Distorted-wave ionization and x-ray production cross sections of the $K$ shell of Cu and the $L$ shells of Ag, In, and Sn by positron impact

We study the ionization cross sections of the $K$ shell of Cu and the $L$ shells of Ag, In, and Sn by positron impact using the distorted-wave Born approximation, focusing on the near-threshold energy range (below 40 keV) to compare with recent measurements. The distorted-wave formalism proves to be an appropriate approach, especially to describe the shape of the cross-section curves for positrons accurately. Furthermore, we calculate x-ray production cross sections of the considered $L$ shells having recourse to two sets of atomic relaxation parameters involved in the conversion from ionization to x-ray production cross sections. The 5%–10% differences in the theoretical values calculated with these parameter sets are apparently not large enough to explain the discrepancy between the distorted-wave curves and the experimental data, particularly for Ag. Other sources of uncertainty that could be affecting these comparisons are discussed.

Figure 1

Cross sections for the ionization of the $K$ shell of Cu by positrons. The solid and dashed curves are the predictions of the DWBA and the PWBA, respectively, whereas the dotted curve indicates Hippler’s PWBA with semiempirical relativistic and Coulomb corrections [7, 17, 20]. The symbols correspond to experimental data from Nagashima et al. [1].

Figure 2

Cross sections for the ionization of the $L$ shells of Ag, In, and Sn by positrons. The solid and dashed curves are the predictions of the DWBA and the PWBA, respectively. Partial DWBA cross sections for the $L_1$, $L_2$, and $L_3$ subshells are depicted as thin solid curves. The symbols correspond to experimental data from Nagashima et al. [1, 2]. Scaled DWBA cross sections, i.e., the DWBA values multiplied by a constant factor equal to 0.67, 0.75, and 0.80 for Ag, In, and Sn, respectively, are represented as dotted-dashed curves.

Figure 3

Total $L$-lines x-ray production cross sections of Ag, In, and Sn by positrons, calculated with Eq. (1). The solid and dashed curves are present results computed with the DWBA and parameter sets A and B, respectively. The symbols correspond to experimental data from Nagashima et al. [8]. X-ray production cross sections for the $L\alpha$, $L\beta$, and $L\gamma$ series obtained with sets A and B are represented as thin solid and dashed curves, respectively.

Figure 4

Total $L$-lines x-ray production cross sections of Ag by electrons, calculated with Eq. (1). The solid and dashed curves are present results computed with the DWBA and parameter sets A and B, respectively. The symbols correspond to experimental data from Wu et al. [16]. X-ray production cross sections for the $L\alpha$, $L\beta$, and $L\gamma$ series obtained with sets A and B are represented as thin solid and dashed curves, respectively.

Figure 5

X-ray production cross sections of In and Sn by electrons, calculated using the DWBA formalism and either parameter set A (solid curves) or B (dashed curves). Left-hand graphs: Cross sections for the production of $L\alpha$, $L\beta$, and $L\gamma$ x rays. Symbols are experimental data for $L\alpha$ and $L\beta$ from Tang et al. [3]. Right-hand graphs: $L\beta /L\alpha$ and $L\gamma /L\alpha$ ratios of cross sections. Symbols are experimental data from Tang et al. [3] (circles) and Baxter and Spicer [21] (triangles).