Angular distribution of L characteristic X-ray emission from Au target impacted by photons

Liu Yu; Xu Zhong-Feng; Wang Xing; Hu Peng-Fei; Zhang Xiao-An

doi:10.7498/aps.69.20191977

Abstract

The vacancy can be produced through impact ionization of target atom by energetic particles. It is of significant importance to study the vacancy state by the measurement of angular distribution of typical X-rays. At present, accurate ionization cross-section data of the atomic inner shell are urgently required in many areas. However, the precise measurement of ionization cross-section of the atomic inner shell is largely dependent on the fact that whether the characteristic radiation (e.g., X-ray) is isotropic. In this experiment, the characteristic L_ι, L_α, L_β and L_γ1 X-rays for Au target are measured by a silicon drift detector in an emission angle range from 130° to 170° in steps of 10°. A mini-X ray source is utilized to produce bremsstrahlung with the center energy of 13.1 keV.Considering detection efficiency of the detector and the absorption of the target, relative intensity ratios, I(L_α)/I(L_γ1) and I(L_ι)/I(L_γ1), are obtained at different detection angles based on the experimental energy spectrum results. Moreover, the angular dependence of X-ray intensity ratio is investigated and it is found that the X-rays L_ι and L_α exhibit anisotropic emission.According to the X-ray intensity ratio I(L_ι)/I(L_γ1) and the P₂(cosθ), and using the least square method, the anisotropic parameter β of characteristic X-ray L_ι is derived to be 0.25. Due to the relation β = ακA₂₀, the value of the alignment degree A₂₀ for L₃ sub-shell is determined to be 0.577 ± 0.08. Alignment degree A₂₀ for L₃ sub-shell is dependent on its intrinsic physical properties, while the anisotropy parameter β of typical X-rays can be affected by Coster-Kronig transition process.The behavior of the alignment for inner-shell vacancy states calls for more research results both in theory and in experiment. Therefore, it is quite relevant and meaningful to perform more experiments to further study the angular distribution of vacancy states by electrons, photons and ions impacting a target.

Keywords:

PACS:

32.30.Rj	(X-ray spectra)
32.70.Fw	(Absolute and relative intensities)
32.80.-t	(Photoionization and excitation)

Authors and contacts

1.
Ion Beam and Optical Physical Laboratory of Xianyang Normal University and Institute of Modern Physics, Chinese Academy of Sciences, Xianyang 712000, China
2.
School of Science, Xi’an Jiaotong University, Xi’an 710049, China

Corresponding author: Liu Yu, liuyuxianyang0625@126.com

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1. 引　言

总角动量为J > 1/2的原子内壳层空穴态, 可由光子、电子或高速离子电离原子产生. 该空穴态的定向行为, 从实验中通过荧光辐射的线性极化程度、X射线或俄歇电子的角分布可以推断出来. 目前很多领域都迫切需要精确的原子内壳层电离截面数据, 例如材料元素分析中的X射线荧光光谱技术^[1,2]、俄歇电子谱仪^[3]、X射线成像技术^[4-6]. 然而原子内壳层电离截面的测量必须考虑特征辐射(如X射线)是否为各向同性. 虽然已经开展了大量的实验研究, 通过测量发射X射线的角分布或极化程度来研究内壳层空穴态的排列, 然而对于低能光子撞击对原子内壳层电离角分布的研究, 到目前为止还不是很清楚. Flügge等^[7]首次预测了光电离过程中产生空穴的定向分布. 随后许多科学家在理论和实验上^[8-14]支持了Flügge等的观点, 即电离过程中L₃支壳层空穴在其退激过程中, 所发射特征X射线辐射为各向异性; 然而在有的研究工作^[15-21]中却得到了与Flügge等相反的观点, 即电离过程中L₃支壳层所产生特征X射线为各向同性分布. 可见, 关于空穴态定向行为的实验研究仍没有定论.

了解原子物理学中的L壳层空穴态的定向分布, 需要了解L壳层X射线的相对强度. 对于由准直非极化光子产生的空穴衰变而产生的偶极型X射线, Berezhko和Kabachnik^[22]在1977年, 初次给出了电离原子退激过程中, 不同出射角θ发射特征X射线的微分强度理论公式:

$\frac{{{\rm{d}}I}}{{{\rm{d}}\varOmega }} = \frac{{{I_0}}}{{4{\text{π}}}}(1 + \beta {P_2}(\cos \theta) ), \tag{1a}$

$\beta = \alpha \kappa {A_{20}},{P_2}(\cos \theta) = [3\cos (2\theta) + 1]/4, \tag{1b}$

(1)式描述了不同出射角度与该出射角度上X射线强度的关系, 文献[22]对(1a)式和(1b)式中各参数的物理意义已进行了详细描述, (1)式对于获得4π立体角内总的X射线发射强度具有重要意义. 对应支壳层空穴态的定向度A₂₀, 由各磁亚态μ_n中的集居截面决定. 例如对于L壳层中, 能级为J = 3/2的L₃支壳层, 定向度可以被表示为^[22] A₂₀ = [σ(3/2, ±3/2) – σ(3/2, ±1/2)]/[σ(3/2, ±3/2) + σ(3/2, ±1/2)], 其中σ(2p_3/2, μ_n)表示磁亚态μ_n中的集居截面.

A₂₀对磁亚态电离截面的依赖使得它是一个非常重要的量, 而且这个量不能从L₃壳层总的电离截面中测量得到. 同时, 定向参数的信息对于总的截面测量是非常重要的. 从(1)式可知, 从不同探测角度下特征X射线的强度分布, 可以得出对应支壳层的各向异性参数.

L₃支壳层发射的特征X射线L_ι和L_α, 其与空穴初态和终态总角动量相关的动力学因子α值分别为0.5和0.05^[22]. 也就是说特征X射线L_ι的各向异性参数β值是特征X射线L_α的10倍, 那么实验结果中特征X射线L_ι的各向异性发射将更容易被观察到. 即使两种相对立的论断^[7,15], 也都认为从L₁和L₂支壳层(J = 1/2)产生的X射线为各向同性发射. 基于上述内容, 本文认为从L₂支壳层发射的X射线L_β₁和L_γ₁为各向同性发射. 实验中可以采用同一探测角度下探测到的光谱中X射线L_ι与L_γ₁的强度比, 来测量特征X射线L_ι的各向异性参数. 对于同一光谱中X射线强度比, 只有谱线计数统计带来的计数误差, 会影响各向异性参数β的不确定度.

本文使用中心能量为13.1 keV的轫致辐射对纯厚Au靶进行轰击, 并在发射角为130°—170°范围内以10°为间隔, 测量了靶的特征L系X射线光谱; 报道了X射线L_ι与L_γ₁的强度比的角依赖关系, 并由此获得特征X射线L_ι的各向异性参数以及L₃支壳层的定向度, 完善了对空穴态定向行为的论断.

2. 实验方法及原理

本文采用的实验仪器分别为美国AMPTEK公司生产的Mini-X射线管、XR-100SDD探测器、PX5多道脉冲处理器、电脑终端以及与上述硬件设施配套的软件部分. 本实验在大气中进行, 实验装置示意图如图1所示, Mini-X射线管在距靶材中心位置16 cm处, 向厚度为40 μm的Au靶发出垂直于靶面正中心的X射线. 探测器位于距离入射束与靶材交点15 cm处, 实验过程中Mini-X射线管与靶材相对位置保持不变. 用X射线探测器在130°—170°的范围内以10°为间隔, 对Au靶的特征X射线L_ι, L_α₁, L_α₂, L_β₁, L_β₂和L_γ₁进行测量. AMPTEK公司生产的Mini-X射线管可快速、高效、稳定地输出不同能量和流强的光子. 通过改变管电流和管电压的方式来控制出射光子的能量和流强; 管电流的可调控范围为5—200 μA, 实验中设置为90 μA. 管电压的可调控范围为10—50 keV, 实验中将其设置为30 keV. Mini-X射线管在无准直的情况下输出光束发散角为120°. 实验过程中, 在X射线出口处加2 mm的准直, 出射X射线的发散角约为5°. 在探测器25 mm²的探测面上, 装有一个用于避光和真空封装的, 厚度为12.5 μm的薄铍窗以便于探测软X射线, 其分辨率可达到在5.9 keV峰处具有125 eV的峰值半高全宽. 所以对Au的特征X射线L_α₁和L_α₂ (L_α₁和L_α₂的能量差是85 eV)不能分辨, 统一记做L_α; 对于Au的特征X射线L_β₁和L_β₂ (L_β₁和L_β₂的能量差是133 eV)谱没有完全区分清楚, 也统一记作L_β. 探测器在此条件下对特征X射线L_ι, L_α, L_β和L_γ₁的探测效率分别为0.989, 0.97, 0.88和0.75.

$图 1 实验装置示意图\r\nFig. 1. Experimental setup.$

图 1 实验装置示意图

Fig. 1. Experimental setup.

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3. 实验结果与分析

图2给出了当X射线垂直入射Au靶时, 在140°的探测角度上所探测到的特征X射线能谱图. 由图2可知, L_ι, L_α, L_β和L_γ₁这4个特征X射线峰区分得非常好. 采用origin软件中高斯函数拟合的功能, 可以准确地求解L_ι, L_α, L_β和L_γ₁特征X射线特征的峰面积. 实验中特定发射角度下, X射线强度比I(L_i)/I(L_j)为

$\frac{{I\left( {{{\rm{L}}_i}} \right)}}{{I\left( {{{\rm{L}}_j}} \right)}} = \frac{{N\left( {{{\rm{L}}_i}} \right)\varepsilon \left( {{{\rm{L}}_j}} \right)\lambda \left( {{{\rm{L}}_j}} \right)}}{{N\left( {{{\rm{L}}_j}} \right)\varepsilon \left( {{{\rm{L}}_i}} \right)\lambda \left( {{{\rm{L}}_i}} \right)}},$

(2)

其中N(L_i)/N(L_j)表示谱线中不同特征X射线经高斯拟合所得面积的比值, ε(L_j)/ε(L_i)是探测器对不同特征X射线的探测效率之比, λ(L_j)/λ(L_i)表示靶材对特征X射线的吸收校准因子之比, 其中i = α或ι, j = γ1. 特征X射线L_j和L_i的自吸收校正因子λ^θ (L_j )和λ^θ(L_i)^[23]具有相同的表述形式, 可表示为

$\begin{split} & {\lambda ^\theta }\left( {{{\rm{L}}_{a}}} \right) = \frac{{1 - \exp \left[ { - \left( {{\mu _{{\rm{inc}}}}/\cos {\theta _1} + {\mu _{{\rm{emt}}}}/\cos {\theta _2}} \right)t} \right]}}{{\left( {{\mu _{{\rm{inc}}}}/\cos {\theta _1} + {\mu _{{\rm{emt}}}}/\cos {\theta _2}} \right)t}} \\ & \qquad (a=i,j),\\[-12pt] \end{split}$

(3)

其中μ_inc表示入射光子(入射中心能量为13.1 keV的轫致辐射光子)的质量吸收系数, μ_emt表示出射光子(出射特征X射线L_i, L_j)的质量吸收系数, 其数值由Storm和Israel^[24]报道的靶材对不同能量光子的吸收系数得到. 入射束和出射束与靶平面法向的夹角由θ₁和θ₂分别表示, Au靶的质量厚度t为77.2 mg·cm^–2.

$图 2 探测角度为140°时、中心能量为13.1 keV轫致辐射入射Au靶产生L系特征X射线能谱图\r\nFig. 2. Fitted L X-ray spectrum of Au induced by impact with bremsstrahlung with central energy of 13.1 keV and measured at the emission angle of 140°.$

图 2 探测角度为140°时、中心能量为13.1 keV轫致辐射入射Au靶产生L系特征X射线能谱图

Fig. 2. Fitted L X-ray spectrum of Au induced by impact with bremsstrahlung with central energy of 13.1 keV and measured at the emission angle of 140°.

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经过(2)式和(3)式的计算, 在图3中完整展示了Au的L壳层X射线L_ι与L_γ₁及L_α与L_γ₁的强度比和P₂(cosθ)之间的关系. 采用最小二乘法对不同探测角度下得到的强度比I(L_ι)/I(L_γ₁)进行拟合, 拟合曲线的斜率, 即为特征X射线L_ι的各向异性参数. 本文数据统计过程中, X射线强度比的误差主要来自于5%的高斯拟合误差、3%的统计误差、6%的背景误差和6%的探测器立体角误差, 系统总体误差大约为14%.

$图 3 Au 靶特征X射线强度比I(Lα)/I(Lγ1)和I(Lι)/I(Lγ1)与P2(cosθ)的关系\r\nFig. 3. Intensity ratios of I(Lα)/I(Lγ1) and I(Lι)/I(Lγ1) as a function of P2(cosθ) for Au.$

图 3 Au 靶特征X射线强度比I(L_α)/I(L_γ₁)和I(L_ι)/I(L_γ₁)与P₂(cosθ)的关系

Fig. 3. Intensity ratios of I(L_α)/I(L_γ₁) and I(L_ι)/I(L_γ₁) as a function of P₂(cosθ) for Au.

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从图3可以看出, 强度比I(L_ι)/I(L_γ₁)与探测角度有明显的相关性. 通过确定L₃支壳层的空穴态产生过程, 可以更好地研究L₃支壳层的定向性行为. 原子受激并在L₃支壳层产生空穴的过程中, 原子处于不稳定状态, 更高壳层的一个电子就会通过辐射或无辐射的方式向L壳层跃迁. 当采用辐射方式跃迁时, 可以通过辐射X射线的形式释放多余的能量; 也可以通过发射俄歇电子或Coster-Kronig (CK)跃迁、超级CK跃迁的方式实现无辐射跃迁过程.

碰撞过程中, L₃支壳层的空穴不单可以由直接电离的方式在L₃支壳层中产生, 也可从K壳层、L₂或L₁支壳层转移而来. L₃支壳层电离截面σ₃计算公式为^[25]

$\begin{split} {\sigma _3} =\; & ({\sigma _{{\rm{L_1}}}} + {\sigma _{\rm{K}}}{\eta _{{\rm{KL_1}}}})({f_{13}} + {f_{12}}{f_{23}}) \\ & + ({\sigma _{{\rm{L}}_2}} + {\sigma _{\rm{K}}}{\eta _{{\rm{KL}}_2}}){f_{23}} + ({\sigma _{{\rm{L}}_3}} + {\sigma _{\rm{K}}}{\eta _{{\rm{KL}}_3}}). \end{split}$

(4)

Au的L壳层X射线电离截面依赖于荧光产额和CK跃迁系数. K壳层和L支壳层光电离截面由(4)式中σ_K, $\sigma_{{\rm L}_1}$ , $\sigma_{{\rm L}_2}$ 和 $\sigma_{{\rm L}_3}$ 来表示. f_ij是从L_i支壳层到L_j支壳层的CK跃迁概率, 是发生在同一主壳层的跃迁. $\eta_{{\rm KL}_i}$ 是从K壳层到L_i支壳层通过辐射跃迁转移和无辐射跃迁转移的空穴数. 在本次测量中入射光子的能量最大为30 keV, 而Au靶的K吸收限是80 keV, 所以当入射能量低于K吸收限时, K壳层电子不能被激发出来, 也就是说L₃支壳层的空穴转移只能由直接电离和L₁和L₂支壳层转移获得. 在这种情况下, (4)式中包含 $\eta_{{\rm KL}_i}$ 的项均可被消掉, L₃支壳层的电离截面可以写成:

${\sigma _3} = {\sigma _{{\rm{L}}_1}}({f_{13}} + {f_{12}}{f_{23}}) + {\sigma _{{\rm{L_2}}}}{f_{23}} + {\sigma _{{\rm{L_3}}}}.$

(5)

Au的CK跃迁概率f_ij可以由文献[25]获得, 如表1所列. 从图2和表1可以推断出L₃支壳层的电离截面σ₃, 显著地由L₁和L₂支壳层的空穴态影响. 空穴从L壳层中较低的支壳层向较高的支壳层转移, 这一行为很可能改变角动量量子数J > 1/2时空穴态的定向行为. CK跃迁矫正因子κ可以表示为

表 1 Au元素的L支壳层CK跃迁概率f_ij数据^[25]

Table 1. L-subshell CK yields f_ij for Au^[25].

f₁₂	f₁₃	f₂₃
0.083	0.644	0.132

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$\begin{split} \; & \kappa =\left[ {{{{\sigma _{{\rm{L}}_3}}}/{\sigma _{{\rm{L_3}}}^{{\rm{total}}}}}} \right] \\ = & [{{\sigma _{{\rm{L}}_3}}}/\{{\sigma _{{\rm{L}}_1}}({f_{12}}{f_{23}} + {f_{13}}) + {\sigma _{{\rm{L_2}}}}{f_{23}} + {\sigma _{{\rm{L_3}}}}\}].\end{split}$

(6)

表2列出了基于相对论Hatree-Fock-Slater模型得到的L₁, L₂, L₃支壳层电离截面值^[26]. 从表中可以看出, 当入射光子能量分别大于12, 13.8, 14.4 keV时, 可以使得L₃, L₂, L₁支壳层发生电离; 当入射光子能量小于13.76 keV时, L₁和L₂支壳层都没有发生电离, κ值为1; 当入射光子能量增加到13.8 keV时, L₃和L₂支壳层都发生电离, κ值为0.92. 在入射光子能量增大至30 keV的过程中, CK跃迁过程逐渐增强, κ值逐渐减小. 由于L₁, L₂支壳层产生的特征X射线为各向同性发射, 那么CK跃迁的发生, 将会改变L₃支壳层产生X射线的定向度A₂₀. 本实验选用的光源中心能量为13.1 keV, 最大能量为30 keV. 当中心能量为13.1 keV的光子入射时, 不会在目标靶材中产生CK跃迁过程. 当能量为13.8—30 keV之间的光子入射时, 将会在目标靶材中产生越来越强的CK跃迁过程. 但是X射线管发射的13.8—30 keV之间的轫致辐射谱强度, 随着出射能量的增大而减小. 13.8—14.4 keV之间的光子数约占有效入射光子数的5%, 14.4—20 keV之间的光子数约占有效入射光子数的45%, 20—30 keV之间的X射线强度几乎为零, 所以总的来说本实验中CK跃迁过程较弱.

表 2 不同入射能量下L支壳层电离截面^[26]及CK跃迁矫正因子κ值

Table 2. Ionization cross-sections (in barn) for L subshells^[26] and CK correction factor κ at different energies.

E/keV	σ_L₁	σ_L₂	σ_L₃	κ
1.9	0	0	0	0
12	0	0	3.5629 × 10⁴	1
13.76	0	0	2.4493 × 10⁴	1
13.8	0	1.5567 × 10⁴	2.3987 × 10⁴	0.92
14.3	0	1.4574 × 10⁴	2.2035 × 10⁴	0.91
14.4	7.8361 × 10³	1.4237 × 10³	2.1575 × 10⁴	0.80
15	7.4098 × 10³	1.2777 × 10⁴	1.9496 × 10⁴	0.75
20	4.4219 × 10³	6.1227 × 10³	8.5173 × 10³	0.7
30	1.993 × 10³	1.9923 × 10³	2.5531 × 10³	0.62

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特征X射线L_ι的定向度β, 由图3中L_ι/L_γ₁曲线的斜率可知为0.25. 考虑到特征X射线L_ι的动力学因子α值为0.5, 由β = ακA₂₀可得L₃支壳层的定向度A₂₀的值为0.577 ± 0.08.

4. 结　论

本文用X射线探测器在130°—170°范围内以10°为间隔, 测量了中心能量为13.1 keV的轫致辐射入射Au靶时, 所产生特征X射线L_ι, L_α, L_β和L_γ₁的光谱. 基于特征X射线L_ι与L_γ₁的强度比的角分布结果, 分析了L₃支壳层空穴态的定向性行为. 实验结果表明: L₃支壳层发射的特征X射线L_ι, L_α表现出明显的各向异性发射. 同时, 空穴从较低的L支壳层向较高的支壳层转移, 这一CK跃迁过程对角动量量子数J > 1/2时的空穴态的定向行为发生改变. 并由实验结果计算出L₃支壳层的定向度A₂₀的值为0.557 ± 0.081.

本实验结果与文献[8—14]的实验或理论结果一致, 然而却与文献[15—20]的结果不同, 他们认为电离过程中L系谱线均为各向同性发射. 所以在将来, 很有必要在原有的实验基础上, 开展更多的电子、光子、离子入射靶材的实验, 进一步研究L壳层产生空穴态的定向分布问题.

References

[1]	杨蒙生, 易泰民, 郑凤成, 唐永建, 张林, 杜凯, 李宁, 赵利平, 柯博, 邢丕峰 2018 物理学报 67 027301 Google Scholar Yang M S, Yi T M, Zheng F C, Tang Y J, Zhang L, Du K, Li N, Zhao L P, Ke B, Xing P F 2018 Acta Phys. Sin. 67 027301 Google Scholar
[2]	曾雄辉, 赵广军, 徐军 2004 物理学报 53 1935 Google Scholar Zeng X H, Zhao G J, Xu J 2004 Acta Phys. Sin. 53 1935 Google Scholar
[3]	Nishimura F, Kim J, Yonezawa S, Takashima M 2014 J. Flu. Chem. 160 52 Google Scholar
[4]	戚俊成, 刘宾, 陈荣昌, 夏正德, 肖体乔 2019 物理学报 68 024202 Google Scholar Qi J C, Liu B, Chen R C, Xia Z D, Xiao T Q 2019 Acta Phys. Sin. 68 024202 Google Scholar
[5]	王琛, 安红海, 方智恒, 熊俊, 王伟, 孙今人 2018 物理学报 67 015203 Google Scholar Wang C, An H H, Fang Z H, Xiong J, Wang W, Sun J R 2018 Acta Phys. Sin. 67 015203 Google Scholar
[6]	张天奎, 于明海, 董克攻, 吴玉迟, 杨靖, 陈佳, 卢峰, 李纲, 朱斌, 谭放, 王少义, 闫永宏, 谷渝秋 2017 物理学报 66 245201 Google Scholar Zhang T K, Yu M H, Dong K G, Wu Y C, Yang J, Chen J, Lu F, Li G, Zhu B, Tan F, Wang S Y, Yan Y H, Gu Y Q 2017 Acta Phys. Sin. 66 245201 Google Scholar
[7]	Flügge S, Mehlhorn M, Schmidt V 1972 Phys. Rev. Lett. 29 7 Google Scholar
[8]	Berezhko E G, Kabachnik N M, Rostovsky V S 1978 J. Phys. B: At. Mol. Phys. 11 1749 Google Scholar
[9]	Raza H S, Kim H J, Ha J M, Cho S O 2013 Appl. Radiat. Isot. 80 67 Google Scholar
[10]	Bansal H, Kaur G, Tiwari M K, Mittal R 2016 Eur. Phys. J. D 70 84 Google Scholar
[11]	Salem S, Stöhlker T, Brauning-Demian A, Hagmann S, Kozhuharov C, Liesen D 2013 Phys. Rev. A 88 012701 Google Scholar
[12]	Özdemir Y, Durak R, Kacal M R, Kurudirek M 2011 Appl. Radiat. Isot. 69 991 Google Scholar
[13]	Han I, Demir L 2011 J. X-Ray Sci. Technol. 19 13 Google Scholar
[14]	Demir L, Şahin M, Söğűt Ö, Şahin Y 2000 Radiat. Phys. Chem. 59 355 Google Scholar
[15]	Cooper J, Zare N 1969 Atomic Collision Processes (New York: Gordon & Breach) pp317−337
[16]	Kumar A, Agnihotri A N, Chatterjee S, Kasthurirangan S, Misra D, Choudhury R K, Sarkadi L, Tribedi L C 2010 Phys. Rev. A 81 062709 Google Scholar
[17]	Alrakabi M, Kumar S, Sharma V, Singh G, Mehta D 2013 Eur. Phys. J. D 67 99 Google Scholar
[18]	Tartari A, Baraldi C, Casnati E, Da Re A, Jorge E F, Taioli S 2003 J. Phys. B 36 843 Google Scholar
[19]	Kumar A, Puri S, MehtaD, Garg M L, Singh N 1999 J. Phys. B: At. Mol. Opt. Phys. 32 3701 Google Scholar
[20]	Kumar A, Puri S, Shahi J S, Garg M L, Mehta D, Singh N 2001 J. Phys. B: At. Mol. Opt. Phys. 34 613 Google Scholar
[21]	Gonzales D, Requena S, Williams S 2012 Appl. Radiat. Isot. 70 301 Google Scholar
[22]	Berezhko E G, Kabachnik N M 1977 J. Phys. B: At. Mol. Opt. Phys. 10 2467 Google Scholar
[23]	Yalçın P, Porikli S, Kurucu Y, Şahin Y 2008 Phys. Lett. B 663 186 Google Scholar
[24]	Storm L, Israel H I 1970 At. Data Nucl. Data Tables 7 565 Google Scholar
[25]	Bambynek W, Crasemann B, Fink R W, Freund H U, Mark H, Swift C D, Price R E, Rao P V 1972 Rev. Mod. Phys. 44 716 Google Scholar
[26]	Scofield J H 1973 Theoretical Photoionization Cross-sections from 1 to 1500 keV (Livermore, CA: Lawrence Livermore Laboratory) Report No. UCRL-51326

图 1 实验装置示意图

Figure 1. Experimental setup.

DownLoad: Full-Size Img PowerPoint

图 2 探测角度为140°时、中心能量为13.1 keV轫致辐射入射Au靶产生L系特征X射线能谱图

Figure 2. Fitted L X-ray spectrum of Au induced by impact with bremsstrahlung with central energy of 13.1 keV and measured at the emission angle of 140°.

DownLoad: Full-Size Img PowerPoint

图 3 Au 靶特征X射线强度比I(L_α)/I(L_γ₁)和I(L_ι)/I(L_γ₁)与P₂(cosθ)的关系

Figure 3. Intensity ratios of I(L_α)/I(L_γ₁) and I(L_ι)/I(L_γ₁) as a function of P₂(cosθ) for Au.

DownLoad: Full-Size Img PowerPoint

表 1 Au元素的L支壳层CK跃迁概率f_ij数据^[25]

Table 1. L-subshell CK yields f_ij for Au^[25].

f₁₂	f₁₃	f₂₃
0.083	0.644	0.132

DownLoad: CSV

表 2 不同入射能量下L支壳层电离截面^[26]及CK跃迁矫正因子κ值

Table 2. Ionization cross-sections (in barn) for L subshells^[26] and CK correction factor κ at different energies.

E/keV	σ_L₁	σ_L₂	σ_L₃	κ
1.9	0	0	0	0
12	0	0	3.5629 × 10⁴	1
13.76	0	0	2.4493 × 10⁴	1
13.8	0	1.5567 × 10⁴	2.3987 × 10⁴	0.92
14.3	0	1.4574 × 10⁴	2.2035 × 10⁴	0.91
14.4	7.8361 × 10³	1.4237 × 10³	2.1575 × 10⁴	0.80
15	7.4098 × 10³	1.2777 × 10⁴	1.9496 × 10⁴	0.75
20	4.4219 × 10³	6.1227 × 10³	8.5173 × 10³	0.7
30	1.993 × 10³	1.9923 × 10³	2.5531 × 10³	0.62

DownLoad: CSV

[1]	杨蒙生, 易泰民, 郑凤成, 唐永建, 张林, 杜凯, 李宁, 赵利平, 柯博, 邢丕峰 2018 物理学报 67 027301 Google Scholar Yang M S, Yi T M, Zheng F C, Tang Y J, Zhang L, Du K, Li N, Zhao L P, Ke B, Xing P F 2018 Acta Phys. Sin. 67 027301 Google Scholar
[2]	曾雄辉, 赵广军, 徐军 2004 物理学报 53 1935 Google Scholar Zeng X H, Zhao G J, Xu J 2004 Acta Phys. Sin. 53 1935 Google Scholar
[3]	Nishimura F, Kim J, Yonezawa S, Takashima M 2014 J. Flu. Chem. 160 52 Google Scholar
[4]	戚俊成, 刘宾, 陈荣昌, 夏正德, 肖体乔 2019 物理学报 68 024202 Google Scholar Qi J C, Liu B, Chen R C, Xia Z D, Xiao T Q 2019 Acta Phys. Sin. 68 024202 Google Scholar
[5]	王琛, 安红海, 方智恒, 熊俊, 王伟, 孙今人 2018 物理学报 67 015203 Google Scholar Wang C, An H H, Fang Z H, Xiong J, Wang W, Sun J R 2018 Acta Phys. Sin. 67 015203 Google Scholar
[6]	张天奎, 于明海, 董克攻, 吴玉迟, 杨靖, 陈佳, 卢峰, 李纲, 朱斌, 谭放, 王少义, 闫永宏, 谷渝秋 2017 物理学报 66 245201 Google Scholar Zhang T K, Yu M H, Dong K G, Wu Y C, Yang J, Chen J, Lu F, Li G, Zhu B, Tan F, Wang S Y, Yan Y H, Gu Y Q 2017 Acta Phys. Sin. 66 245201 Google Scholar
[7]	Flügge S, Mehlhorn M, Schmidt V 1972 Phys. Rev. Lett. 29 7 Google Scholar
[8]	Berezhko E G, Kabachnik N M, Rostovsky V S 1978 J. Phys. B: At. Mol. Phys. 11 1749 Google Scholar
[9]	Raza H S, Kim H J, Ha J M, Cho S O 2013 Appl. Radiat. Isot. 80 67 Google Scholar
[10]	Bansal H, Kaur G, Tiwari M K, Mittal R 2016 Eur. Phys. J. D 70 84 Google Scholar
[11]	Salem S, Stöhlker T, Brauning-Demian A, Hagmann S, Kozhuharov C, Liesen D 2013 Phys. Rev. A 88 012701 Google Scholar
[12]	Özdemir Y, Durak R, Kacal M R, Kurudirek M 2011 Appl. Radiat. Isot. 69 991 Google Scholar
[13]	Han I, Demir L 2011 J. X-Ray Sci. Technol. 19 13 Google Scholar
[14]	Demir L, Şahin M, Söğűt Ö, Şahin Y 2000 Radiat. Phys. Chem. 59 355 Google Scholar
[15]	Cooper J, Zare N 1969 Atomic Collision Processes (New York: Gordon & Breach) pp317−337
[16]	Kumar A, Agnihotri A N, Chatterjee S, Kasthurirangan S, Misra D, Choudhury R K, Sarkadi L, Tribedi L C 2010 Phys. Rev. A 81 062709 Google Scholar
[17]	Alrakabi M, Kumar S, Sharma V, Singh G, Mehta D 2013 Eur. Phys. J. D 67 99 Google Scholar
[18]	Tartari A, Baraldi C, Casnati E, Da Re A, Jorge E F, Taioli S 2003 J. Phys. B 36 843 Google Scholar
[19]	Kumar A, Puri S, MehtaD, Garg M L, Singh N 1999 J. Phys. B: At. Mol. Opt. Phys. 32 3701 Google Scholar
[20]	Kumar A, Puri S, Shahi J S, Garg M L, Mehta D, Singh N 2001 J. Phys. B: At. Mol. Opt. Phys. 34 613 Google Scholar
[21]	Gonzales D, Requena S, Williams S 2012 Appl. Radiat. Isot. 70 301 Google Scholar
[22]	Berezhko E G, Kabachnik N M 1977 J. Phys. B: At. Mol. Opt. Phys. 10 2467 Google Scholar
[23]	Yalçın P, Porikli S, Kurucu Y, Şahin Y 2008 Phys. Lett. B 663 186 Google Scholar
[24]	Storm L, Israel H I 1970 At. Data Nucl. Data Tables 7 565 Google Scholar
[25]	Bambynek W, Crasemann B, Fink R W, Freund H U, Mark H, Swift C D, Price R E, Rao P V 1972 Rev. Mod. Phys. 44 716 Google Scholar
[26]	Scofield J H 1973 Theoretical Photoionization Cross-sections from 1 to 1500 keV (Livermore, CA: Lawrence Livermore Laboratory) Report No. UCRL-51326

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