Dielectronic recombination experiment of Na-like Kr<sup>25+</sup> at heavy ion storage ring CSRe

Shao Lin; Huang Zhong-Kui; Wen Wei-Qiang; Wang Shu-Xing; Huang Hou-Ke; Ma Wan-Lu; Liu Chang; Wang Han-Bing; Chen Dong-Yang; Liu Xin; Zhou Xiao-Peng; Zhao Dong-Mei; Zhang Shao-Feng; Zhu Lin-Fan; Ma Xin-Wen

doi:10.7498/aps.73.20240211

Abstract

The experimental study of precision spectroscopy of dielectronic recombination (DR) of highly charged ions is not only important for astronomical plasma and fusion plasma, but also can be used as a new precision spectroscopy to test the strong-field quantum electrodynamic effect, measure isotope shift, and extract the radius of atomic nuclei. An specially designed electron beam energy detuning system for electron-ion recombination precision spectroscopy experiments has been installed on the heavy ion storage ring CSRe in Lanzhou, China, where the electron-ion collision energy in the center-of-mass system can be detuned to 1 keV, and an independently-developed plastic scintillator detector and multiwire proportional chamber detector have been installed downstream of the electron cooler of the CSRe for detecting recombined ions. The multiwire proportional chamber detector has the ability to non-destructively monitor the profile of the ion beam in real-time while acquiring the recombined ion counts, providing guidance for optimizing the ion beam. On this basis, the first test experiment on dielectronic recombination of Kr²⁵⁺ ions is carried out at the CSRe, and the dielectronic recombination rate coefficients in a range of 0–70 eV in the frame of center-of-mass are measured. In order to fully understand the experimental results, we calculate the dielectronic recombination rate coefficient of the Kr²⁵⁺ ion by using the flexible atomic code (FAC) and make a detailed comparison with the experimental result, showing that they are in good agreement with each other, and only the resonance energy values of the two resonance peaks at 1.695 eV and 2.573 eV are significantly different. In addition, the DR resonance energy values and intensities are obtained by fitting the experimental results in a range of 0–35 eV, and we find that the transition 3s→4l (∆n = 1) contributes significantly to the experimental spectral lines. Furthermore, we compare the plasma rate coefficients derived from the DR rate coefficients with those derived from the AUTOSTRUCTURE and FAC theories, which differ by 20 percent in a temperature range less than 10⁶ K. The experimental results show that the DR experimental platform of the CSRe has very good stability and reproducibility, and can provide support for the future DR experiments of highly charged ion, i.e. for testing strong-field quantum electrodynamics effect and measuring the properties of atomic nuclei.

Keywords:

Authors and contacts

1.
Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics, South China Normal University, Guangzhou 510006, China
2.
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
3.
Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China

Corresponding author: Wen Wei-Qiang, wenweiqiang@impcas.ac.cn ; Zhu Lin-Fan, lfzhu@ustc.edu.cn ; Ma Xin-Wen, x.ma@impcas.ac.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2022YFA1602500), the National Natural Science Foundation of China (Grant Nos. 12393824, 12334010, U1932207), the Strategic Priority Research Program (B) of Chinese Academy of Science (Grant No. XDB34020000), and the Youth Innovation Promotion Association of the Chinese Academy of Science.

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References

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Cited By

图 1 $ {Z}^{q+} $离子的双电子复合过程示意　　(a) 第一步共振过程, 离子在俘获一个自由电子的同时将一个内壳层电子激发, 从而形成自电离态$ {{[Z}^{(q-1)+}]}^{{\mathrm{*}}{\mathrm{*}}} $; (b) 第二步过程, 自电离态离子通过辐射光子从而退激发到稳定态

Figure 1. Schematic of DR of $ {Z}^{q+} $ ions: (a) The first resonance step, in which the ion captures a free electron and simultaneously excites an inner shell electron, resulting in the formation of the autoionized state $ {{[Z}^{(q-1)+}]}^{{\mathrm{*}}{\mathrm{*}}} $; (b) the second step, in which the ion is deexcited to the stable state by radiative decay.

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图 2 储存环CSRm与CSRe上的双电子复合实验平台示意图

Figure 2. Schematic view of the DR experimental platforms at the storage ring CSRm and CSRe.

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图 3 (a) CSRe上的高压电源调制系统示意图; (b) 电子束能量调制时序图, 插图为放大后的一个周期内的调制电压变化图

Figure 3. (a) Schematic diagram of the high voltage power supply modulation system of the CSRe; (b) the timing sequence of electron beam detuning voltage which is used in the DR experiment of Kr²⁵⁺.

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图 4 储存环CSRe上的多丝正比探测器实物图, 黑色虚线方框内为延迟读出电路

Figure 4. Physical view of the MWPC detector, the black dashed box shows the delayed read-out circuitry.

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图 5 多丝正比探测器实时探测到的冷却前后的离子束包络分布图

Figure 5. Experimentally measured beam profiles before and after electron-cooling by the MWPC detector.

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图 6 (a) 复合离子探测器探测的复合离子计数-电子束调制能量谱; (b) 总的复合速率系数-质心系碰撞能量谱, 插图中的红色曲线为拟合结果, 拟合得到了电子束的横向温度与纵向温度; (c) 减去背景与RR的贡献后得到的绝对DR速率系数-碰撞能量谱

Figure 6. (a) Counts of recombined ions detected by the ion detector as a function of the electron beam detuning voltage; (b) total recombined rate coefficient at the center-of-mass collision energy; (c) the absolute DR rate coefficient by subtracting the contributions of the background and RR. In addition, the red curve in the inset of panel (b) is the fitting results.

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图 7 蓝色点线和红色实线分别为CSRe测量的Kr²⁵⁺离子双电子复合速率与FAC计算的理论结果, 阴影部分为$ \Delta n=1 $的部分. 竖线为基于里德伯公式估算的双电子复合共振位置

Figure 7. Experimental (dotted blue line) and theoretical (red solid line) dielectronic recombination rate coefficients of the Na-like Kr²⁵⁺ ions. The shaded part is the part with $ \Delta n=1 $ core excitation.

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图 8 Kr²⁵⁺离子的实验(黑色实线)与FAC(红色虚线)及AUTOSTRUCTURE^[22](蓝色实线)理论导出的等离子体速率系数谱对比

Figure 8. Comparision of plasma rate coefficients of sodium-like Kr²⁵⁺ ions between experimental results (black solid line) and calculations by FAC (red dashed line) and AUTOSTRUCTURE (blue line) code.

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表 1 CSRe上Kr²⁵⁺离子双电子复合实验参数

Table 1. Parameters of the DR experiment of Kr²⁵⁺ at CSRe.

实验参数	实验装置(CSRe)
储存环周长/m	128.8
相互作用长度/m	4.0
离子束能量/(MeV·u^–1)	80
离子束流强/μA	300—450
电子束流强/mA	287.5
电子束半径/cm	2.60
横向电子温度/meV	75.14
纵向电子温度/meV	1.26
冷却段磁场强度/G	390
枪区磁场强度/G	1250

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表 2 实验测量拟合结果与理论计算结果对比

Table 2. Comparison of experimental measurement fitting results with theoretical calculations.

双激发态组态	共振能量/eV		共振强度/(10^–19 eV·cm²)
双激发态组态	FAC	实验	FAC	实验
4s[²S_1/2]4d_5/2 (J = 2)	1.530	1.695±0.001	75.2	93.8±0.6
3d[²D_3/2]8s (J = 1)	2.090	2.119±0.009	7.1	8.4±0.6
3d[²D_3/2]8s (J = 2)	2.405	2.573±0.001	62.2	56.1±0.6
3p[²P_1/2]13s	3.869	3.804±0.049	1.5	1.9±0.6
3d[²D_5/2]8s (J = 3)	4.530		7.3
3p[²P_1/2]13p_1/2	4.565^a		4.4
Blend	4.543^a	4.561±0.012	11.7	17.4±1.2
3d[²D_3/2]8p_1/2 (J = 2)	4.660		6.4
3d[²D_5/2]8s (J = 2)	4.690		11.0
3d[²D_3/2]8p_1/2 (J = 1)	4.754		3.9
Blend	4.693^a	4.789±0.013	21.2	15.8±1.2
3d[²D_3/2]8p_3/2	5.338	5.216±0.021	14.8	13.8±1.7
3p[²P_1/2]13d	5.384^a	5.448±0.032	7.2	11.5±1.4
3p[²P_1/2]13f	5.838^a	5.747±0.029	12.4	13.9±1.5
3p[²P_1/2]13l (l ≥ g)	6.003^a	6.000±0.006	40.4	44.7±1.9
3d[²D_5/2]8p_1/2 (J = 2, 3)	7.129^a	7.154±0.022	14.6	12.5±1.3
3p[²P_3/2]12s (J = 1, 2)	7.465^a	7.494±0.095	2.0	6.8±2.3
3d[²D_5/2]8p_3/2 (J = 2, 3, 4)	7.705^a	7.767±0.034	26.8	18.6±2.2
4s[²S_1/2]4f_5/2 (J = 2)	8.129	8.161±0.028	37.9	39.2±5.2
3d[²D_5/2]8p_3/2 (J = 1)	8.063		2.3
3p[²P_3/2]12p_1/2	8.245		2.2
3p[²P_3/2]12p_3/2 (J = 1, 2, 3)	8.404^a		3.8
3d[²D_3/2]8d_3/2	8.596		12.7
Blend	8.466^a	8.391±0.045	21.0	20.1±5.2
4s[²S_1/2]4f_5/2(J = 3)	8.880	8.790±0.010	53.9	58.2±1.3
3d[²D_3/2]8d_5/2	8.813^a		21.1
3p[²P_3/2]12d	9.404^a		8.9
Blend	8.988^a	9.143±0.014	30.0	41.2±1.3
4s[²S_1/2]4f_5/2 (J = 4)	9.577	9.546±0.018	65.7	60.6±4.0
4s[²S_1/2]4f_5/2 (J = 3)	9.737	9.842±0.023	55.8	75.1±3.2
3p[²P_3/2]12l (l ≥ f )	10.139^a	10.138±0.020	77.5	67.0±3.8
3d[²D_3/2]8f	10.721^a	10.694±0.041	39.8	51.9±2.0
3d[²D_5/2]8d	11.227^a	11.224±0.023	33.1	58.3±2.8
3d[²D_3/2]8l (l ≥ g )	11.313^a	11.504±0.009	70.7	60.3±4.5
3p[²P_1/2]14d	12.443^a	12.732±0.044	3.5	10.1±1.7
3p[²P_1/2]14l (l ≥ f )	12.907^a	13.101±0.013	19.4	41.0±1.4
3d[²D_5/2]8f	13.276^a	13.616±0.018	25.4	39.2±1.8
3d[²D_5/2]8l (l ≥ g)	13.770^a	13.964±0.006	83.4	67.5±2.2
4p[²P_1/2]4d_5/2 (J = 3)	16.337		12.3
4p[²P_1/2]4d_5/2 (J = 2)	16.500		4.0
Blend	16.377^a	16.482±0.013	16.3	14.1±1.0
3p[²P_3/2]13p	17.491^a	17.36±0.14	2.4	2.0±1.0
3p[²P_1/2]15p	17.601^a	17.74±0.12	0.8	3.0±0.8
Blend	17.517^a	17.579±0.036	3.2	3.3±0.3
3p[²P_1/2]15d	18.131^a		1.4
3p[²P_3/2]13d	18.313^a		3.6
Blend	18.262^a	18.226±0.057	5.1	7.2±1.4
4p[²P_1/2]4d_5/2 (J = 1)	18.466		5.2
3p[²P_1/2]15l (l ≥ f)	18.533^a		8.8
Blend	18.508^a	18.609±0.031	14.0	21.6±1.0
3p[²P_3/2]13l (l ≥ f)	18.930^a	18.976±0.008	25.5	32.2±1.6
4p[²P_3/2]4d_5/2 (J = 2)	20.038	20.162±0.022	5.1	4.2±0.3
4p[²P_3/2]4d_5/2 (J = 0)	21.802		1.7
4p[²P_3/2]4d_5/2 (J = 1)	22.054		4.2
Blend	21.984^a	22.086±0.025	5.9	5.1±0.3
4p[²P_3/2]4d_5/2 (J = 3)	22.444		4.3
4p[²P_3/2]4d_5/2 (J = 2)	22.502		5.4
Blend	22.476^a	22.614±0.020	9.7	8.7±0.3
3p[²P_1/2]16l	23.005^a	23.164±0.018	9.5	7.3±0.3
3p[²P_3/2]14p	24.715^a		1.4
3p[²P_3/2]14d	25.371^a		2.2
Blend	25.111^a	25.480±0.052	3.6	7.1±1.0
3p[²P_3/2]14l (l ≥ f)	25.865^a	25.941±0.013	20.7	21.2±1.0
3p[²P_1/2]17l	26.821^a	26.917±0.022	7.2	7.0±0.4
3p[²P_1/2]18l	30.020^a	30.277±0.024	6.1	6.8±0.3
3p[²P_3/2]15l	31.348^a	31.695±0.011	16.4	22.6±0.9
4p[²P_1/2]4f_5/2 (J = 3)	32.424		1.6
3p[²P_1/2]19l	32.739^a		7.5
Blend	32.683^a	32.804±0.028	9.2	9.5±0.5
^a Weighted energy: $ {E}_{{\mathrm{d}}}= {\displaystyle\sum {E}_{{\mathrm{d}}}{S}_{{\mathrm{d}}}}\Big/{\displaystyle\sum {S}_{{\mathrm{d}}}} $

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表 3 实验与FAC理论计算得到的复合速率系数导出的等离子体速率系数拟合参数, c_i与E_i的单位分别为cm³·s^–1与eV, 括号内的数字为10的幂

Table 3. Fitted coefficients for the plasma rate coefficients of DR experiment and FAC, the c_i are in units of cm³·s^–1, and the E_iare in eV. The numbers in the square brackets are power of 10.

i	实验		FAC
i	c_i	E_i	c_i	E_i
1	1.01[–1]	37.1	4.65[–2]	24.7
2	2.28[–1]	63.9	2.07[–1]	53.4
3	1.95[–3]	1.74	7.35[–2]	92.9
4	3.30[–2]	121	1.05[–2]	6.15
5	3.99[–2]	15.5	8.90[–4]	1.42
6	4.34[–2]	9.07	1.57[–3]	2.36
7	3.88[–3]	4.17	5.37[–2]	5.37

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[1]	Gillaspy J D 2001 J. Phys. B: At. Mol. Opt. Phys. 34 R93 Google Scholar
[2]	Kozlov M, Safronova M, López-Urrutia J C, Schmidt P 2018 Rev. Mod. Phys. 90 045005 Google Scholar
[3]	Lindroth E, Danared H, Glans P, Pešić Z, Tokman M, Vikor G, Schuch R 2001 Phys. Rev. Lett. 86 5027 Google Scholar
[4]	Brandau C, Kozhuharov C, Müller A, et al. 2003 Phys. Rev. Lett. 91 073202 Google Scholar
[5]	Schuch R, Lindroth E, Madzunkov S, Fogle M, Mohamed T, Indelicato P 2005 Phys. Rev. Lett. 95 183003 Google Scholar
[6]	Brandau C, Kozhuharov C, Harman Z A, et al. 2008 Phys. Rev. Lett. 100 073201 Google Scholar
[7]	啜晓亚, 黄忠魁, 汶伟强, 等 2018 原子核物理评论 35 196 Google Scholar Chuai X Y, Huang Z K, Wen W Q, et al. 2018 Nucl. Phys. Rev. 35 196 Google Scholar
[8]	Kieslich S, Schippers S, Shi W, et al. 2004 Phys. Rev. A 70 042714 Google Scholar
[9]	Budker G, Kiselev A, Konkov N, Naumov A, Niffontov V, Ostreiko G, Petrov V, Yudin L, Yasnov G 1965 V International Conference on High Energy Accelerators Proceedings Frascati, September 9–16, 1965 p455
[10]	Poth H 1990 Phys. Rep. 196 135 Google Scholar
[11]	Mitchell J, Ng C, Forand J, Levac D, Mitchell R, Sen A, Miko D, McGowan J W 1983 Phys. Rev. Lett. 50 335 Google Scholar
[12]	Dittner P, Datz S, Miller P, et al. 1983 Phys. Rev. Lett. 51 31 Google Scholar
[13]	Müller A 2008 Advances In Atomic, Molecular, and Optical Physics (Academic Press) pp293–417
[14]	Schippers S 2015 Nucl. Instrum. Methods Phys. Res. , Sect. B 350 61 Google Scholar
[15]	Huang Z K, Wen W Q, Xu X, et al. 2018 Astrophys. J. Suppl. Ser. 235 2 Google Scholar
[16]	Khan N, Huang Z K, Wen W Q, Mahmood S, et al. 2018 Chin. Phys. C 42 064001 Google Scholar
[17]	Wang S X, Xu X, Huang Z K, et al. 2018 Astrophys. J. 862 134 Google Scholar
[18]	Wang S X, Huang Z K, Wen W Q, et al. 2019 Astron. Astrophys. 627 171 Google Scholar
[19]	Huang Z K, Wang S X, Wen W Q, et al. 2020 X-Ray Spectrom. 49 155 Google Scholar
[20]	Wen W Q, Huang Z K, Wang S X, et al. 2020 Astrophys. J. 905 36 Google Scholar
[21]	Khan N, Huang Z K, Wen W Q, et al. 2022 J. Phys. B: At. Mol. Opt. Phys. 55 035001 Google Scholar
[22]	Huang Z K, Wen W Q, Wang S X, et al. 2020 Phys. Rev. A 102 062823 Google Scholar
[23]	Shevelko V P, Stöhlker T, Tawara H, Tolstikhina I Y, Weber G 2010 Nucl. Instrum. Methods Phys. Res., Sect. B 268 2611 Google Scholar
[24]	Yan K, Zhou Y, Ma X, Tang M, Gao D, Zhao H, Huang Z, Wen W, Mao L 2023 Nucl. Instrum. Methods Phys. Res. , Sect. A 1046 167699 Google Scholar
[25]	Skorobogatov D, Bryzgunov M, Kondaurov M, Putmakov A, Reva V, Repkov V 2019 Proceedings of the 12th Workshop on Beam Cooling and Related Topics Novosibirsk, Russia, September 24–27, 2019 pp86–88
[26]	Menz E B, Hahn C, Pfäfflein P, Weber G, Stöhlker T 2020 J. Phys. Conf. Ser. 1412 232006 Google Scholar
[27]	Westman S, Kerek A, Klamra W, Norlin L O, Novak D 2002 Nucl. Instrum. Methods Phys. Res., Sect. A 481 655 Google Scholar
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Dielectronic recombination experiment of Na-like Kr²⁵⁺ at heavy ion storage ring CSRe

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Corresponding author: Wen Wei-Qiang, wenweiqiang@impcas.ac.cn ; Zhu Lin-Fan, lfzhu@ustc.edu.cn ; Ma Xin-Wen, x.ma@impcas.ac.cn

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Dielectronic recombination experiment of Na-like Kr25+ at heavy ion storage ring CSRe

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Corresponding author: Wen Wei-Qiang, wenweiqiang@impcas.ac.cn ; Zhu Lin-Fan, lfzhu@ustc.edu.cn ; Ma Xin-Wen, x.ma@impcas.ac.cn

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Dielectronic recombination experiment of Na-like Kr²⁵⁺ at heavy ion storage ring CSRe