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在天体物理和惯性约束聚变研究中涉及到的温稠密物质通常包含多种元素的混合, 并且每种元素还被电离成多种离子价态, 不同价态离子结构及其丰度将直接影响温稠密物质的诊断及其物理性质. 同时, 从电子结构计算出发来研究宏观物理性质时, 还需要考虑温度、密度效应对离子结构的影响. 本文从不同价态离子的电子结构计算出发, 采用考虑了离子间相互作用的Saha方程获得了稠密环境下的离子丰度, 并使用超网链(hypernetted-chain)近似对铝、金以及碳-氢混合物的径向分布函数进行了计算, 结合离子周围电子的密度分布, 最后获得X-射线汤姆逊散射的弹性散射谱. 在X-射线散射谱计算中, 计算了温稠密物质中同时存在不同离子价态时的电子结构和径向分布函数, 发现在相同的等离子体环境下不同价态离子的径向分布函数和电子结构差别较大. 这将对依赖于微观统计过程的物理性质, 比如散射光谱, 将产生较大的影响.The study of warm dense matter is very important for the evolution of celestial bodies and inertial confinement fusion, which often contains a mixture of multiple elements and different charge-state ions. The ionic structure and distribution of different charge-states directly affect the diagnosis and physical properties of warm dense matter. At the same time, the influence of high-temperature dense plasma on the ionic structure should be considered when we study the physical properties from the first-principle calculation of electron structure. In the present work, the radial distribution functions of multiple charge-state ions (gold, carbon-hydrogen mixture, and aluminum) are developed in the hypernetted-chain approximation, and elastic x-ray scattering of different charge-state ions are calculated in the warm dense matter regime. Firstly, the electron structure of different charge-state ions is self-consistently computed in the ionic sphere, in which the ion-sphere radii are determined by the plasma density and their charges. And then the ionic fraction is obtained by solving the modified Saha equation, with the interactions among different charge-state ions taken into account, and ion-ion pair potentials are obtained by Yukawa model. Finally, the ion features of x-ray elastic scattering for Al are calculated on the basis of electronic distribution around the nuclei and ionic radial distribution function. By comparing the results of different charge-sate ions with the result of mean charge-sate ion, it is shown that different statistical methods can affect the physical properties which are dependent on the electronic and ionic structure.
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Keywords:
- warm dense matter /
- radial distribution function /
- hypernetted-chain approximation /
- elastic scattering
[1] Clérouin J, Arnault P, Gréa B J, Guisset S, Vandenboomgaerde M, White A J, Collins L A, Kress J D, Ticknor C 2020 Phys. Rev. E 101 033207
Google Scholar
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Google Scholar
[3] Hou Y, Bredow R, Yuan J M, Redmer R 2015 Phys. Rev. E 91 033114
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Google Scholar
[5] 马桂存, 张其黎, 宋红州, 李琼, 朱希睿, 孟续军 2017 物理学报 66 036401
Google Scholar
Ma G C, Zhang Q L, Song H Z, Li Q, Zhu X R, Meng X J 2017 Acta Phys. Sin. 66 036401
Google Scholar
[6] Dai J Y, Hou Y, Yuan J M 2010 Phys. Rev. Lett. 104 245001
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Google Scholar
[8] Kuhne T D, Krack M, Mohamed F R, Parrinello M 2007 Phys. Rev. Lett. 98 066401
Google Scholar
[9] 汤文辉, 徐彬彬, 冉宪文, 徐志宏 2017 物理学报 66 030505
Google Scholar
Tang W H, Xu B B, Ran X W, Xu Z H 2017 Acta Phys. Sin. 66 030505
Google Scholar
[10] Zérah G, Clérouin J, Pollock E L 1992 Phys. Rev. Lett. 69 446
Google Scholar
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Google Scholar
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Google Scholar
Wang T H, Wang K, Zhang Y, Jiang L C 2020 Acta Phys. Sin. 69 099101
Google Scholar
[17] Brush S G, Sahlin H L, Teller E 1966 J. Chem. Phys. 45 2102
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[18] Deutsch C 1977 Phys. Lett. A 60 317
Google Scholar
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[20] Kelbg G 1964 Ann. Phys. 13 354
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Google Scholar
[22] Wünsch K, Vorberger J, Gregorz G, Gericke D O 2011 EPL 94 25001
Google Scholar
[23] Iglesias C A 2018 High Energy Density Phys. 26 81
Google Scholar
[24] Rüter H R, Redmer R 2014 Phys. Rev. Lett. 112 145007
Google Scholar
[25] Souza A N, Perkins D J, Starrett C E, Saumon D, Hansen S B 2014 Phys. Rev. E 89 023108
Google Scholar
[26] Ma T, Döppner T, Falcone R W, Fletcher L, Fortmann C, Gericke D O, Landen O L, Lee H J, Pak A, Vorberger J, Wünsch K, Glenzer S H 2013 Phys. Rev. Lett. 110 065001
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Google Scholar
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Google Scholar
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图 1 在温度为104 K、离子数密度为1024 cm–3时, Au1+和Au2+混合离子价态的径向分布函数. Present表示本文工作的计算结果(实线); HNC表示文献[2]中采用HNC近似计算的结果(虚线 + 上三角); OCP表示平均成一种价态离子的径向分布函数; average表示各价离子的径向分布函数的算数平均
Fig. 1. The radial distribution function of Au1+, Au2+ in gold plasma with ion number density of 1024 cm–3 and temperature of 104 K. Present represents the result of the present paper (solid line); HNC represents the result of HNC approximation in the Ref. [2] (dotted line + upper triangle); OCP is the radial distribution function of mean charge-state ion; average labels the average results of the radial distribution function of different charge-state ions.
图 2 在离子数密度为nH = nC = 2.5 × 1023 cm–3、温度为T = 2 × 104 K时, 碳-氢混合等离子体中C4+和H+的径向分布函数; Present是本文计算结果(实线), HNC是文献[2]中用HNC近似的计算结果(虚线 + 上三角)
Fig. 2. The radial distribution function of C4+ and H+ in the CH mixture plasma at number density, nH = nC = 2.5 × 1023 cm–3, and the temperature, T = 2 × 104 K. And solid lines label the present results; and dashed lines with upper triangles are the results of Ref. [2].
图 3 在密度为8.1 g/cm3、不同温度下温稠密铝中, 采用多组分HNC近似给出不同价态离子(虚线)的径向分布与AAHNC模型(实线)计算结果的比较
Fig. 3. Different ion species pair distribution functions (dashed lines) of Al at density, 8.1 g/cm3, and different temperatures calculated by HNC approximation, comparing with that of AAHNC model (orange solid lines).
图 4 密度为8.1 g/cm3、不同温度下温稠密铝等离子体中, 不同价态离子(虚线)、AAHNC模型计算(实线)的形状结构因子随着散射角度的变化.
Fig. 4. Form factor of different ion species (dashed lines) of Al at density, 8.1 g/cm3, and different temperatures, comparing with that of AAHNC (orange solid lines).
图 5 在密度为8.1 g/cm3、温度10 eV下温稠密铝等离子体中, 离子结构随不同散射角的变化关系. Multi-ion表示本文使用的方法给出的计算结果(虚线); AAHNC表示AAHNC模型的计算结果(实线)[3]; QMD表示量子分子动力学计算结果(点-虚线)[24]; HNC表示文献[25]中采用HNC近似计算离子结构的结果(点线); 带有误差范围的点表示实验结果[26]
Fig. 5. Ion feature for Al as function of k at a temperature of 10 eV and a density of 8.1 g/cm3: Multi-ion (dashed line), AAHNC (solid line)[3], QMD (dot-dashed line)[24], HNC (dot line)[25] and experimental data (points with error bars)[26].
表 1 在密度为8.1 g/cm3、不同温度下温稠密铝的离子丰度, A表示平均电离度
Table 1. Charge-state fractions of Al at density, 8.1 g/cm3, A is average charge state.
100 eV价态 A = 7.196丰度 40 eV价态 A = 4.28丰度 20 eV价态 A = 3.27丰度 10 eV价态 A = 3.007丰度 4 0.016 2 0.001 2 0.003 2 0.001 5 0.081 3 0.175 3 0.735 3 0.991 6 0.212 4 0.438 4 0.251 4 0.008 7 0.247 5 0.315 5 0.011 8 0.290 6 0.067 9 0.132 7 0.004 10 0.021 
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[1] Clérouin J, Arnault P, Gréa B J, Guisset S, Vandenboomgaerde M, White A J, Collins L A, Kress J D, Ticknor C 2020 Phys. Rev. E 101 033207
Google Scholar
[2] Wünsch K, Hilse P, Schlanges M, Gericke D.O 2008 Phys. Rev. E 77 056404
Google Scholar
[3] Hou Y, Bredow R, Yuan J M, Redmer R 2015 Phys. Rev. E 91 033114
[4] Daligault J, Baalrud S D, Starrett C E, SaumonD, Sjostrom T 2016 Phys. Rev. Lett. 116 075002
Google Scholar
[5] 马桂存, 张其黎, 宋红州, 李琼, 朱希睿, 孟续军 2017 物理学报 66 036401
Google Scholar
Ma G C, Zhang Q L, Song H Z, Li Q, Zhu X R, Meng X J 2017 Acta Phys. Sin. 66 036401
Google Scholar
[6] Dai J Y, Hou Y, Yuan J M 2010 Phys. Rev. Lett. 104 245001
[7] Desjarlais M P 2003 Phys. Rev. B 68 064204
Google Scholar
[8] Kuhne T D, Krack M, Mohamed F R, Parrinello M 2007 Phys. Rev. Lett. 98 066401
Google Scholar
[9] 汤文辉, 徐彬彬, 冉宪文, 徐志宏 2017 物理学报 66 030505
Google Scholar
Tang W H, Xu B B, Ran X W, Xu Z H 2017 Acta Phys. Sin. 66 030505
Google Scholar
[10] Zérah G, Clérouin J, Pollock E L 1992 Phys. Rev. Lett. 69 446
Google Scholar
[11] Fu Y S, Hou Y, Kang D D, Gao C, Jin F T, Yuan J M 2018 Phys. Plasmas 25 012701
Google Scholar
[12] Bredow R, Bornath T, Kraeft W D, Redmer R 2013 Contrib. Plasma Phys. 53 276
Google Scholar
[13] Salzmann D 1998 Atomic Physics in Hot Plasmas (Oxford : Oxford University Press) pp54−55
[14] Tanaka S 2016 J. Chem. Phys. 145 214104
Google Scholar
[15] Gu M F 2008 Can. J. Phys 86 675
[16] 王天浩, 王坤, 张阅, 姜林村 2020 物理学报 69 099101
Google Scholar
Wang T H, Wang K, Zhang Y, Jiang L C 2020 Acta Phys. Sin. 69 099101
Google Scholar
[17] Brush S G, Sahlin H L, Teller E 1966 J. Chem. Phys. 45 2102
Google Scholar
[18] Deutsch C 1977 Phys. Lett. A 60 317
Google Scholar
[19] Schwarz V, Bornath T, Kraeft W D, Glenzer S H, Höll A, Redmer R 2007 Contrib. Plasma Phys. 47 324
Google Scholar
[20] Kelbg G 1964 Ann. Phys. 13 354
[21] Chihara J 2000 J. Phys. Condens. Matter 12 231
Google Scholar
[22] Wünsch K, Vorberger J, Gregorz G, Gericke D O 2011 EPL 94 25001
Google Scholar
[23] Iglesias C A 2018 High Energy Density Phys. 26 81
Google Scholar
[24] Rüter H R, Redmer R 2014 Phys. Rev. Lett. 112 145007
Google Scholar
[25] Souza A N, Perkins D J, Starrett C E, Saumon D, Hansen S B 2014 Phys. Rev. E 89 023108
Google Scholar
[26] Ma T, Döppner T, Falcone R W, Fletcher L, Fortmann C, Gericke D O, Landen O L, Lee H J, Pak A, Vorberger J, Wünsch K, Glenzer S H 2013 Phys. Rev. Lett. 110 065001
Google Scholar
[27] Clérouin J, Robert G, Arnault P 2015 Phys. Rev. E 91 011101(R
Google Scholar
[28] Hou Y, Fu Y S, Bredow R, Kang D D, Redmer R, Yuan J M 2017 High Energy Density Phys. 22 21
Google Scholar
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