等离子体屏蔽效应对Ar<sup>16+</sup>基态和激发态能级的影响

马堃; 陈展斌; 黄时中

doi:10.7498/aps.68.20181915

摘要

基于Rayleigh-Ritz变分原理, 发展了一套处理弱耦合等离子体环境中多电子原子(离子)非相对论能量及其相对论修正的解析方法. 通过考虑电子间交换相互作用以及内外壳层电子的屏蔽效应, 计算了Ar¹⁶⁺基态1s² ¹S、单激发态1sns ^1,3S (n = 2—5), 1snp ^1,3P (n = 2—5) 和双激发态2snp ¹P (n = 2—5)非相对论能量及其相对论修正值(包括质量修正、单体和双体达尔文修正以及自旋-自旋接触相互作用项), 讨论了等离子体屏蔽效应对能级的影响. 结果表明: 相对论质量修正和第一类达尔文修正占主导, 比其他相对论修正项高出三个数量级. 此外, 等离子体屏蔽效应具有明显的态选择性, 屏蔽效应对外壳层电子的影响大于内壳层电子, 随着等离子体屏蔽参数的增加, 外壳层电子轨道向外延展, 激发态越高, 延展程度越大.

关键词:

等离子体 /
能级 /
相对论修正

Abstract

A systematical knowledge of the atomic properties in plasma is of great interest for various research areas, such as the explanation of the X-ray radiation from universe, plasma diagnostics, extreme ultraviolet (EUV) and X-ray sources and so on. Among these researches, the detailed information about how the plasma influences the atomic energy level and transition spectrum are crucial for understanding the X-ray emission mechanism and the state of plasma. An analytic calculation method of treating the non-relativistic energy and its relativistic corrections for the multi-electron atoms embedded in weakly coupled plasma is developed based on the Rayleigh-Ritz variation method. The systematical investigations are performed for the ground state 1s² ¹S, single excited states 1sns ^1,2S (n = 2−5), 1snp ^1,3P (n = 2−5) and double excited state 2s2p ¹P of Ar¹⁶⁺ ion in weak coupled plasma. The analytic formulas for calculating the non-relativistic energy and its relativistic correction energy are derived, which include mass correction, one and two-body Darwin correction, spin-spin contact interaction and orbit-orbit interaction. All the angular integration spin sums involved in the problem are worked out explicitly by using the irreducible theory. The influence of plasma on non-relativistic energy and relativistic correction energy are discussed. The results show that the mass correction and the one-body Darwin correction are the main ones among the terms of relativistic correction, and are three orders of magnitude greater than the other relativistic terms. The plasma shielding effect mainly affects the non-relativistic energy, and has little effect on the relativistic correction. At the same time, it has a more significant selectivity for the electronic configuration. Further research shows that the influence of plasma on the energy of the outer shell electron is greater than that of the inner shell electron. With the increase of the plasma shielding parameters, the outer shell electron extends outward, and the higher the excited state, the greater the degree of extension is. This work should be useful for astrophysical applications where such a plasma environment exists.

Keywords:

作者及机构信息

1.
黄山学院信息工程学院, 黄山　245041

2.
湖南工业大学理学院, 株洲　412007

3.
安徽师范大学物理与电子信息学院, 芜湖　241000

通信作者: 马堃, makun@hsu.edu.cn

基金项目: 国家自然科学基金(批准号: 11804112, 11504421)、安徽省自然科学基金(批准号: 1808085QA22)、安徽省高校优秀青年人才支持计划重点项目(批准号: gxyqZD2016301)和安徽省高校自然科学研究项目(批准号: KJHS2015B01)资助的课题.

Authors and contacts

1.
School of Information Engineering, Huangshan University, Huangshan 245041, China

2.
School of Science, Hunan University of Technology, Zhuzhou 412007, China

3.
College of Physics and Electrical Information, Anhui Normal University, Wuhu 241000, China

Corresponding author: Ma Kun, makun@hsu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11804112, 11504421), the Natural Science Foundation of Anhui Province, China (Grant No. 1808085QA22), the Key Project for Young Talents in College of Anhui Province, China (Grant No. gxyqZD2016301), and the Natural Science Foundation of the Higher Education Institutions of Anhui Province, China (Grant No. KJHS2015B01).

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参考文献

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施引文献

图 1 A¹⁶⁺ 1s² ¹S, 1s2s ^1,3S, 1s2p ^1,3P和2s2p ¹P 的相对论修正能量随参数u的变化

Fig. 1. Relativistic corrections against parameter u for 1s² ¹S, 1s2s ^1,3S, 1s2p ^1,3P and 2s2p ¹P of Ar¹⁶⁺.

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图 2 等离子能级偏移与参数u之间的关系

Fig. 2. Plasma energy shifts against parameter u.

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图 3 内外壳层电子径向波函数模方

Fig. 3. Module of radial wave functions for inner and outer shell electron.

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表 1 相对论修正对C⁴⁺基态1s² ¹S能级的影响(单位: a.u.)

Table 1. Effects of relativistic correction on ground state 1s² ¹S energies level in C⁴⁺ (unit: a.u.).

u	${\alpha _{1{\rm{s}}}}$	E_NR	E_MC	E_D1	ΔE_RS	E_T	Ref.[20]	Ref.[25,26]
0	5.6875	−32.3477	−0.0696508	0.0587822	−0.01087	−32.35857	−32.4176	−32.3612
0.1	5.68614	−31.1633	−0.0695843	0.0587401	−0.01084	−31.17414	−31.2324	−31.177
0.2	5.68218	−30.0095	−0.0693905	0.0586174	−0.01077	−30.02027	−30.079	−30.0237
0.3	5.67577	−28.8854	−0.0690781	0.0584193	−0.01066	−28.89606	−28.9557	—
0.4	5.66706	−27.7899	−0.0686549	0.0581507	−0.01050	−27.80040	−27.8614	—
0.5	5.65616	−26.7223	−0.0681282	0.0578158	−0.01031	−26.73261	−26.7963	−26.7395
0.6	5.64318	−25.6817	−0.067505	0.0574187	−0.01009	−25.69179	−25.7576	—
0.7	5.62821	−24.6674	−0.0667916	0.0569630	−0.00983	−24.67723	−24.7457	—
0.8	5.61134	−23.6788	−0.0659942	0.0564522	−0.00954	−23.68834	−23.7006	−23.7594
0.9	5.59263	−22.7151	−0.0651186	0.0558895	−0.00923	−22.72433	−22.7986	—
1.0	5.57215	−21.7758	−0.0641701	0.0552778	−0.00889	−21.78469	−21.8629	—

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表 2 Ar¹⁶⁺ 1sns, 1snp和2s2p组态变分参数

Table 2. Variation parameters of 1sns, 1snp and 2snp configurations in Ar¹⁶⁺.

2S+1	n	1sns ^2S+1S			1snp ^2S+1P			2snp ^2S+1P
2S+1	n	${\alpha _{1{\rm{s}}}}$	${\alpha _{n{\rm{s}}}}$	E_NR	${\alpha _{1{\rm{s}}}}$	${\alpha _{n{\rm{p}}}}$	E_NR	${\alpha _{2{\rm{s}}}}$	${\alpha _{n{\rm{p}}}}$	E_NR
1	1	17.6875	—	−312.848	—	—	—	—	—	—
	2	17.9324	17.3433	−198.384	18.0107	16.9176	−197.969	17.4113	17.8229	−77.601
	3	17.9815	17.2194	−178.14	18.0008	16.9725	−178.018	17.9428	17.2934	−56.8575
	4	17.9924	17.1623	−171.068	18.0001	16.9852	−171.017	17.9766	17.2143	−49.655
	5	17.9961	17.129	−167.799	18	16.9901	−167.773	17.9882	17.1692	−46.3425
3	2	18.0137	17.1931	−199.196	17.9577	17.266	−198.504	—	—	—
	3	18.0031	17.1286	−178.355	17.99	17.1509	−178.162	—	—	—
	4	18.0012	17.0962	−171.155	17.9961	17.1079	−171.076	—	—	—
	5	18.0006	17.0768	−167.843	17.9981	17.0845	−167.803	—	—	—

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表 3 Ar¹⁶⁺基态1s² ¹S相对论性能量(单位: a.u.)

Table 3. Relativistic correction on ground state 1s² ¹S energies level in Ar¹⁶⁺ (unit: a.u.).

u	${\alpha _{1{\rm{s}}}}$	E_NR	E_MC	E_D1	ΔE_RS	E_T
0	17.6875	−312.848	−6.51488	5.30399	−1.21089	−314.05889
0.1	17.6871	−309.263	−6.51425	5.30360	−1.21065	−310.47365
0.2	17.6858	−305.708	−6.51238	5.30246	−1.20992	−306.91792
0.3	17.6837	−302.184	−6.50929	5.30057	−1.20872	−303.39272
0.4	17.6808	−298.688	−6.50501	5.29796	−1.20705	−299.89505
0.5	17.6771	−295.222	−6.49957	5.29463	−1.20494	−296.42694
0.6	17.6726	−291.785	−6.49299	5.29061	−1.20238	−292.98738
0.7	17.6674	−288.377	−6.48530	5.28591	−1.19939	−289.57639
0.8	17.6614	−284.997	−6.47652	5.28055	−1.19597	−286.19297
0.9	17.6547	−281.645	−6.46668	5.27453	−1.19215	−282.83715
1.0	17.6473	−278.32	−6.45580	5.26787	−1.18793	−279.50793

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表 8 Ar¹⁶⁺基态2s2p ¹P相对论性能量(单位: a.u.)

Table 8. Relativistic correction on excited state 2s2p ¹P energies level in Ar¹⁶⁺ (unit: a.u.).

u	${\alpha _{2{\rm{s}}}}$	${\alpha _{2{\rm{p}}}}$	E_NR	E_MC	E_D1	E_D2	E_SSC	E_OO	ΔE_RS	E_T
0	17.4113	17.8229	−77.6010	−0.59499	0.31621	−8.39310 × 10⁻⁴	1.67862 × 10⁻³	−0.0006009	−0.27854	−77.87954
0.1	17.4043	17.8174	−74.0566	−0.59406	0.31583	−8.38360 × 10⁻⁴	1.67672 × 10⁻³	−6.00393 × 10⁻⁴	−0.27800	−74.33460
0.2	17.3839	17.8014	−70.6207	−0.59139	0.31472	−8.35602 × 10⁻⁴	1.67120 × 10⁻³	−5.98927 × 10⁻⁴	−0.27644	−70.89714
0.3	17.351	17.7755	−67.2898	−0.58711	0.31294	−8.31163 × 10⁻⁴	1.66233 × 10⁻³	−5.96551 × 10⁻⁴	−0.27393	−67.56373
0.4	17.3064	17.7402	−64.0605	−0.58132	0.31053	−8.25157 × 10⁻⁴	1.65031 × 10⁻³	−5.93313 × 10⁻⁴	−0.27055	−64.33105
0.5	17.2508	17.6959	−60.9298	−0.57415	0.30754	−8.17686 × 10⁻⁴	1.63537 × 10⁻³	−5.89259 × 10⁻⁴	−0.26637	−61.19617
0.6	17.1845	17.6429	−57.8948	−0.56569	0.30401	−8.08845 × 10⁻⁴	1.61769 × 10⁻³	−5.84432 × 10⁻⁴	−0.26146	−58.15626
0.7	17.1081	17.5816	−54.9531	−0.55606	0.29998	−7.98720 × 10⁻⁴	1.59744 × 10⁻³	−5.78871 × 10⁻⁴	−0.25586	−55.20896
0.8	17.0219	17.5122	−52.1022	−0.54534	0.29546	−7.87391 × 10⁻⁴	1.57478 × 10⁻³	−5.72611 × 10⁻⁴	−0.24966	−52.35186
0.9	16.9262	17.4349	−49.3398	−0.53361	0.29051	−7.74933 × 10⁻⁴	1.54987 × 10⁻³	−5.65688 × 10⁻⁴	−0.24289	−49.58269
1.0	16.8213	17.3499	−46.6639	−0.52098	0.28514	−7.61414 × 10⁻⁴	1.52283 × 10⁻³	−5.58134 × 10⁻⁴	−0.23563	−46.89953

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表 4 Ar¹⁶⁺激发态1s2s ¹S相对论性能量(单位: a.u.)

Table 4. Relativistic correction on excited state 1s2s ¹S energies level in Ar¹⁶⁺ (unit: a.u.).

u	${\alpha _{1{\rm{s}}}}$	${\alpha _{2{\rm{s}}}}$	E_NR	E_MC	E_D1	E_D2	E_SSC	ΔE_RS	E_T
0	17.9324	17.3433	−198.384	−3.93094	3.07620	−7.249983 × 10⁻³	1.450003 × 10⁻²	−0.84749	−199.23149
0.1	17.9319	17.3364	−194.822	−3.92982	3.07562	−7.245793 × 10⁻³	1.44916 × 10⁻²	−0.84695	−195.66895
0.2	17.9306	17.3164	−191.335	−3.92657	3.07394	−7.233613 × 10⁻³	1.44672 × 10⁻²	−0.84540	−192.18040
0.3	17.9285	17.284	−187.921	−3.92130	3.07121	−7.213953 × 10⁻³	1.44279 × 10⁻²	−0.84288	−188.76388
0.4	17.9256	17.2401	−184.577	−3.91415	3.06749	−7.187233 × 10⁻³	1.43745 × 10⁻²	−0.83947	−185.41647
0.5	17.9218	17.1852	−181.301	−3.90522	3.06284	−7.153833 × 10⁻³	1.43077 × 10⁻²	−0.83523	−182.13623
0.6	17.9173	17.1198	−178.092	−3.89462	3.05729	−7.114063 × 10⁻³	1.42281 × 10⁻²	−0.83022	−178.92222
0.7	17.912	17.0445	−174.947	−3.88245	3.05090	−7.068203 × 10⁻³	1.41364 × 10⁻²	−0.82448	−175.77148
0.8	17.906	16.9594	−171.866	−3.86880	3.04371	−7.016463 × 10⁻³	1.40329 × 10⁻²	−0.81807	−172.68407
0.9	17.8992	16.865	−168.847	−3.85377	3.03575	−6.959053 × 10⁻³	1.39181 × 10⁻²	−0.81106	−169.65806
1.0	17.8918	16.7615	−165.889	−3.83745	3.02706	−6.896133 × 10⁻³	1.37923 × 10⁻²	−0.80349	−166.69249

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表 5 Ar¹⁶⁺激发态1s2s ³S相对论性能量(单位: a.u.)

Table 5. Relativistic correction on excited state 1s2s ³S energies level in Ar¹⁶⁺ (unit: a.u.).

u	${\alpha _{1{\rm{s}}}}$	${\alpha _{2{\rm{s}}}}$	E_NR	E_MC	E_D1	ΔE_RS	E_T
0	18.0137	17.1931	−199.196	−3.97703	3.10590	−0.87113	−200.06713
0.1	18.0133	17.1858	−195.635	−3.97594	3.10534	−0.87060	−196.50560
0.2	18.0122	17.1646	−192.149	−3.97276	3.10370	−0.86906	−193.01806
0.3	18.0104	17.1305	−188.735	−3.96761	3.10104	−0.86657	−189.60157
0.4	18.0078	17.0841	−185.392	−3.96062	3.09742	−0.86320	−186.25520
0.5	18.0046	17.0263	−182.119	−3.95189	3.09289	−0.85900	−182.97800
0.6	18.0006	16.9574	−178.912	−3.94152	3.08748	−0.85404	−179.76604
0.7	17.996	16.878	−175.77	−3.92962	3.08124	−0.84838	−176.61838
0.8	17.9907	16.7885	−172.692	−3.91627	3.07421	−0.84206	−173.53406
0.9	17.9847	16.6891	−169.676	−3.90156	3.06643	−0.83513	−170.51113
1.0	17.9781	16.5803	−166.721	−3.88557	3.05792	−0.82765	−167.54865

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表 6 Ar¹⁶⁺激发态1s2p ¹P相对论性能量(单位: a.u.)

Table 6. Relativistic correction on excited state 1s2p ¹P energies level in Ar¹⁶⁺ (unit: a.u.).

u	${\alpha _{1{\rm{s}}}}$	${\alpha _{2{\rm{p}}}}$	E_NR	E_MC	E_D1	E_D2	E_SSC	E_OO	ΔE_RS	E_T
0	18.0107	16.9176	−197.969	−3.58167	2.80005	−2.073823 × 10⁻³	4.147643 × 10⁻³	−0.0064010	−0.78595	−198.75495
0.1	18.0103	16.9115	−194.403	−3.58123	2.79986	−2.071283 × 10⁻³	4.142563 × 10⁻³	−6.394563 × 10⁻³	−0.78569	−195.18869
0.2	18.0091	16.8936	−190.903	−3.57994	2.79929	−2.063883 × 10⁻³	4.127763 × 10⁻³	−6.375753 × 10⁻³	−0.78496	−191.68796
0.3	18.007	16.8646	−187.467	−3.57782	2.79834	−2.051933 × 10⁻³	4.103873 × 10⁻³	−6.345353 × 10⁻³	−0.78377	−188.25077
0.4	18.0042	16.8251	−184.094	−3.57490	2.79703	−2.035733 × 10⁻³	4.071453 × 10⁻³	−6.304033 × 10⁻³	−0.78214	−184.87614
0.5	18.0007	16.7755	−180.783	−3.57121	2.79536	−2.015513 × 10⁻³	4.031023 × 10⁻³	−6.252373 × 10⁻³	−0.78009	−181.56309
0.6	17.9963	16.7162	−177.532	−3.56677	2.79335	−1.991533 × 10⁻³	3.983063 × 10⁻³	−6.190923 × 10⁻³	−0.77762	−178.30962
0.7	17.9913	16.6477	−174.339	−3.56161	2.79099	−1.963993 × 10⁻³	3.927983 × 10⁻³	−6.120133 × 10⁻³	−0.77478	−175.11378
0.8	17.9855	16.57	−171.203	−3.55574	2.78830	−1.933093 × 10⁻³	3.866193 × 10⁻³	−6.040453 × 10⁻³	−0.77155	−171.97455
0.9	17.979	16.4835	−168.124	−3.54919	2.78527	−1.899033 × 10⁻³	3.798063 × 10⁻³	−5.952253 × 10⁻³	−0.76797	−168.89197
1.0	17.9718	16.3883	−165.101	−3.54198	2.78193	−1.861983 × 10⁻³	3.723953 × 10⁻³	−5.855883 × 10⁻³	−0.76404	−165.86504

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表 7 Ar¹⁶⁺基态1s2p ³P相对论性能量(单位: a.u.)

Table 7. Relativistic correction on excited state 1s2p ³P energies level in Ar¹⁶⁺ (unit: a.u.).

u	${\alpha _{1{\rm{s}}}}$	${\alpha _{2{\rm{p}}}}$	E_NR	E_MC	E_D1	E_OO	ΔE_RS	E_T
0	17.9577	17.266	−198.504	−3.54736	2.77539	6.7643 × 10⁻³	−0.76521	−199.26921
0.1	17.9573	17.26	−194.937	−3.54694	2.77522	6.75783 × 10⁻³	−0.76496	−195.70196
0.2	17.9562	17.2424	−191.436	−3.54571	2.77469	6.738923 × 10⁻³	−0.76428	−192.20028
0.3	17.9543	17.2138	−187.998	−3.54369	2.77381	6.70833 × 10⁻³	−0.76317	−188.76117
0.4	17.9517	17.1749	−184.622	−3.54091	2.77260	6.66673 × 10⁻³	−0.76164	−185.38364
0.5	17.9483	17.1261	−181.306	−3.53739	2.77106	6.61473 × 10⁻³	−0.75972	−182.06572
0.6	17.9443	17.0678	−178.05	−3.53315	2.76919	6.55273 × 10⁻³	−0.75741	−178.80741
0.7	17.9396	17.0002	−174.852	−3.52822	2.76700	6.48123 × 10⁻³	−0.75474	−175.60674
0.8	17.9342	16.9237	−171.71	−3.52262	2.76450	6.40083 × 10⁻³	−0.75172	−172.46172
0.9	17.9281	16.8384	−168.624	−3.516370	2.76170	6.31163 × 10⁻³	−0.74836	−169.37236
1.0	17.9214	16.7445	−165.593	−3.509490	2.75859	6.21423 × 10⁻³	−0.74469	−166.33769

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