Re30+离子双电子复合速率系数的理论研究

复杂结构离子的双电子复合速率系数在极紫外光刻光源、核聚变等应用研究的等离子体光谱模拟和诊断中具有重要的应用价值。利用全相对论组态相互作用方法,详细计算了基组态为4p64d9的Re30+离子经双激发态（4p64d9）-1nln'l'（n=4~6,n'=4~23）的双电子复合（DR）过程。研究分析了激发、辐射通道,组态相互作用,级联退激对DR速率系数的影响。其中内壳层4p电子激发的DR速率系数是总DR速率系数的28.2%~44.9%,所以内壳层4p电子激发的贡献不可以忽略。级联退激对DR速率系数的最大贡献为12.9%,也必须要予以考虑。通过对双电子复合、辐射复合、以及三体复合速率系数的比较,辐射复合速率系数的最大值为DR速率系数的22.6%,三体复合速率系数的最大值仅为DR速率系数的0.3%。因此,DR速率系数远远大于辐射复合和三体复合速率系数。该结果表明DR过程对于等离子体离化态分布、能级布居以及光谱模拟都极为重要。为了方便应用,对基态和第一激发态的总DR速率系数进行了参数拟合。该研究结果将为Re激光等离子体的光谱模拟及复杂结构离子DR过程的进一步研究提供参考。Dielectronic recombination (DR) rate coefficients of complex ions are very important in some application research, such as extreme ultraviolet lithography and nuclear fusion. Based on the fully relativistic configuration interaction method, theoretical calculations are carried out to research the DR processes, in which Re30+ ions in the ground state 4p64d9 to (4p64d9)-1nln'l'(n=4~6, n'=4~23). Influence of excitation and radiation channels, configuration interaction, the effect of decays to autoionizing levels possibly followed by radiative cascades (DAC) are analyzed. The contributions through 4p subshell excitations to the total rate coefficient are 28.2%~44.9% in the whole temperature region. Hence the contributions from inner-shell electron excitation are very important. The contributions from the DAC transitions increase smoothly with the increasing temperature and are about 12.9% at 50 000 eV. The contributions of DAC can not be neglected. By means of compared total DR rate coefficients to radiative recombination rate coefficients and three-body recombination rate coefficients, it shows that the maximum value of the radiation recombination rate coefficient is 22.6% of the DR rate coefficient and the maximum value of the three-body recombination rate coefficient is only 0.3% of the DR rate coefficient. The total DR rate coefficient is greater than either the radiative recombination or three-body recombination coefficients in the whole temperature range. The corresponding DR process is very important for plasma ionization distribution, population level and spectrum simulation. In addition to facilitate the application, the total DR rate coefficients for the ground state and the first excited state are fitted to an empirical formula. These results will provide the reference for the further analyses of rhenium laser plasma spectrum simulation and the complex structures ions DR process.     

Absolute dielectronic recombination rate coefficients of highly charged ions at the storage ring CSRm and CSRe

Dielectronic recombination(DR) is one of the dominant electron–ion recombination mechanisms for most highly charged ions(HCIs) in cosmic plasmas, and thus, it determines the charge state distribution and ionization balance therein.To reliably interpret spectra from cosmic sources and model the astrophysical plasmas, precise DR rate coefficients are required to build up an accurate understanding of the ionization balance of the sources. The main cooler storage ring(CSRm) and the experimental cool...     

Investigations of the dielectronic recombination of phosphorus-like tin at CSRm

The electron–ion recombination for phosphorus-like~(112) Sn~(35+)has been measured at the main cooler storage ring of the Heavy Ion Research Facility in Lanzhou, China, employing an electron–ion merged-beams technique. The absolute total recombination rate coefficients for electron–ion collision energies from 0 e V–14 e V are presented. Theoretical calculations of recombination rate coefficients were performed using the Flexible Atomic Code to compare with the experimental results. The contributions of dielectronic recombination and trielectronic recombination on the experimental rate coefficients have been identified with the help of the theoretical calculation. The present results show that the trielectronic recombination has a substantial contribution to the measured electron–ion recombination spectrum of~(112)Sn~(35+). Although a reasonable agreement is found between the experimental and theoretical results the precise calculation of the electron–ion recombination rate coefficients for M-shell ions is still challengeable for the current theory.     

Enhancement of electron–ion recombination rates at low energy range in the heavy ion storage ring CSRm

Recombination of Ar¹⁴⁺, Ar¹⁵⁺, Ca¹⁶⁺, and Ni¹⁹⁺ ions with electrons has been investigated at low energy range based on the merged-beam method at the main cooler storage ring CSRm in the Institute of Modern Physics, Lanzhou,China. For each ion, the absolute recombination rate coefficients have been measured with electron–ion collision energies from 0 meV to 1000 meV which include the radiative recombination(RR) and also dielectronic recombination(DR)processes. In order to interpret the measured results, RR cross sections were obtained from a modified version of the semiclassical Bethe and Salpeter formula for hydrogenic ions. DR cross sections were calculated by a relativistic configuration interaction method using the flexible atomic code(FAC) and AUTOSTRUCTURE code in this energy range. The calculated RR + DR rate coefficients show a good agreement with the measured value at the collision energy above 100 meV.However, large discrepancies have been found at low energy range especially below 10 meV, and the experimental results show a strong enhancement relative to the theoretical RR rate coefficients. For the electron–ion collision energy below 1 meV, it was found that the experimentally observed recombination rates are higher than the theoretically predicted and fitted rates by a factor of 1.5 to 3.9. The strong dependence of RR rate coefficient enhancement on the charge state of the ions has been found with the scaling rule of q^3.0, reproducing the low-energy recombination enhancement effects found in other previous experiments.     

Xe8+离子双电子复合速率系数的理论研究

利用基于全相对论组态相互作用理论的FAC程序包, 详细研究了温度在0.1~1650 eV范围内Xe8+离子的双电子复合(DR)过程。 通过比较4s, 4p和4d壳层电子激发的双电子复合速率系数, 发现温度在10 eV以上时, 内壳层4p电子激发的双电子复合速率数对总双电子复合速率系数有很重要的贡献, 而4s电子激发对总双电子复合速率数贡献小于7.5%。 给出了△n=0, 1和2 三类芯激发对总双电子复合速率系数的贡献以及自由电子俘获到不同主量子数的双电子复合速率系数, 发现△n=2的芯激发和n′＞15的DR速率系数对总DR速率系数的贡献也很重要。 进一步给出了△n=0, 1和2 三类芯激发和总DR速率系数的拟合参数, 拟合结果和计算值符合, 偏差小于1%。 通过对双电子复合、 辐射复合以及三体复合速率系数的比较得知, 在温度高于1 eV时, DR过程是Xe8+离子的主要复合过程。Based on the fully relativistic configuration interaction method, theoretical calculations are carried out for the dielectronic recombination (DR) rate coefficients of Xe8+ ions in the temperature region from 0.1 to 1 650 eV. The comparison of the DR rate coefficients from 4s, 4p and 4d subshell excitations shows that 4d subshell excitation dominates in the whole temperature region. The contribution from 4p subshell excitation is very important at temperature above 10 eV and the contributions from 4s subshell excitation is lower than 7.5% in the whole temperature region. Similarly, the comparison of the DR rate coefficients through △n=0, 1 and 2 core excitation shows that the contribution from △n=2 core excitation can not be neglected, the contributions from n′＞15 can also not be neglected. The DR rate coefficients of △n=0, 1 and 2 core excitation and the total DR rate coefficients are fitted with some parameters, which are in good agreement with theoretical calculations values (within 1% difference). The total DR rate coefficients are greater than radiative recombination (RR) and three body recombination (TBR) rate coefficients at temperature above 1 eV. Therefore, the DR process can strongly influence the ionization balance of laser produced xenon plasmas.     

DIELECTRONIC RECOMBINATION OF Co-LIKE Ag AND Ta IONS

Ab initio calculations of the rate coefficients for dielectronic recombination (DR) of Co-like Ag and Ta ions are performed based on Cowan's quasi-relativistic multi-configuration Hartree－Fock code. Co-like (3s ²3p⁶3d¹⁰)^-1 configurations and Ni-like (3s²3p⁶3d¹⁰)^-24l4l' autoionization configurations are included in the present calculation. Because of the extensive distribution of autoionization state energy levels, the DR rate coefficients cannot be reproduced or interpolated by a simple analytical formula, such as the Burgess－Merts formula, or the Hagelstein approximation. We propose to use multi-set Hagelstein parameters, which is convenient in practice and can reproduce well the ab initio calculated DR rate coefficients.     

W44+ 离子双电子复合速率系数的理论研究

利用全相对论组态相互作用方法,详细研究了W44+ 离子从基组态3s23p63d104s2俘获一个电子形成双激发态(3s23p63d104s2)nln′l′(n = 4 ~ 6,n′= 4 ~7) 的双电子复合(DR) 过程。通过比较不同壳层电子激发的DR 速率系数,得知4s 电子激发和3d 电子激发的DR 速率系数分别在低温和中高温度时给出了主要贡献,得到了主要的电子激发DR通道。在1 eV~50 keV 温度范围内,计算了n = 4~18 的DR速率系数,并外推到了n= 100,得到总DR 速率系数。比较总DR 速率系数、三体复合(TBR) 以及辐射复合(RR) 速率系数,结果表明DR 速率系数在研究的温度范围内远大于TBR 和RR 速率系数,其将明显地影响ITER 等离子体的电离平衡和离化态布居。Based on the fully relativistic configuration interaction method, theoretical calculations are carried out to research the dielectronic recombination (DR) processes, in which W44+ ions in the ground state 3s23p63d104s2 trap an electron to form doubly excited states (3s23p63d104s2)nln’l’(n =4~6,n′= 4~7). The comparison of the DR rate coefficients of different shells shows that DR approach is as follow: the 4s subshell excitation dominates to DR at low temperature, but 3d subshell excitation attributes to DR at high temperature. Total DR rate coefficients from n=4~18 are evaluated directly, and the results are extrapolated up to n = 100 in the temperature range from 1 to 5×104 eV, and thus get the total DR rate coefficients. Compared total DR rate coefficients to three-body recombination (TBR) rate coefficients and radiative recombination (RR) rate coefficients, it showed that the total DR rate coefficients obviously significantly greater than other two recombination rate coefficients, and thus it obviously influence ionization equilibrium and ionization state population of ITER plasma.     

Measurement of the KLL Dielectronic Recombination Resonances in He-like to C-like Kr Ions

The KLL dielectronic recombination processes of highly charged He-like to C-like Kr ions have been studied experimentally. The measurement was performed on the newly developed Shanghai electron beam ion trap （Shanghai-EBIT） facility. Characteristic x-rays from both dielectronic recombination and radiative recombination are detected as the electron beam energy is scanned through the resonances. The KLL resonant strengths obtained are 5.41×10^-19, 4.33×10^-19, 3.59×10^-19, 2.05×10^-19 and 0.98×10^-19 cm^2 eV for He-like to C-like Kr ions, respectively.     

The effect of configuration complex on dielectronic recombination process in highly ionized plasmas

This paper analyses the effect of configuration complex on dielectronic recombination （DR） process in highly ionized plasmas （Xe^26＋, Dy^38＋, W^46＋） by using the multiconfiguration relativistic Hartree-Fock method. Resonant and nonresonant radiative stabilizing transitions and decays to autoionizing levels followed by radiative cascades are included. Collisional transitions following electron capture are neglected. The remarkable difference between the isoelectronic trend of the rate coefficients for DR through 3d^94l4l′ and through 3d^94l5l′ is emphasized. The trend of DR through 3d^94l4l′ shows irregularities at relatively low temperature due to the progressive closing of DR channels as atomic number Z increases.     

Dielectronic recombination rate coefficient for Cu-like Au^50＋ ion

The rate coefficients α^{DR} of dielectronic recombination (DR) for Cu-like Au^{50+} ion collided with the incident free electron are calculated based on the quasi-relativistic multi-configuration Hartree－Fock theory. The results clearly show that the α^{DR} of all recombination channels exhibits resonance characters with electron temperature. At lower temperatures, the recombination for electrons caused by 4s excitation is dominant through outer electron radiative transitions among the intermediate doubly excited autoionizing levels, in which the most components come from 3d^{10}5pns states, whereas with increasing electron temperature, DR caused by 3d excitation turns out to be dominant, and the contribution from the 3d^94s4fnf state to the total rate coefficient of electron 3d is the largest with α^{DR}=1.15×10^{- 11} cm^3·s^{-1} at an electron temperature of T_e=0.35 keV. Under this condition, there exists a strong competition between the two types of recombination channels.     

Theoretical study of the KLL dielectronic recombination for highly charged iodine ions

With a developed program for calculation of dielectronic recombination (DR) process, which is based on multi-configuration Dirac-Fock (MCDF) method, the KLL DR processes of the highly charged helium-like to carbon-like iodine ions have been studied systematically. The contributions to doubly excited states from quantum electrodynamic (QED) and Breit effects have been discussed. The KLL DR resonant energies and corresponding resonant strengths have been calculated. The behavior of KLL resonant strengths with increasing Z are analyzed for He-like ions in particular. The theoretical DR spectra for each highly charged ion species are obtained in the KLL region. Comparison has been made between the present calculations and the latest experiments in Tokyo-EBIT.     

Dielectronic recombination rate coefficients of Ni-like barium and tungsten

Ab initio calculations of the total dielectronic recombination (DR) rate coefficient of Ni-like barium () and tungsten () in the ground state have been performed using the HULLAC atomic code package. Resonant and nonresonant stabilizing radiative transitions are included. Collisional transitions following electron capture are neglected. The present level-by-level calculations include the DR contributions of all of the levels (over 17000) in the Cu-like inner-shell excited configurations 3d ⁹ 4ln'l' (), 3p ⁵ 3d ¹⁰ 4ln'l' (), and 3s3p ⁶ 3d ¹⁰ 4ln'l' (). For both ions, the configuration complexes with a hole in the 3p inner shell contribute almost 10% to the total DR rate coefficient, while the complexes with a hole in the 3s inner shell contribute about 1%. The converging contributions of the 3d ⁹ 4ln'l' (n' > 9) configurations are evaluated by applying the complex-by-complex extrapolation method and are found to comprise up to about 20% of the total DR rate coefficients throughout a wide electron temperature range. The total DR rate coefficients are fitted to an easy-to-use analytic expression which reproduces the original data with an accuracy of about 2% or better in a very wide temperature range. Received: 1 February 1999     

Au~(34+)离子双电子复合过程的理论研究

复杂结构离子的双电子复合(DR)速率系数在核聚变、极紫外光刻光源等应用研究的等离子体谱模拟中具有重要的价值.利用基于全相对论组态相互作用理论的FAC程序包,详细计算了Au~(34+)离子的双电子复合速率系数.研究分析了激发、辐射通道,组态相互作用,级联退激对DR速率系数的影响.其中,级联退激对DR速率系数的贡献必须予以考虑.对双电子复合、辐射复合以及三体复合速率系数做了比较,在温度大于1 eV范围,双电子复合都大于辐射复合以及三体复合速率系数,相应的DR过程对于等离子体离化态分布和能级布居以及光谱模拟都极为重要.对基态和第一激发态的DR速率系数进行了参数拟合,拟合值与计算值的偏差小于1.73%.研究结果将为复杂结构离子双电子复合过程的进一步研究提供参考.     

Calculation of dielectronic recombination cross sections and rate coefficients for heliumlike carbon

A simplified relativistic configuration interaction method is used to calculate the dielectronic recombination cross sections and rate coefficients for heliumlike carbon. In this method, the infinite resonant doubly excited states can be treated conveniently in the frame of Quantum Defect Theory. Our calculated cross sections are in agreements with the experimental measurements except for the 1s2lnl'(n=6,7) resonances. The total energy-integrated cross sections and rate coefficients over all dielectronic resonances are in agreements with the experimental measurements within percent. Received: 7 July 1997 / Revised: 7 October 1997 / Accepted: 8 December 1997     

Ionization Energies of Ions in Hot and Dense Plasma: Beryllium-Like Ions for Z=26-36

Ionization energies of beryllium-like ions for Z = 26 - 36 in hot ana aense plasmas （ne=10^22 -10^24 cm^-3,kT= 500 - 2000 eV） are obtained by using an approach developed for electronic structure and transition property of ions in hot and dense plasmas based on the multi-configuration Dirac-Fock model. Influence of the plasma environment is considered by introducing a correction to the one-electron potential to account for the screening of the ionized electrons. This correction is calculated from the ionized electron micro-space distribution, which is obtained based on an ＂average atom model for the temperature and density-dependent average ionization of atoms in plasmas. Comparison between the present and the ion sphere models is made to display the significance of the ionized electron micro-space distribution.     

Dielectronic recombination at low energy range with Boron-like Ar13+at the CSRm

In order to extend the dielectronic recombination (DR) experiments from the main cooler storage ring CSRm with intermediate charge state ions to the experimental cooler storage ring CSRe with highly charged ions and even radioactive ions, a test electron-ion recombination experiment of B-like Ar¹³⁺ ions was performed with a section of the new electron beam energy detuning system, which will be installed at the CSRe. We present the measured and also the calculated DR spectra for the ∆n = 0 resonances from 0 to 3 eV. The experimental results agree very well with the previous DR experimental data from CRYRING, and the energy resolution reached 30 meV full width at half maximum. This test experiment demonstrates that the reliability and stability of the newly developed electron beam energy detuning system are satisfactory for the upcoming DR experiments at the CSRe. However, we found large discrepancies between the experimental result and the calculation in both resonance positions and the intensities of the recombination spectrum below 0.7 eV, which indicate that precise calculation of the DR spectrum of multielectron ions is still a challenge.     

类铷W37+离子双电子复合速率系数的理论研究

 利用全相对论组态相互作用理论方法,研究了类铷W³⁷⁺离子从基组态3s²3p⁶3d¹⁰4s²4p⁶4d经过双激发态(3s²3p⁶3d¹⁰4s²4p⁶4d)^-1nln′l′(n,n′=4,5)的双电子复合过程,得到了该离子在温度为1~5×10⁴ eV范围内的总双电子复合速率系数。分析比较了不同电子激发的双电子复合速率系数,结果表明:4p电子激发的双电子复合速率系数在低温时给出了主要贡献,而3d的贡献在高温时突出。由于强组态相互作用,两电子一光子跃迁对双电子复合速率系数的贡献不可忽略,其中辐射跃迁4p⁵4d5d5f-4p⁶4f5d的贡献是双激发态4p⁵4d5d5f总的双电子复合速率系数的5%。对双电子复合、辐射复合以及三体复合速率系数的比较表明,在所研究的温度范围内双电子复合速率系数最大。