Research Article  Open Access
Safdar Ali, "KLL Dielectronic Recombination of Highly Charged Sulfur and Silicon Ions", Journal of Atomic and Molecular Physics, vol. 2014, Article ID 752934, 5 pages, 2014. https://doi.org/10.1155/2014/752934
KLL Dielectronic Recombination of Highly Charged Sulfur and Silicon Ions
Abstract
Dielectronic recombination measurements for highly charged ions were performed at the Stockholm refrigerated electron beam ion trap. We have obtained KLL DR resonance strengths for highly charged H and Helike sulfur and silicon ions. The experimental results are compared with the theoretical data obtained from GRASP II code. Both the experimental and calculated results agree well within the experimental error bars. Moreover, the dielectronic recombination resonance strengths are used to obtain the new scaling parameters by incorporating our results with the previous measurements and to check the behaviour of scaling formula for H and Helike isoelectronic sequences.
1. Introduction
Dielectronic recombination (DR) process has been observed in hightemperature astrophysical and laboratory plasmas and thus affects the charge state distributions of the plasmas. It plays a crucial role in modelling and diagnosing of these plasmas [1]. For example, DR satellite lines from fusion plasma devices are often used to determine plasma temperature for diagnostics [2]. On the other hand, plasma modelling codes such as XSTAR [3], CLOUDY [4], and CHIANTI [5] crucially depend upon the input atomic data such as DR cross sections and rate coefficients to obtain ionization balance and physical conditions of the plasmas [6]. Highly charged sulfur and silicon ions are present in astrophysics and laboratory plasmas [7, 8]. Accurate atomic data for these ions is therefore needed for the identification of the emission lines and to derive ion abundances and plasma temperatures.
Historically, DR process was first suggested as recombination mechanism by Sayers in 1939 [9]. Later, Massy and Bates [10] considered it theoretically to explain atomic processes related to O^{+} ions in the upper atmosphere. However, it was Burgess [11] who for the first time pointed that DR had a large recombination rate in hightemperature plasmas and dominates over the radiative recombination in the solar corona. DR is a resonant twostep electronion recombination process, in which a free electron is captured into a vacant shell of the ion, while one of the bound electrons is simultaneously excited producing a doubly excited state. The process is completed by stabilization through photon emission, reducing the ion energy below the ionization threshold. This process can be schematically represented as where is the charge state of ion , and subscripts , , and denote the initial, doubly excited, and final states, respectively.
In this paper, we present the results for H and Helike KLL DR resonances of highly charged sulfur and silicon ions obtained from the measurements performed at the Stockholm EBIT.
2. Experimental Details
The measurement for the ions discussed in this paper was performed using Stockholm Refrigrated electron beam ion trap (REBIT) [12, 13]. For the measurements, the gas atoms are injected into the EBIT through one of the ports. These atoms make collision with the electrons emitted from the electron gun and trapped in the potential well. The trapping region consists of three drift tubes: bottom, middle, and top starting from electron gun side. The whole drift tubes assembly is floating on high positive voltage plate form. The voltage of the middle drift tube determines the energy of the electron beam relative to the trapped ions. The ions are trapped radially by the space charge produced by the electron beam and axially by the positive potential applied on bottom and top drift tubes.
In the first stage of the experiment, the electron beam energy was set to ionization energy of 8 keV to produce a suitable charge state distribution of these ions by collisions for 900 ms with trapped ions/atoms. In order to scan for DR resonances, the electron beam energy was ramped linearly up and down for 300 ms. The electron beam current was kept constant at about 10 mA with the trap depth of 10 V throughout the measurements. At the same time, Xrays emitted from the trapped ions were recorded using a SiLi detector, placed at 90° to the electron beam direction. The signal was taken into computer by using electronics and multiparameter data acquisition system. The Xray energy, electron energy, and time were recorded in the computer in event mode following the procedure described in [13].
3. Results and Discussions
A twodimensional event mode data plot is shown in Figure 1 for highly charged sulfur ions. The horizontal and vertical axes indicate the photon energy and the electron energy, respectively. Xray signal due to LRR processes is seen along diagonal line (since in radiative recombination, Xrays energy is the sum of beam energy and the binding energy of the recombined state, so this increases linearly with the electron beam energy). Xrays corresponding to transition from LK can be seen along the vertical column denoted with LK ridge. The DR resonances form the intense spots and are labelled as KLL, KLM, and KLN parallel to the electron energy axis. There are two specific decay channels after the production of the doubly excited state. If the inner electron decays to Kshell, the resonances appear on LK ridge. The resonances observed on LRR ridge are due to the decay of the outer electron to Kshell. Since both the initial and final states are the same as for nonresonant RR process, the Xrays due to DR and RR are observed on the same position. The 2D spectrum allows projecting the selected regions either onto the photon energy axis or onto electron beam energy axis.
The natural width of the DR cross section is smaller than the beam energy width of 25 eV FWHM. Thus, instead of working with the theoretical narrow profiled DR cross section, DR resonance strength is normally used, which is cross section integrated over all energies. The resonance strength is defined by where and are the electron beam energy spread, obtained by using the KLM resonance peak of Helike sulfur. The experimental DR resonance strength can be obtained using the relation where and are the total count rates of the photons over an energy spread , is the theoretical RR cross section of Hlike ions, is the ratio of H to Helike ions, and is a correction factor to the photon intensity due to the anisotropy of DR and RR photon emission.
The experimental results obtained for KLL resonances of H and Helike sulfur are compared with the calculations as shown in Figure 2. A distorted wave approximation method was used for the calculations of the continuum wave functions of the incident electrons. Atomic structures of the target and recombined ions were calculated with the GRASP II code [14]. The Auger decay rates and resonant strengths were calculated by using a code developed by Y. M. Li et al. [15]. These codes were already used successfully for the calculations of DR resonance strengths and energy position of different atomic ions [6, 16, 17]. The generalized Breit interactions (GBI) and the decay through forbidden radiation are very weak; therefore such effects were not taken into account. In the calculations, all possible decay paths were taken into account, including radiative decay to lower doubly excited states and autoionizing decay to excited states.
Previously, an empirical formula was given by Watanabe et al. [18] to estimate the DR resonant strength of Helike isoelectronic sequence by defining the radiative transition rate , the autoionization rate , and the resonance energy in terms of their dependence: where is the atomic number and and are fitting parameters. By taking the present results and incorporating the results from previous measurements, the parameters and can be recalculated to update the scaling formula. We have also performed similar measurements for highly charged silicon ions and the results are shown in Figure 3. In addition, we have also obtained fitting parameters for Hlike isoelectronic sequence as given in Table 1.

(a)
(b)
The KLL DR resonance strengths of H and Helike isoelectronic sequences for experimental and theoretical results published so far are shown in Figure 3 along with our experimental and theoretical data. The solid squares with error bars are the experimental values, while the filled circles are the theoretical values. Our measurements for sulfur and silicon are shown with dotted vertical lines. It is clear that this scaling law provides a very good fit to the experimental and theoretical results. As shown in the figure, the resonant strength decreases with increasing except for , 16, and 18. This is due to the fact that the capture of electron into the doubly excited states becomes more difficult as increases; as a result, the resonant strengths become smaller with increasing . However, for the elements with atomic number , 16, and 18, the Auger processes become significant and the doubly excited states could decay through the Auger processes to a significant extent. For large differences in the magnitude of the two transition rates (radiative and Auger), the DR resonance strength is proportional to the weaker of the two decay channels; hence, radiative decay is weaker in these low elements which increase the resonance strengths (see (4)).
4. Conclusions
We have measured the KLL DR resonance strengths for highly charged H and Helike sulfur and silicon ions. The results agreed well within the experimental error bars with our calculations performed with the fully relativistic distorted wave approximation approach. In addition, we have obtained the new fitting parameters to estimate the DR resonance strengths by using scaling formula. More benchmark measurements are required over a wide range of atomic numbers to extend the applicability of this formula, especially for low elements (below ).
Conflict of Interests
The author declares that there is no conflict of interests regarding the publication of this paper.
References
 U. Hwang, J. Martin Laming, C. Badenes et al., “A million second chandra view of cassiopeia A,” Astrophysical Journal Letters, vol. 615, no. 2, pp. L117–L120, 2004. View at: Publisher Site  Google Scholar
 S. Ali, Electronion recombination data for plasma applications [Ph.D. thesis], Stockholm University, 2012.
 T. Kallman and M. Bautista, “Photoionization and highdensity gas,” Astrophysical Journal, Supplement Series, vol. 133, no. 1, pp. 221–253, 2001. View at: Publisher Site  Google Scholar
 G. J. Ferland, K. T. Korista, D. A. Verner, J. W. Ferguson, J. B. Kingdon, and E. M. Verner, “CLOUDY 90: numerical simulation of plasmas and their spectra,” Publications of the Astronomical Society of the Pacific, vol. 110, no. 749, pp. 761–778, 1998. View at: Google Scholar
 E. Landi, G. Del Zanna, P. R. Young, K. P. Dere, H. E. Mason, and M. Landini, “CHIANTI—an atomic database for emission lines. VII. New data for xrays and other improvements,” Astrophysical Journal, Supplement Series, vol. 162, no. 1, pp. 261–280, 2006. View at: Publisher Site  Google Scholar
 S. Ali, I. Orban, S. Mahmood, Z. Altun, P. Glans, and R. Schuch, “Electron–ion recombination rate coefficients for C II Forming C I,” The Astrophysical Journal, vol. 753, p. 132, 2012. View at: Publisher Site  Google Scholar
 N. Sultana, “ElectronIron recombination rate coefficients and photoionization cross section for S XIV and SXV for Xray and UV modeling,” The Open Astronomy Journal, vol. 1, no. 1, pp. 1–26, 2008. View at: Publisher Site  Google Scholar
 F. Gaillard and B. Scaillet, “The sulfur content of volcanic gases on Mars,” Earth and Planetary Science Letters, vol. 279, no. 12, pp. 34–43, 2009. View at: Publisher Site  Google Scholar
 M. J. Seaton and P. J. Storey, “Dielectronic recombination,” in Atomic Processes and Applications, P. J. Burke and B. L. Moiseiwitsch, Eds., North Holland, Amsterdam, The Netherlands, 1976. View at: Google Scholar
 H. S. W. Massey and D. R. Bates, “The properties of neutral and ionized atomic oxygen and their influence on the upper atmosphere,” Reports on Progress in Physics, vol. 9, no. 1, pp. 62–74, 1942. View at: Publisher Site  Google Scholar
 A. Burgess, “Delectronic recombination and the temperature of the solar corona,” The Astrophysical Journal, vol. 139, pp. 776–780, 1964. View at: Publisher Site  Google Scholar
 S. Böhm, A. Enulescu, T. Fritio, I. Orban, S. Tashenov, and R. Schuch, “First results from the Stockholm electron beam ion trap,” Journal of Physics: Conference Series, vol. 58, no. 1, pp. 303–306, 2007. View at: Publisher Site  Google Scholar
 S. Ali, S. Mahmood, I. Orban et al., “Photorecombination studies at REBIT with a Labview control and data acquisition system,” Journal of Instrumentation, vol. 6, Article ID C01016, 2010. View at: Publisher Site  Google Scholar
 I. P. Grant, B. J. McKenzie, P. H. Norrington, D. F. Mayers, and N. C. Pyper, “An atomic multiconfigurational DiracFock package,” Computer Physics Communications, vol. 21, no. 2, pp. 207–231, 1980. View at: Google Scholar
 “Y. M. Li”. View at: Google Scholar
 B. E. O'Rourke, H. Kuramoto, Y. M. Li et al., “Dielectronic recombination in Helike titanium ions,” Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 37, no. 11, pp. 2343–2353, 2004. View at: Publisher Site  Google Scholar
 S. Ali, S. Mahmood, I. Orban et al., “Electronion recombination of H and Helike sulfur,” Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 44, no. 22, Article ID 225203, 2011. View at: Publisher Site  Google Scholar
 H. Watanabe, H. Tobiyama, A. P. Kavanagh et al., “Dielectronic recombination of Helike to Clike iodine ions,” Physical Review A—Atomic, Molecular, and Optical Physics, vol. 75, no. 1, Article ID 012702, 2007. View at: Publisher Site  Google Scholar
 A. J. Smith, P. Beiersdorfer, K. Widmann, M. H. Chen, and J. H. Scofield, “Measurement of resonant strengths for dielectronic recombination in heliumlike Ar^{16+},” Physical Review A—Atomic, Molecular, and Optical Physics, vol. 62, no. 5, Article ID 052717, 2000. View at: Publisher Site  Google Scholar
 R. Ali, C. P. Bhalla, C. L. Cocke, M. Schulz, and M. Stockli, “Dielectronic recombination on and electronimpact excitation of heliumlike argon,” Physical Review A, vol. 44, no. 1, pp. 223–231, 1991. View at: Publisher Site  Google Scholar
 P. Beiersdorfer, T. W. Phillips, K. L. Wong, R. E. Marrs, and D. A. Vogel, “Measurement of levelspecific dielectronicrecombination cross sections of heliumlike Fe xxv,” Physical Review A, vol. 46, no. 7, pp. 3812–3820, 1992. View at: Publisher Site  Google Scholar
 H. Watanabe, F. J. Currell, H. Kuramoto et al., “The measurement of the dielectronic recombination in Helike Fe ions,” Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 34, no. 24, pp. 5095–5102, 2001. View at: Publisher Site  Google Scholar
 D. A. Knapp, R. E. Marrs, M. B. Schneider, M. H. Chen, M. A. Levine, and P. Lee, “Dielectronic recombination of heliumlike ions,” Physical Review A, vol. 47, no. 3, pp. 2039–2046, 1993. View at: Publisher Site  Google Scholar
 T. Fuchs, C. Biedermann, R. Radtke, E. Behar, and R. Doron, “Channelspecific dielectronic recombination of highly charged krypton,” Physical Review A—Atomic, Molecular, and Optical Physics, vol. 58, no. 6, pp. 4518–4525, 1998. View at: Google Scholar
 H. Watanabe, H. Tobiyama, A. P. Kavanagh et al., “Dielectronic recombination of Helike to Clike iodine ions,” Physical Review A—Atomic, Molecular, and Optical Physics, vol. 75, no. 1, Article ID 012702, 2007. View at: Publisher Site  Google Scholar
 K. Yao, Z. Geng, J. Xiao et al., “KLL dielectronic recombination resonant strengths of Helike up to Olike xenon ions,” Physical Review A, vol. 81, Article ID 022714, 2010. View at: Publisher Site  Google Scholar
 A. P. Kavanagh, H. Watanabe, Y. M. Li et al., “Dielectronic recombination in Helike, Lilike, and Belike highly charged ions in the KLL and KLM manifolds,” Physical Review A, vol. 81, Article ID 022712, 2010. View at: Publisher Site  Google Scholar
 G. Kilgus, J. Berger, P. Blatt et al., “Dielectronic recombination of hydrogenlike oxygen in a heavyion storage ring,” Physical Review Letters, vol. 64, no. 7, pp. 737–740, 1990. View at: Publisher Site  Google Scholar
 H. Watanabe, A. P. Kavanagh, H. Kuramoto et al., “Dielectronic recombination of hydrogenlike ions,” Nuclear Instruments and Methods in Physics Research B, vol. 235, no. 1–4, pp. 261–264, 2005. View at: Google Scholar
 M. S. Pindzola, N. R. Badnell, and D. C. Griffin, “Dielectronic recombination cross sections for Hlike ions,” Physical Review A, vol. 42, no. 1, pp. 282–285, 1990. View at: Publisher Site  Google Scholar
 G. El Machtoub, “Channelspecific dielectronic recombination of Ge(XXXII), Se(XXXIV), and Kr(XXXVI),” Canadian Journal of Physics, vol. 82, no. 4, pp. 277–289, 2004. View at: Publisher Site  Google Scholar
 D. Bernhardt, C. Brandau, Z. Harman et al., “Breit interaction in dielectronic recombination of hydrogenlike uranium,” Physical Review A–Atomic, Molecular, and Optical Physics, vol. 83, no. 2, Article ID 020701, 2011. View at: Publisher Site  Google Scholar
Copyright
Copyright © 2014 Safdar Ali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.