya’s data [7, 8] (dotted lines).

Figure 4

Experimentally determined PCSs for the $L$ subshells of Pd and fifth order polynomial fits (solid lines) as well as the relative uncertainties in the inset. Comparisons to Scofield data [3] (solid lines) and Trzhaskovskaya data [7, 8] (dotted lines) are shown on the right-hand side.

Figure 5

Experimentally determined PCSs for the $\mathrm{Pd}\text{−}{L}_1$ absorption edge in comparison to the data of Ebel [4], Cullen [6], X-raylib [5], and Scofield [3], as well as McMaster [10] and Elam data [9]. The McMaster and Elam data were calculated from the total PCS using the jump ratio approximation.