2. L-Shell Ionization Cross Section Measurements for Some Heavy Elements by Low-Energy Electron Impact LUO Zheng-Ming, AN Zhu, GOU Cheng-Jun, WU Zhang-Wen, YANG Dai-Lun, HE Fu-Qing, and PENG Xiu-Feng Key lab for radiation physics and technology of the education ministry of China and Institute of Nuclear Science and Technology, Sichuan University, Chengdu, China

3. CONTENT 1. Introduction 2. Experimental Method and Data Processing 3. Measurement Results 4. Next Works

4. 1. INTRODUCTION Sichuan University group (1991-present) : Origin of research: impurity diagnosis problems from the fusion research centers of China. Thin target with a thick substrate method was proposed in 1994 1994-present, the inner shell ionization cross sections by electron impact for 35 elements have been measured, including 28 elements (Sc 、 V 、 Cr, Fe, Co, Zn, Ga, Se, Y, Zr, Nb, Rh, In, Hf, Ta, W, Re, Os, Ir, Pr, Sm, Tb, Dy, Ho, Er) which are measured first time.

5. 2. EXPERIMENTAL METHOD AND DATA PROCESSING 2.1 Difficulty and new idea It is very difficult to prepare a self-supporting thin target. New idea: Application of vacuum coating technique to prepare thin target on thick film. 2.2 Our experimental method: Using thin target with a thick substrate Advantage: it is very easy to prepare the targets. However, ionization contribution in thin target by electrons reflected from the substrate must be corrected. The corrected measurement formulae is given below

6. e Si (Li) detector This target Substrate Our experimental illustration

7. Experimental set up: scanning electron microscopy

9. 2.3 Measurement data processing I. Energy spectrum of reflected electrons at a substrate surface The reflection energy spectrum of 20 KeV electrons incident onto mylar film (solid curve) and aluminum baking (broken curve) calculated by using the bipartition model. The incident angle is 45 degree.

10. II. The mean track length correction: d'/d: ratios of electron mean track length to target thickness (figure) The effect here is very small for low or middle Z elements, it become larger in the measurement of L, M- shells for medium and high Z elements. EGS4

11. III. Efficiency calibration: The calibrated radioactive sources are used to determine the detective efficiency of the Si(Li) detector. The Calibrated Radioactive sources were provided by China Metrology Institute

12. IV. The preparation of thin target with thick substrate and measurement of thin target thickness Using vacuum coating technique to prepare thin target on a mylar film or an aluminum backing made by in CIAE The thickness of thin target were measured by using a precise balance. The uncertainty is about 10%. Homogeneity of the target was tested by probing the target with electron beam while registering the emitted x-ray. The uncertainty is about 1%.

13. L-shell ionization cross sections deduced from production cross sections In order to obtain L-shell mean ionization cross sections of target Elements it is necessary to measure the total x-ray production cross sections, because the mean L-shell ionization cross sections of target atoms can be deduced from the total x-ray production cross sections where is the L-shell mean fluorescence yield whose definition is as follows:

14. where is the fluorescence yield for the i-th subshell and is the Coster-Kronig transition probability between the i-th and j-th subshells

15. For comparison of experimental data with the Gryzinsky’s and McGuire’s theories, from which only obtained are ionization cross sections of three sub-shells, therefore we have to convert them into the partial production cross sections. The conversion formulas can be taken from Shima et al. The partial production cross Sections are functions of L1-, L2-, and L3- subshell ionization cross sections, and as below

17. The experimental values of -rays production cross sections for tungsten. The symbol Gr represents Gryzinski’s theory. Mc represents McGuire’s theory. The hollow circles are experimental data and the filled circles are corrected experimental data for the reflected electron effect. Figure 8. Experimental values of

18. The experimental values of -rays production cross sections for tungsten. The symbol Gr represents Gryzinski’s theory. Mc represents McGuire’s theory, The hollow circles are experimental data and the filled circles are corrected data for the reflected electron effect.

19. The experimental data of -rays production cross sections for tungsten. The symbol Gr represents Gryzinski’s theory. Mc represents McGuire’s theory, The hollow circles are experimental data and the filled circles are the corrected experimental data for the reflected electron effect.

20. The total production cross sections (Lp) and ionization cross sections (Li) of tungsten as functions of electron energy. The hollow circles are experimental data and the filled circles are corrected experimental data. The symbol Gr represents Gryzinski’s theory. Mc represents McGuire’s theory.

21. Fig.1 Fig.1 ray production cross sections of Ta atom as function of electron energy. The hollow symblos are experimental values and the filled symbol are correted experimental values for the reflected electron effect. The solid and dash line are from MCGuire and Gryzinski theory respectively.

22. Fig.2 ray production cross sections of Ta atom as function of electron energy. The hollow symbols are experimental values and the filled symbols are corrected experimental values for the reflected electron effect. The solid and dash line are from MCGuire and Gryzinski theory respectively.

23. Fig. 3 Fig.3 ray production cross sections of Ta atom as function of electron energy. The hollow symbols are experimental values and the filled symbols are corrected experimental values for the reflected electron effect. The solid line and the dash line are from MCGuire and Gryzinski theory respectively.

24. Fig.4 Total x-ray production cross sections and average ionization cross sections of Ta atom as function of electron impact energy. The symbols are same as those in Fig. 1.

25. Fig.5 ray production cross sections of Tm atom as function of electron energy. The hollow symbols are experimental values and the filled symbols are corrected experimental values for the reflected electron effect. The solid and dash line are from MCGuire and Gryzinski theory respectively.

26. Fig.6 ray production cross sections of Tm atom as function of electron energy. The hollow symbols are experimental values and the filled symbols are corrected experimental values for the reflected electron effect. The solid line and the dash line are from MCGuire and Gryzinski theory respectively.

27. Fig. 7 Fig. 7 ray production cross sections of Tm atom as function of electron energy. The hollow symbols are experimental values and the filled symbols are corrected experimental values for the reflected electron effect. The solid and dash line are from MCGuire and Gryzinski theory respectively.

28. Fig.8 Total x-ray production cross sections and average ionization cross sections of Tm atom as function of electron impact energy. The symbols are same as those in Fig. 5.

29. Fig.9 Lα x-ray production cross sections of Dy atom as function of electron energy. The hollow symbols are uncorrected experimental values and the filled symbols are corrected experimental values. The solid and dash lines are from McGuire and Gryzinski theory respectively.

30. Fig.10 Lβx-ray production cross sections of Dy atom as function of electron energy. The symbols are same as those in Fig. 1.

31. Fig.11 Lγ x-ray production cross sections of Dy atom as function of electron energy. The symbols are same as those in Fig. 1.

32. Fig.12 Lα x-ray production cross sections of Sm atom as function of electron energy. The symbols are same as those in Fig. 1.

33. Fig.13 Lβx-ray production cross sections of Sm atom as function of electron energy. The symbols are same as those in Fig. 1.

34. Fig.14 Lγ x-ray production cross sections of Sm atom as function of electron energy. The symbols are same as those in Fig. 1

35. Fig.15 The Dy’s total x-ray production cross sections (LP) and average ionization cross sections (LI) as function of electron impact energy. The symbols are same as those in Fig. 1.

36. Fig.16 The Sm’s total x-ray production cross sections (LP) and average ionization cross sections (LI) as function of electron impact energy. The symbols are same as those in Fig. 1.

37. CONCLUSION From the description above, some conclusions can be given below: 1) From some recent measurements, we conclude that the K-shell ionization cross-section data can be measured with combined standard uncertainties of about 10% (no more than 15%) although discrepancies among some experimental data sets are still existing.

38. 2) Further measurements of K-shell ionization cross-sections are still needed, especially with higher accuracy better than 10% and for the higher-Z elements. In addition the measurements for L- and M-shells, which are more complicated and more difficult, should be paid more attention due to very scarce available data and also as a set of very useful data for fusion technology. 3) Some theoretical work still needs to be done to improve the agreement between theories and experiments. The theoretical models developed recently have made progress in this aspect.

39. 4. FURTHER WORKS 4.1 Improving the electron beam quality and enhancing the electron beam stability. 4.2 Improving the accuracy of measurement of thin target with thick substrate 4.3 Measurement of inner shell ionization cross sections of main impurity elements for fusion technology including that of C, O, N which will be measured by using thick compound target technique 4.4 Better theoretical models such as DWBA will be used to analysis the experimental data.

40. 4.1 Improving the electron beam quality and enhancing the electron beam stability. using a current stable device using a filament with better emission ability improving target chamber

41. 1.Improving measurement accuracy of thickness of thin target with thick substrate: RBS 2. Extended calibration curve to lower energy range by using Monte Carlo method 3.A better evaluation of influence of target- substrate on measurement: Improving electron transport calculation. 4.Using new standard active sources with higher accuracy to efficiency calibration. 4.2 Improving the accuracy of measurement of thin target with thick substrate

42. 4.3 Measurement of inner shell ionization cross sections of O, N which will be measured by using thick compound target technique Generally speaking, the ionization cross sections by electron impact for chemically active elements such as O,N,Cl …. can not be used thin target method, due to the difficulty in preparation of thin target. Therefore thick target method become an option. However, some new mathematic problems will appeared. We present a solution for the problem.

43. Si(Li) X-ray e The measurement principle is shown as follows

44. let We obtain the 1-st kind of Fredholm integral equation as follows: (A)

45. Above equation is a first kind of Fredholm integral equation which is ill-posed. We are carrying out the programming compilation works. The main works include: 1. Calculation of the kernel H (E,T): We use bipartition model of electron transport to calculate electron energy spectrum at any depth, further to obtain the kernel function H(E,T). 2. How to solve equation (A) We shall solve the 1st kind of Fredholm integral equation to obtain an applicable solution by using Tikhonov Regularization method.

46. 4.4 Better theoretical models will be used to analysis experimental data. We have found that some newer atomic collision theory, such as DWBA, can be used to quantitatively analysis the experimental data. We collaborate with colleagues in CIEP to carry out the research.

47. THANK YOU

48. the number of photons of the characteristic x-rays of the element to be determined produced by one electron in the target in the region The characteristic x-rays emitted by atomic de-excitation are basically isotropic, a part of which are recorded by the Si(Li) detector after passing through the thick target. The total number of photons recorded is represented by. It is evident that

49. The essence of using the regularization method to solve the first kind of integral equations Eq.(1) is that we can consider it as a conditional extremum problem of a functional to be solved. In this way, the method is in fact an optimization method. Now we describe solving Eq.(1) as seeking for such a function it satisfies integral equations within a given error. Under the condition of satisfying the given accuracy, i.e. At the same time it minimize the following square functional (2) (3)

50. The conditional extremum of the functional composed of Eqs.(2) and (3) can be turned to be an unconditional extremum problem of the functional by using the Lagrange multiplier The solution of Eq.(4) corresponds to the condition that the variety of the unconditional functional should be zero, i.e. (4)

51. That is Thus, an ill-posed first kind of Fredholm integral equation become a stable second kind of Fredholm integral equation. It is easy to be solved, where (5)

52. If we take the discretization, then we can obtain the following matrix equations This is a stable standard algebraic system. It is easy to find it solution (6) (7)