L 3 -subshell alignment of Ag in collision with 15 keV electrons

Abstract

It is of great importance to study the alignment of atoms in collision process in elementary analysis with a Particle Induced X-ray Emission (PIXE) technique. The measurement of alignment can also offer an effective testing ground for developing theory models in ionization process. The typical L X-ray spectra are measured for Ag thin target by 15 keV electron impact at emission angles from 0° to 25°. Angular dependence of intensity ratios L_α/L_β1, L_β2/L_β1 and L_γ/L_β1 are investigated as a function of the second-order Legendre polynomial P₂(cosθ). This study found that L_β2 line exhibits anisotropic emission spatially, while the emission of L_α, L_β1 and L_γ1 lines is isotropic. The results are interpreted by the influence of the Coster-Kronig (CK) transitions on the spatial distribution of X-ray emission. The anisotropy parameter β for L_β2 lines is obtained experimentally and consequently the alignment degree A₂₀ for L₃ subshell is determined by taking CK transition into account. Namely, the alignment does exist in L₃-subshell for atomic ionization by electron impact. The measurements offer an evidence to the existence of alignment for atomic ionization in electron-impact process.

Keywords

X-ray angular distribution particle induced X-ray emission (PIXE)electron impact alignment of atoms

1 Introduction

As a quantum system, the atom does not rotate collectively [1]. Hence, it is an intriguing phenomenon that ionization or excitation by electron-impact can align the angular momentum in spite of the spherical symmetry of the initial wave function of target. It is suggested theoretically that the emission of fluorescent radiation have anisotropic distribution following the vacancy decay with total angular momentum j > 1/2 [2]. The alignment of atomic outer-shells in the excitation by electron-impact has been thoroughly studied for several decades [3], while it has not been observed conclusively in the case of electron-impact ionization. For L₃-subshell (j = 3/2), the magnitude of alignment degree is quantified by the parameter A₂₀ which is determined as the relative difference of the ionization cross sections σ (j, m_j) pertaining to the magnetic sub-states with m_j = 3/2 and m_j = 1/2 . In experiment, A₂₀ can be derived by the measurement of angular distribution of characteristic X-rays or Auger electrons in the subsequent de-excitation of singly ionized atoms [4 –8]. In addition, it is also of significant importance to investigate angular dependence of characteristic X-rays in atomic physics, plasma physics and astrophysics [9, 10].

According to the dipole approximation, the differential intensity dI(θ) can be described as Equation (1) for the X-rays emitted after decay of vacancy in L₃-subshell produced by unpolarized particle beam [2]. $\frac{dI (θ)}{d Ω} = \frac{I_{0}}{4 π} [1 + β P_{2} (cos θ)]$ (1) where θ is the emission angle related to the incident electron beam direction, dΩ is the solid angle subtended to the target in experimental geometry, β (= ακA₂₀) is the anisotropy parameter for a characteristic X-ray, and P₂(cosθ) is the second-order Legendre polynomial. In parameter β, α is the anisotropy coefficient which depends on the total angular momentum j of the initial and final vacancy states of target atom, κ is the Coster-Kronig (CK) correction coefficient. In this work, the corresponding anisotropy coefficients α for L_α1 (L₃M₅), L_α2 (L₃M₄) and L_β2(L₃N₅) lines are 1/10, – 2/5 and 1/10, respectively.

The characteristic X-rays can be measured normally to determine total ionization cross sections for L-subshell by electron impact. The total ionization cross section is insensitive to the projection of angular momentum of the ionized atom since it is an average over the magnetic states. As a matter of fact, the current measurement of ionization cross sections [11, 12] is supposed to take the angular distribution of typical radiation into consideration in order to avert systematic errors, although it has been suggested that the errors are evaluated to be very small except in special circumstances [4]. Thus, the alignment measurement can reveal new information and offer an effective and significant testing ground for theory models in ionization process.

Most measurements focus on the photoionization and ion-impact ionization to study alignment of atoms in collision process. In order to explore new information in electron-impact ionization and provide fundamental data for theoretical study, the typical X-ray spectra for Ag-L_α, L_β1, L_β2 and L_γ1 lines are investigated with 15 keV electron impact at emission ranging from 0° to 25°. The anisotropy parameters β for L_β2 lines and alignment parameter A₂₀ for L₃-subshell are determined from the angular dependence of L X-rays on P₂(cosθ). The results provide a clear indication of alignment in L₃-subshell. Particularly, Ag L_α (L₃M_4,5), L_β1 (L₂M₄), L_β2(L₃N₅) and L_γ1(L₂N₄) are the characteristic X-ray lines produced by vacancy transfer from L shell to higher energy levels. For L_α line, the vacancy transfer is from L₃-subshell to M_4,5-subshell. For L_β1 line, the vacancy transfer is from L₂-subshell to M₄-subshell. For L_β2 line, the vacancy transfer is from L₃-subshell to N₅-subshell. For L_γ1 line, the vacancy transfer is from L₂-subshell to N₄-subshell. The investigation of characteristic X-rays is of extensive application in atomic physics, plasma physics and astrophysics. For example, it is frequently applied in elementary analysis with Particle Induced X-ray Emission (PIXE) technique.

2 Experimental setup

The experimental setup is implemented for measurement of X-ray spectra at different emission angles conveniently. The schematic diagram of the experimental setup is presented in Fig. 1. An X-ray source (Mini-X) is fixed at the center of a stage, and an AMPTEK production-X-ray Silicon Drift Detector (XR-100SDD) is mounted on a rotatable stage so as to change detection angle. The detector has wide detection range, and in our experimental setting, it can measure X-rays simultaneously with energy from 1 keV to 14 keV. The X-ray source works with 0.75μm silver anode and 127μm beryllium window. The Ag anode in Mini-X is irradiated by electrons with voltage of 15 kV and current of 90μA. Since the binding energy of electrons is about 25 keV in K-shell and 4 keV in L₁-subshell for Ag, we choose the incident energy of 15 keV that can ionize the electrons in L-subshell and cannot ionize the electrons in K-shell. In this circumstance, the alignment of vacancy in L-subshell can be studied taking no account of the effect of vacancy transfer from K- to L-shell. The current of 90μA is chosen to ensure high detection efficiency and avoid generation of dead time in X-ray detector. Ag L X-ray spectra can be measured after transmitting a 16 cm air column with detection angle ranging from 0° to 25°. The X-ray detector has an active crystal area of 25 mm² and an effective depth of 500μm. A beryllium window with thickness of 12.5μm is integrated in X-ray detector to improve signal to noise ratio (SNR). The detection efficiency of X-ray detector is more than 0.98 for the X-ray energy regime in this work, and the energy resolution is 125eV (Full Width at Half Maximum, FWHM) at 5.9 keV. The net counts for each X-ray line is normalized by the quantity of incident electrons at each angle.

Fig.1

Schematic diagram of the experimental setup.

Fig.2

Characteristic L X-ray spectra for Ag at emission angle of 20°. L_α, L_β1, L_β2 and L_γ1 X-rays are distinguished in the spectra.

3 Results and discussion

The typical spectra for Ag are very similar for detection angle from 0° to 25°. Therefore, it is shown only at one detection angle to introduce the structure of L X-rays for Ag in the paper. The measured characteristic L X-ray spectra at emission angle of 20° are shown in Fig. 2. The energy difference between Ag-L_α1 (L₃M₅) and L_α2 (L₃M₄) X-rays is only about 6eV which is much less than energy resolution of X-ray detector. Therefore, both lines cannot be resolved in the measured spectra. Finally, Ag L_α (L₃M_4,5), L_β1 (L₂M₄), L_β2(L₃N₅) and L_γ1(L₂N₄) X-rays are distinguished and presented as dashed lines in Fig. 2. The peaks are determined by multi-peak Gaussian fitting procedure. The FWHM of L_α, L_β1, L_β2 and L_γ1 lines are 168eV, 168eV,179eV and 192eV, respectively, which is consistent with energy resolution of X-ray detector. As a result, net counts for each X-ray lines can be acquired by data processing of the area under corresponding peaks.

In view of L_β1 and L_γ1 lines originating from 2p_1/2 (j = 1/2 ) subshell, they are expected to exhibit isotropic emission. The experimental results actually demonstrate that both lines are found to have isotropic emission spatially within uncertainties in the measurement. Therefore, the angular distribution of L_β1 and L_γ1 X-ray intensities can be taken as good reference to eliminate the geometry misalignment, if any, in experimental setup. Taking L_β1 X-ray originating from L₂ (2p_1/2, j = 1/2 ) subshell into account, the angular distribution of intensity ratios L_α/L_β1, L_β2/L_β1 and L_γ1/L_β1 is investigated in this work. The experimental values of X-ray intensity ratios L_β2/L_β1 and L_γ1/L_β1 can be derived by equation [13] $\frac{I (L_{i})}{I (L_{j})} = \frac{\frac{N (L_{i})}{ɛ (L_{i}) β (L_{i})}}{\frac{N (L_{j})}{ɛ (L_{j}) β (L_{j})}} = \frac{N (L_{i}) ɛ (L_{j}) β (L_{j})}{N (L_{j}) ɛ (L_{i}) β (L_{i})}$ (2) where N(L_i) and N(L_j) are the net counts of L_i and L_j X-ray lines; ɛ(L_i) and ɛ(L_j) are the detection efficiency for L_i and L_j X-rays; β(L_i) and β(L_j) are the correction coefficient on account of attenuation of the emitted typical X-rays in the air column between target and detector. It should me mentioned that the self-absorption effect of X-rays inside the Ag target can be approximately offset in the intensity ratios because the X-ray energies are very close to one another and the Ag anode is thin enough. The total experimental error for X-ray intensities is less than 8% combining statistic error (3%, considered for incident electrons and emitted X-rays) with errors estimated for solid angle (6%), background subtraction (2%) and fitting procedure (2%). Consequently, the X-ray intensity ratios I (L_α)/I (L_β 1) , I (L_β 2)/I (L_β 1) and I (L_γ 1)/I (L_β 1) are obtained according to Equation (2) and plotted as a function of P₂(cosθ) in Figs. 3– 5, respectively. It can be seen from Figs. 3 and 5 that the intensity ratios for I (L_α)/I (L_β 1) and I (L_γ 1)/I (L_β 1) exhibits no increase or decrease trend integrally with emission angle within experimental errors. While the intensity ratio for I (L_β 2)/I (L_β 1) exhibits anisotropic emission in Fig. 4, and consequently the anisotropy parameter β for L_β2 line is deduced to be 0.061 by linear fitting procedure according to Eqs. (1) and (2).

Fig.3

Intensity ratio of I (L_α)/I (L_β 1) as a function of P₂(cosθ). The dashed line illustrates the trend only.

Fig.4

Intensity ratio of I (L_β 2)/I (L_β 1) as a function of P₂(cosθ).

Fig.5

Intensity ratio of I (L_γ 1)/I (L_β 1) as a function of P₂(cosθ).

In electron-impact ionization, the vacancy in L₃ subshell can originate not only from direct ionization but also by vacancy transfer from L₁- or L₂-subshells in Coster-Kronig (CK) process. In addition, the binding energy of electrons in K-shell for Ag (25 keV) is much higher than the energy of incident electrons (15 keV), therefore the electrons in K-shell cannot be ionized and vacancy transfer from K-shell do not need to be taken into account. As a result, the CK correction coefficient κ is expressed by $κ = [σ_{L_{3}} / σ_{L_{3}}^{total}] = [σ_{L_{3}} / {σ_{L_{1}} (f_{12} f_{23} + f_{13}) + σ_{L_{2}} f_{23} + σ_{L_{3}}}]$ (3) where σ_{L
_i} is ionization cross section by direct ionization in L _i -subshell by electron impact [12]. $σ_{L_{3}}^{total}$ is the total probability for vacancy production in L₃-subshell. f_ij is the CK transition probability and shown in Table 1 [14]. Therefore, the CK correction coefficient κ is determined to be 0.932 in this work.

Table 1

Theoretical Coster-Kronig yields f_ij in L-subshells for Ag taken from Ref. [14]

Coster-Kronig probabilities
f ₁₂	f ₁₃	f ₂₃
0.064	0.070	0.130

In the present work, a weighted average value of α= 0.050 is employed according to the relative intensities of L_α1 and L_α2 lines for investigation of alignment degree A₂₀ involving the L_α line since both lines cannot be separated with Si(Li) detector. The value of anisotropy coefficient α for L_β2 line is 0.1, which indicates that the anisotropy parameter β for L_β2 line is supposed to be twice as much as that for L_α line. Consequently, the anisotropy parameter β for L_β2 lines and the corresponding alignment degree A₂₀ (= β/(ακ) ) for L₃-subshell are listed in Table 2. As a result, the alignment property is verified for vacancy in L₃-subshell and the alignment degree A₂₀ is derived quantitatively to be 0.65±0.14 in this measurement, while vacancy states in L₁- and L₂-subshells are not aligned. It should be mentioned that the influence of vacancy transfer from unaligned L₁- and L₂-subshells can only affect the alignment in L₃ subshell slightly.

Table 2

The measured anisotropy parameter β for L_β2 line and alignment degree for L₃-subshell

Coster-Kronig probabilities
f ₁₂	f ₁₃	f ₂₃
0.064	0.070	0.130

As a result, the alignment of L₃-subshell is demonstrated and the alignment degree is determined quantitatively. Different from photoionization and ion-impact ionization, we investigate the alignment of atom by electron-impact at 15 keV and consequently the influence of vacancy transfer from K- to L-shell is eliminated since K-shell electrons cannot be ionized. It is also manifested that the CK transition from unaligned L₁ and L₂ subshells can only affect the alignment in L₃-subshell slightly. Comparing to previous work, the alignment degree is determined quantitatively in the experiment.

4 Conclusions

The angular dependence of L X-ray intensity ratios is investigated for Ag target by 15 keV electron impact. The experimental results suggest that the L_β2 line has an anisotropic emission spatially; whereas L_α, L_β1 and L_γ1 lines exhibit isotropic emission. Therefore, it is concluded that vacancy states in L₁- and L₂-subshells are not aligned while vacancy in L₃-subshell is aligned. The anisotropy parameters β are determined to be 0.061 for L_β2 line. The alignment degree A₂₀ is derived quantitatively to be 0.65±0.14 for L₃-subshell from the results of anisotropy parameters in this measurement. It demonstrates that the alignment does exist in L₃-subshell for atomic ionization by electron impact, and the influence of CK transition from unaligned L₁ and L₂ subshells can only affect the alignment in L₃-subshell slightly. Particularly, the angular correlation effects of X-ray emission originating from L₃-subshell will not affect the results significantly in the measurement of L-subshell ionization cross sections on the basis of the current experimental precision.

Footnotes

Acknowledgments

This work is supported by the Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2018JM1027), and National Natural Science Foundation of China (Grant Nos. 11875219 and 11405123).

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