$L\alpha$, $L\beta$, and $L\gamma$ x-ray production cross sections of Hf, Ta, W, Re, Os, Au, Pb, and Bi by electron impact: Comparison of distorted-wave calculations with experiment

We study the emission of $L\alpha$, $L\beta$, and $L\gamma$ characteristic x rays by the impact of electrons on Hf, Ta, W, Re, Os, Au, Pb, and Bi atoms. To this end, ionization cross sections of the $L_1$, $L_2$, and $L_3$ subshells of these atoms are calculated within the distorted-wave Born approximation. The considered energy interval spans from the ionization threshold up to 50 keV. Atomic relaxation parameters (i.e., Coster-Kronig and radiative transition probabilities, fluorescence yields, and emission rates) taken from the literature are then used to evaluate x-ray production cross sections. The theoretical predictions are compared with published experimental information. Good agreement is found for Ta, W, Os, Au, Pb, and Bi. In the case of Hf and Re, the measured cross sections are lower than the theoretical estimates by around 30%. The observed discrepancies might be attributed to the methods employed to correct the raw experimental data for the excess of detected characteristic x rays caused by the finite thickness of the sample’s active layer and the presence of the thick substrate.

Figure 1

X-ray production cross sections ${\sigma }_{L\alpha }^x$, ${\sigma }_{L\beta }^x$, and ${\sigma }_{L\gamma }^x$ of Hf as a function of energy. The continuous, dashed, and dot-dashed curves correspond to the theoretical cross sections calculated with sets $A$, $B$, and $A$${}^{\prime }$, respectively. Symbols are experimental data from Ref. [22].

Figure 2

X-ray production cross sections ${\sigma }_{L\alpha }^x$, ${\sigma }_{L\beta }^x$, and ${\sigma }_{L\gamma }^x$ of Ta as a function of energy. The continuous, dashed, and dot-dashed curves correspond to the theoretical cross sections calculated with sets $A$, $B$, and $A$${}^{\prime }$ (only $L\alpha$), respectively. Symbols are experimental data from Ref. [24].

Figure 3

X-ray production cross sections ${\sigma }_{L\alpha }^x$, ${\sigma }_{L\beta }^x$, and ${\sigma }_{L\gamma }^x$ of W as a function of energy. The continuous, dashed, and dot-dashed curves correspond to the theoretical cross sections calculated with sets $A$, $B$, and $A$${}^{\prime }$, respectively. Symbols are experimental data from Refs. [21, 22].

Figure 4

X-ray production cross sections ${\sigma }_{L\alpha }^x$, ${\sigma }_{L\beta }^x$, and ${\sigma }_{L\gamma }^x$ of Re as a function of energy. The continuous and dashed curves correspond to the theoretical cross sections calculated with sets $A$ and $B$, respectively. Symbols are experimental data from Ref. [20].

Figure 5

X-ray production cross sections ${\sigma }_{L\alpha }^x$, ${\sigma }_{L\beta }^x$, and ${\sigma }_{L\gamma }^x$ of Os as a function of energy. The continuous and dashed curves correspond to the theoretical cross sections calculated with sets $A$ and $B$, respectively. Symbols are experimental data from Ref. [25].

Figure 6

X-ray production cross sections ${\sigma }_{L\alpha }^x$, ${\sigma }_{L\beta }^x$, and ${\sigma }_{L\gamma }^x$ of Au as a function of energy. The continuous, dashed, and dot-dashed curves correspond to the theoretical cross sections calculated with sets $A$, $B$, and $A$${}^{\prime }$ (only $L\alpha$), respectively. Symbols are experimental data from Refs. [19, 21, 23].

Figure 7

X-ray production cross sections ${\sigma }_{L\alpha }^x$, ${\sigma }_{L\beta }^x$, and ${\sigma }_{L\gamma }^x$ of Pb as a function of energy. The continuous, dashed, and dot-dashed curves correspond to the theoretical cross sections calculated with sets $A$, $B$, and $A$${}^{\prime }$, respectively. Symbols are experimental data from Ref. [26].

Figure 8

X-ray production cross sections ${\sigma }_{L\alpha }^x$, ${\sigma }_{L\beta }^x$, and ${\sigma }_{L\gamma }^x$ of Bi as a function of energy. The continuous and dashed curves correspond to the theoretical cross sections calculated with sets $A$ and $B$, respectively. Symbols are experimental data from Ref. [27].