† Corresponding author. E-mail:
Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300) and the National Natural Science Foundation of China (Grant Nos. U1932207, 11904371, and U1732133).
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 semi-classical 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 q3.0, reproducing the low-energy recombination enhancement effects found in other previous experiments.
Electron–ion recombination is one of the most fundamental atomic collision processes, and plays an important role in plasma physics, astrophysics as well as accelerator physics.[1] The experimentally obtained electron–ion recombination rate coefficients can be not only used to study the energy level structure of highly charged ions, thereby testing the theoretical methods for atomic structures calculation, but also used as the basic input parameters for plasma diagnosis and modeling to interpret the emission spectrum of astrophysical and man-made plasmas.[2] Additionally, the electron–ion recombination also reduces the lifetime of the ion beam which leads to the positive ions loss mechanism during electron cooling, particularly at high ion charge state and high beam velocity when the residual gas processes become less important.[3] The electron–ion recombination with its large cross section and rates at the low energies also provides a very favorable scheme for the production of antihydrogen.[4] However, most of these electron–ion recombination cross sections are calculated by different theories with limited accuracy, and experimental studies to benchmark these theories are very important and have been already investigated for decades. There are two most dominating electron–ion recombination channels for low energy collision range called radiative recombination (RR) and dielectronic recombination (DR). The RR is a one-step non-resonant process where a free electron recombines with an ion by simultaneously emitting a photon to release the excess energy
The first radiative recombination experiment at low energy was performed by merging C6+ ion beam with an electron beam in a single pass arrangement by Andersen et al.[6] In that experiment a good agreement has been found between measured recombination rates and calculated results in the energy range from Erel = 0 eV to 1 eV, where Erel is the relative collision energy between electrons and ions. However, a significant enhancement effect beyond the theoretical calculation has been found in a range of low relative energies between electron and ions in the RR experiments. In order to understand this rate enhancement phenomenon, a series of electron–ion recombination experiments with many bare ions (D+, He2+, C6+, N7+, Ne10+, Si14+, Ar18+, Bi83+) have been performed to investigate this RR enhancement effect at different storage rings.[5,7–13] These works test the variation of electron beam density,[14] the influence of magnetic field,[5] and also the dependence of charge state.[9] Strong enhancement effects have been observed for all of these measured RR rate coefficients as compared with the theoretical rate coefficients at a very low electron–ion collision energies (Erel < 10 meV).
In addition to the bare-ions, the RR rate enhancement has also been observed in experiments with non-bare ions at the storage rings.[15–19] However, because of the complex electronic structure of non-bare ions, neither a concentrated study is available for these enhanced rates, nor have detailed quantitative spectra in low relative energy region have been presented. To explain this surprising discrepancy between the measured RR recombination rate coefficients and the theoretical predictions, several theoretical models and mechanisms have been proposed ranging from the contributions from three body recombination (TBR),[9] the electron density enhancement in the surrounding of the ions due to plasma screening effect[20] and the effect of magnetic field taking into account the chaotic dynamic as a result of the magnetic field inside the electron cooler which directly influence the cross sections.[21] Some of the models also included the contribution of transient field effects by a magnetic field in the electron-cooler[22] and relativistic effects by using Dirac–Slater method together with multichannel quantum defect theory (MQDT).[23,24] Finally, one model by taking into account of the transient field effects from a magnetic field explained the observed RR enhancement phenomenon with only bare ions.[25]
An approach presented in this work is mainly focused on the investigation of RR rate enhancement in electron–ion recombination spectra for non-bare highly charged ions. Recombination of Ar14+, Ar15+, Ca16+, and Ni19+ ions with electrons at low energy range have been investigated based on the merged-beam method at the main cooler storage ring CSRm. In order to interpret the measured results, RR cross sections were obtained from a modified version of the semi-classical 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 total rate coefficients show a good agreement with the measured rate coefficients above 100 meV. However, large discrepancies have been found at the low energy range especially below 10 meV. As the relative collision energy decreases below 1 meV, it is found that the observed recombination rates are a factor of 1.5 to 3.9 higher than the predicted rates. The dependence of RR rate coefficient enhancement as a function of the charge state of the ions has been obtained and compared with bare ions.
The article is arranged as follow. In Section
The measurement of electron–ion recombination with highly charged ions has been performed by employing the merged beams method at the CSRm at Institute of Modern Physics (IMP) in Lanzhou, China (See Fig.
The ion beams have been cooled for several seconds by employing electron cooler (EC-35) before starting a measurement until the beam profile reached to their equilibrium spread. The electron-beam was confined at the cathode section of the electron cooler with magnetic field of 125 mT and adiabatically expanded at the cooler section with 39 mT, respectively. This expansion gives rise to cold electron beam for high resolution spectroscopy. The magnetically confined electron beam at the cooler section has a radius of ∼ 25 mm, with a typical electron density of 1 × 106 cm−3. Besides electron cooling, the electron cooler is also used as an electron target during the electron–ion recombination measurement. For a change of the electrons energy from cooling energy, the detuning system has been applied to the cathode of the electron cooler. For introducing non-zero mean relative velocities between the electrons and ions, the electron energy was stepped through a preset range of values different from the cooling energy during the measurement cycle. The measurement cycle includes different detuning voltages of 1 V in laboratory system. In each measurement interval, the electron energy was detuned for 10 ms and again set to the cooling energy (Erel = 0) for 90 ms or 190 ms in order to maintain a good ion-beam quality. The recombined ions formed in the merging section were separated by the first dipole magnet downstream the electron cooler and detected by a scintillator detector.[30]
At storage rings, the recombination rate coefficients α measured at scanning energy Erel, between electron and ion is determined by
The calculation of the RR cross section is based on the modified semi-classical formula of Bethe & Salpeter in this work. RR of high-Z bare ions with cold electrons can be treated within the non-relativistic dipole approximation. Bethe and Salpeter derived a simple formula for RR cross section calculation,[32]
In the present experiments all of the ions which have been measured are non-bare and the contribution from DR resonance process could not be avoided. Therefore, the DR process must be considered in the theoretical calculations for better investigation of the electron–ion recombination spectra at very low energy range. The theoretical calculations of DR for Be-like Ar14+ and Be-like Ca16+ have been performed by using distorted-wave collision package AUTOSTRUCTURE.[33] For the Li-like Ar15+ and F-like Ni19+ the FAC[34] was used to calculate DR resonance cross sections. It should be noted that the difference between these two codes are described in Ref. [35] The integrated DR cross section for state d can be written as
Figure
![](cpb_29_3_033401/cpb_29_3_033401_ieqn1.gif)
![](cpb_29_3_033401/cpb_29_3_033401_ieqn2.gif)
![](cpb_29_3_033401/cpb_29_3_033401_ieqn3.gif)
![](cpb_29_3_033401/cpb_29_3_033401_ieqn4.gif)
Therefore, from the fitting of the line profile given by Eq. (
From the theoretical model described in,[38] the relationship between the recombination rate coefficient enhancement ΔαRR to the main physical parameters concerning to electron–ion recombination experiments can be written as
![]() | Fig. 3. (a) The dependence of the RR rate coefficient enhancement Δα of bare-ions on charge state of ions. The violet empty triangles represents experimental data of the CRYRING[8,9] and the blue color empty square is the TSR data.[5] The error bars represent the contribution from the uncertainty of the excess rate, in this plot 20% uncertainty has been assumed for all the data. The solid line is the q2.8 scaling for the bare ions. (b) The dependence of the RR rate coefficient enhancement Δα of non-bare ions on the charge state q of the ions. The empty green circles represent experimental RR rate enhancement data of the CSRm for non-bare ions. The 30% experimental uncertainty has been taken and the solid red line is the q3.0 scaling. |
In Fig.
In Fig.
In this work, a series of measurement of the absolute recombination rate coefficients of Be-like Ar14+, Li-like Ar15+, Be-like Ca16+, and F-like Ni19+ have been performed at the storage ring CSRm at Institute of Modern Physics, Lanzhou, China. Data analysis is focused on the electron–ion collision energy range from 0 meV to1000 meV. The experimental electron–ion recombination spectra have been fitted with flattened Maxwellian function which include the contributions from RR and DR processes. The theoretical results for RR rate coefficients were calculated by using modified semi-classical formula given by Bethe and Salpeter (1957). The contribution from DR rate coefficients to the recombination spectra were calculated by employing AUTOSTRUCTUTRE and FAC codes. A strong enhancement of the measured RR rate coefficient over the fitted and calculated rate coefficients have been observed in all recombination spectra for the collision energies below 10 meV.
The present evaluation of the nuclear charge dependence of the RR rate enhancement Δα results in ∼ Z3.0 scaling for non-bare ions. We have also compared our results with the RR enhancement factors from other storage rings for bare ions. Our recent findings indicate that the RR rate enhancement is a general phenomenon found in all storage ring measurements for both bare and non-bare ions. A smooth dependence of RR rate coefficient enhancement on nuclear charge states has been found for bare-ions. For the non-bare ions the RR rate enhancement dependence on nuclear charge is not smooth, which indicates that the enhancement is partly coming from the low-n DR resonances located close to the threshold. In addition, we have also pointed out that the RR enhancement rate strongly influences the DR resonances at very low relative energies which will also be translated to the plasma rate coefficient used for astrophysical implications.
[1] | |
[2] | |
[3] | |
[4] | |
[5] | |
[6] | |
[7] | |
[8] | |
[9] | |
[10] | |
[11] | |
[12] | |
[13] | |
[14] | |
[15] | |
[16] | |
[17] | |
[18] | |
[19] | |
[20] | |
[21] | |
[22] | |
[23] | |
[24] | |
[25] | |
[26] | |
[27] | |
[28] | |
[29] | |
[30] | |
[31] | |
[32] | |
[33] | |
[34] | |
[35] | |
[36] | |
[37] | |
[38] | |
[39] |