$L$-subshell fluorescence yields and Coster-Kronig transition probabilities with a reliable uncertainty budget for selected high- and medium-$Z$ elements

Photon-in/photon-out experiments at thin specimens have been carried out to determine $L$-subshell fluorescence yields as well as Coster-Kronig transition probabilities of Au, Pb, Mo, and Pd using radiometrically calibrated instrumentation in the Physikalisch-Technische Bundesanstalt (PTB) laboratory at the electron storage ring BESSY II in Berlin. An advanced approach was developed in order to derive the fluorescence line intensities by means of line sets of each subshell that were corrected for self-absorption and broadened with experimentally determined detector response functions. The respective photoelectric cross sections for each subshell were determined by means of transmission measurements of the same samples without any change in the experimental operating condition. All values derived were compared to those of earlier works. A completely traceable uncertainty budget is provided for the determined values.

Figure 1

Experimental setup showing the calibrated instrumentation employed in XRF beam geometry.

Figure 2

Determination of $L$3 fluorescence line set from the spectrum of Au recorded at an incident photon energy of 12.42 keV. As background contributions, bremsstrahlung as well as resonant Raman scattering at the $L$2 edge (with respect to the $M$4 and $N$4/5 shells) were considered. In the left part of the figure the escape lines of the detector response can be seen. In the background of the diagram lines, satellite lines are obviously present, the relative contribution of which can be estimated to be about or less than 1$\%$. At 7.48 keV a low Ni $K\alpha$ line is visible, which is due to the nickel front contact of the detector part of its response function.

Figure 3

Determination of the $L$2 fluorescence line sets from the spectrum of Au recorded at an incident photon energy of 14.03 keV employing the $L$3 fluorescence lines set determined at energies below the $L$2 absorption edge with bremsstrahlung background contribution. The contribution of resonant Raman scattering at the $L$1 absorption edge in comparison with the bremsstrahlung is very low and not visible in this spectrum. At 7.48 keV a low Ni $K\alpha$ line is visible, which is due to the nickel front contact of the detector part of its response function.

Figure 4

Determination of the $L$1 fluorescence line intensities from the spectrum of Pb recorded at an incident photon energy of 16.5 keV employing the $L$3 fluorescence lines set determined at energies below the $L$2 absorption edge and the $L$2 fluorescence lines set determined at energies below the $L$1 absorption edge.

Figure 5

Spectrum of Pd recorded at an incident photon energy of 3.8 keV (above the $L$1 absorption edge) and its fit employing the multiplets (MP) of fluorescence lines set for each of the three $L$ subshells and a bremsstrahlung background contribution.

Figure 6

Determination of the energy dependence of the $L$-subshell photoelectric cross sections τ of Au from transmittance measurements modifying the respective cross sections of the Ebel database ($a_3=-5.71$, $b_3=-1.59$, $a_2=1.11$, $b_2=-5.00$, $a_1=8.54$, $b_1=-3.17$). The relative contributions of elastic and inelastic scattering ($4.0\times {10}^{-2}$ and $4.0\times {10}^{-4}$ at 10 keV and $2.5\times {10}^{-2}$ and $6.5\times {10}^{-4}$ at 18 keV, respectively) to the total mass absorption coefficient were included in the transmittance evaluation based on the ratio of their theoretical values to the value of the photoelectric effect.

Figure 7

Determination of the energy dependence of the $L$-subshell photoelectric cross sections τ of Mo from transmittance measurements modifying the respective cross sections of the Ebel database ($a_3=-8.2$, $b_3=0$, $a_2=-3.8$, $b_2=0$, $a_1=2.5$, $b_1=-2.2$). The relative contributions of elastic and inelastic scattering ($1.0\times {10}^{-2}$ and $3.7\times {10}^{-5}$ at 2.5 keV and $4.7\times {10}^{-3}$ and $3.4\times {10}^{-5}$ at 4 keV, respectively) to the total mass absorption coefficient were included in the transmittance evaluation based on the ratio of their theoretical values to the one of the photoelectric effect.

Figure 8

Comparison of the fluorescence yield ${\omega }_{L\mathrm{III}}$ in dependence on the atomic number as published by different authors.

Figure 9

Comparison of the Coster-Kronig factor f13 in dependence on the atomic number as published by different authors.