ELECTRON-IMPACT INNER SHELL IONIZATION CROSS- CROSS-SECTION MEASUREMENTS FOR HEAVY ELEMENT
4. MEASUREMENTS WITH THE THICK-TARGET METHOD
In the thick-target method, the atomic inner-shell ionization cross-sections were obtained previously by employing the derivatives of polynomials which were fitted to the experimental data of characteristic x-ray yields. However, the relation between the characteristic x-ray yields and the atomic inner-shell ionization cross-sections is expressed by a Fredholm integral equation of first kind, for which the solution is an ill-posed inverse problem [25]. Therefore, it is hard to appropriately obtain the atomic inner-shell ionization cross-sectionsby simply employing the derivatives of polynomials which are fitted to the experimental characteristic x-ray yields. Based on our previous work [26], we use two methods to extract the inner-shell ionization cross-sections in the thick-target method. The first method is the well-known Tikhonov regularization method, which can deal with a wide range of ill-posed inverse problems. Another method is the classical molecular dynamics (CMD), which has been successfully used to handle some inverse problems in recent years by our group. We found that these two methods can solve the inverse problem involved in the thick-target method successfully [25]. The total estimated error is about 10%, which is the same order as that in thin-target with thick substrate method [25]. Therefore, the thick-target method can be reliably used in the measurement of inner-shell ionization cross-sections by electron-impact near the threshold energy region, and the difficulty of thin-target film fabrication and the film thickness determination can be avoided. By using Tikhonov regularization method, we have measured the K-shell ionization cross-sections of Si and Ni elements by electron-impact with the thick-target method [25,27]. The experimental results for Si and Ni elements with the thick-target method are summarized in Tables 9–10, and comparisons with some theoretical results and the other available experimental data for Si and Ni elements are also shown in Figs. 9–10.
95 TABLE 9. MEASURED K-SHELL IONIZATION CROSS-SECTIONS FOR Si ELEMENT
(E: keV; VK AND ERROR: cm2)
TABLE10. MEASURED K-SHELL IONIZATION CROSS-SECTIONS FOR Ni ELEMENT (E: keV; VKAND ERROR: cm2)
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FIG. 9. The measured K-shell ionization cross-sections for Si element by the thick-target method. The predictions of DWBA [28] and PWBA-C-Ex [13,14] theories and the values of Casnati empirical formula [18] are also shown for comparison.
FIG. 10. The K-shell ionization cross-sections for Ni element determined by the Tikhonov regularization method and the classical molecular dynamics (CMD) method. The experimental data of Llovet et al. [29] and the predictions of DWBA [28] and PWBA-C-Ex [13,14] theories are also shown for comparison.
The effect of surface roughness has also been studied by using Monte Carlo simulations when measuring the electron-impact inner-shell ionization cross-section with the thick-target method [30]. The definition of surface roughness structures was a series of hemispheres produced randomly on the smooth surface of a thick Ni target. We used Monte Carlo simulations to obtain the characteristic x-ray yields of Ni K-shell ionization by electron-impact for the target with smooth surface and the targets with various surface roughness.
Then we used Tikhonov regularization method to deal with the inverse problem and obtained the K-shell ionizationcross-sections. The Ni K-shell ionization cross-sections obtained with smooth surface and various surface roughness have been compared. The result shows that the influence of surface roughness increases as the roughness increases, and the surface roughness of the target should be less than 100 nm if the experimental error originated from surface roughness would be kept less than 2%.
5. SUMMARY
In this paper, the K-shell ionization cross-sections for S, Cl, Ca, Zn elements and the L-shell x-ray production cross-sections for W-LD, LE, Bi-LD, LE, Ba-LD and Gd-LD have been measured from the threshold energy to several ten keV by using the thin-target with thick substrate method. The effect of multiple scattering of incident electrons in the thin films, the effect of backscattering of incident electrons from the thick substrates, and the effect of bremsstrahlung photons produced by incident electrons in both thin films and thick substrates have been corrected by using Monte Carlo method. Moreover, the K-shell ionization cross-sections for Si and Ni elements have also been measured by using the thick-target method, in which the ill-posed inverse problem has been dealt with successfully by the Tikhonov regularization method and the classical molecular dynamics. The experimental results
6 8 10 12 14 16 18 20 22 24 26
97 reported in this paper have been compared with some theoretical values and the values of empirical formulae.
ACKNOWLEDGEMENT
This work is supported by the National Natural Science Foundation of China under Grant Nos. 10774106 and 10674097 and the IAEA Research Contract No. RC-13491/R2.
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