Electron Impact Excitation Rate Coefficients Research Articles

Excitation and recombination studies with silicon and sulphur ions at an EBIT

Measurements of electron-impact excitation and recombination rate coefficients of highly charged Si and S ions at the Stockholm electron beam ion trap are reported. The experimental method was a combination of photon detection from the trapped ions during probing and subsequently extraction and time-of-flight (TOF) charge analysis of these ions. The TOF technique allows to measure recombination rate coefficients separately for every charge state, and together with the photon spectra of these ions also the excitation rate coefficients. In this paper, we present more details of the experimental procedure and summarize the experimental results in comparison with two different state-of-the-art calculations of recombination and excitation rates for Si10+–Si13+ and S12+–S15+ ions. One of these uses a relativistic configuration interaction approach (flexible atomic code) and the other is a relativistic many-body perturbation theory. A good to excellent agreement with both of them is found in energy and resonance strength for the investigated ions.

Fine structure resolved excitation cross sections of singly ionized Ga for the modeling and diagnostics of Ga plasmas

Calculation of electron impact excitation cross sections for singly charged Ga ions plays a crucial role in plasma modeling, facilitating the comprehension of plasma behavior, characteristics, and dynamics in diverse domains, such as astrophysics, fusion research, the semiconductor industry, etc. In the available literature, there is a notable scarcity of, or even a complete absence of, these cross sections. Hence, in the present work, electron impact excitation cross sections are calculated for the transitions from the fine structure resolved energy levels of the configurations 4s2 and 4s4p to the fine structure resolved energy levels of the configurations 4s4p , 4s5s , 4p2 and 4s4d of the singly charged Ga ion (Ga+) using the relativistic distorted wave approximation theory with the target states represented by multi configurational Dirac Fock wavefunctions. The cross sections are calculated for projectile electron energy varying from threshold to 500 eV. Furthermore, the electron impact excitation rate coefficients for all the transitions under investigation are also calculated for electron temperatures ranging from 0.5 to 5 eV. In addition, analytic fitting of the rate coefficients is also performed, providing a practical resource for directly utilizing in plasma modeling applications.

Calculations of electron-impact excitation and dielectronic recombination rate coefficients of highly charged silicon ions

The rate coefficients for dielectronic recombination and electron-impact excitation processes with H-like to Be-like silicon ions (${\mathrm{Si}}^{13+}\text{\ensuremath{-}}{\mathrm{Si}}^{10+}$) are calculated using relativistic distorted-wave approach. The prominent $▵n=1$ and the weaker $▵n=2$ and 3 dielectronic recombination (DR) resonances with $K$-shell excitations are presented, and compared with the existing DR experimental rate coefficients of ${\mathrm{Si}}^{13+}, {\mathrm{Si}}^{12+}$, and ${\mathrm{Si}}^{11+}$ ions, it is found that the theoretical DR rate coefficients are in very good agreement with the experimental results. With the same approach, the direct and resonant electron-impact excitation (EIE) cross sections associated with $1s\ensuremath{-}{n}^{\ensuremath{'}}{l}^{\ensuremath{'}}$ core excitations are calculated for the ground states of ${\mathrm{Si}}^{13+}\text{\ensuremath{-}}{\mathrm{Si}}^{10+}$ ions and found in excellent agreement with the available experiment. Finally, we present the synthesized DR and EIE rate coefficients for the sum of all detected $(13+\ensuremath{\sim}10+)$ charge states of Si and these agree well with the experimental results.

Atomic data calculations for Au i–Au iii and exploration in the application of collisional-radiative theory to laboratory and neutron star merger plasmas

ABSTRACT Neutron binary star mergers have long been proposed as sufficiently neutron rich environments that could support the synthesis of rapid neutron capture elements (r-process elements) such as gold. However, the literature reveals that beyond neutral and singly ionized systems, there is an incompleteness of atomic data for the remaining ion stages of importance for mergers. In this work, we report on relativistic atomic structure calculations for Au i–Au iii using the grasp0 codes. Comparisons to calculations using the Flexible Atomic Code suggest uncertainties on average of 9.2 per cent, 5.7 per cent, and 3.8 per cent for Au i–Au iii level energies. Agreement around ∼50 per cent is achieved between our computed A-values and those in the literature, where available. Using the grasp0 structure of Au i, we calculated electron-impact excitation rate coefficients and use a collisional-radiative model to explore the excitation dynamics and line ratio diagnostics possible in neutron star merger environments. We find that proper accounting of metastable populations is critical for extracting useful information from ultraviolet–visible line ratio diagnostics of Au i. As a test of our data, we applied our electron-impact data to study a gold hollow cathode spectrum in the literature and diagnosed the plasma conditions as Te = 3.1 ± 1.2 eV and $n_\textrm {e} = 2.7^{+1.3}_{-0.9}\times 10^{13}$ cm−3.

Electron-impact rotational excitation cross-sections and rate coefficients of molecular ion: HCO+

ABSTRACT HCO+ is one of the most abundant polyatomic ion in the Universe, also its presence in the planetary atmospheres and interstellar medium (ISM) makes it an interesting case to study. Low energy e−-HCO+ collisions result in rotational excitation and other molecular processes. In this study, the cross-sections for rotational transitions in HCO+ are evaluated for four rotational levels (j = 0, 1, 2, and 3) using the UK R-matrix method and the multichannel quantum defect theory (MQDT). The UK R-matrix method used to generate scattering matrices, through which cross-sections are computed. In past two decades, after developments and implementations of different theoretical approaches, the improved channel elimination procedure applied here is more promising to evaluate more accurate results near rotational thresholds important for the analysis of intensities of microwave region in plasma modelling. The rate coefficients are deduced from the computed cross-sections and studied over a wide electron temperature range.

Electron-impact recombination and excitation rates for charge-state-selected highly charged Si ions

Charge-state selective recombination rate coefficients were measured by time of flight (TOF) analyzed highly charged Si ions extracted from an electron-beam ion trap. Additionally, the combination of simultaneous TOF and x-ray measurements and a separation of the dielectronic recombination contribution in the x-ray spectra is used for extracting electron-impact excitation rate coefficients for several overlaying charge states. Experimentally derived dielectronic recombination spectra for XIII and XIV Si are compared and found in excellent agreement with the results of relativistic many-body perturbation theory calculations.

Calculations of Dielectronic Recombination and Electron-impact Excitation Rate Coefficients of Highly Charged Sulfur Ions

Abstract Connected to the experiment performed at the Stockholm electron beam ion trap, a systematic relativistic configuration-interaction calculation is carried out to compare with the experimental spectra. In particular, separate rate coefficients are calculated for dominant recombination and excitation processes in the range of the impact electron energy determined by the experiment. By means of the relevant experimental parameters, the presently calculated dielectronic recombination rate coefficients for and S14+ ions and electron-impact excitation ones for S15+, S14+, and S13+ ions are employed further to synthesize overall theoretical spectra for comparison with the experimentally measured spectra. Overall, very good agreements with the experimental results are found except for one missing excitation peak around the impact electron energy 2.52 keV, which cannot be explained by the present calculations and thus remains open.

Resonance contribution to electron-impact excitation rate coefficients of helium-like S14+ ions

SynopsisElectron-impact excitation rate coefficients of S14+ ions have been studied by using a relativistic flexible atomic code that can account systematically for configuration interactions. Moreover, we also considered the resonance excitation contributions to the rate coefficients. It is found that the contributions of resonance excitation on rate coefficients is very important.

Energy levels, oscillator strengths, radiative transition probabilities, level lifetimes and electron-impact excitation rate coefficients for Ne-like Mo XXXIII

The energy levels, oscillator strengths, radiative decay rates, lifetimes, collision strengths, direct and resonance electron-impact excitation rate coefficients have been computed for the 257 fine-structure levels arising from 1s22s22p5nl and 1s22s2p6n′l′ configurations belonging to the Mo32+ ion with n≤7, l≤4 and n′≤5, l′≤4. The model-potential approach is used for the target ion structure calculations. Additionally, we employ the multiconfiguration Dirac–Hartree–Fock method to further assess the energy levels and transition probabilities. The collision strengths for the electron-impact direct excitation are computed within the relativistic distorted-wave approximation at 34, 135, 680, 1700, 5436, and 12,740 eV scattered electron energy values. We also perform collision calculations at 85, 175, and 450 keV electron energies using the plane-wave approximation and interpolate the reduced cross section within Fano plots, thus accounting for relativistic effects at asymptotic energies. This assures the convergence of Maxwellian integration for effective collision strengths calculation at electron temperatures up to 80 keV. The resonance contribution to the excitation rates is accounted for within the independent process isolated resonance approximation by including Na-like Mo31+ doubly excited autoionization states arising from the 1s227nln′l′ configurations with n≤7,l≤4,n′≤20,l′≤8. Contributions from high n′≥21 Rydberg states to the excitation rate coefficients are included by employing the n′−3 extrapolation law for radiative and autoionization decay rates. Radiative decay of resonances to lower autoionization states followed by autoionization cascade as well as radiative damping via core transitions are included in our model. The highest rate coefficients corresponding to ground state excitations are the 2p–3d allowed and 2p–3p electric monopole transitions, respectively. Intercombination and generally higher-order electric multipole transitions amount to lower excitation rate coefficients but are not to be neglected. Magnetic transitions are only relevant for low electron temperatures since both their direct and resonance contributions to excitation significantly decrease with increasing electron energy. Present results compare well with existing data from literature. The resonance contributions play an important role in the accuracy of rate coefficients, especially for weak forbidden transitions at low electron temperatures. These results may be useful in fusion related plasmas, astrophysics and fundamental physics.

Excitation of Electronic States of N2 in Radio-Frequency Electric Field by Electron Impact

Electron impact excitation rate coefficients for singlet and triplet electronic states of the carbon monoxide molecule have been calculated under non-equilibrium conditions in the presence of radio-frequency electric field. A Monte Carlo simulation of electron transport has been performed in order to determine non-equilibrium electron energy distribution functions within one period of applied electric field. By using these distribution functions and corresponding cross sections, the excitation rate coefficients have been calculated for all electronic states of CO in the frequency range from 13.56 up to 500 MHz, at reduced root mean square electric field values ranging from 200 to 700 Td. We expect these rates to be valuable for modeling radio-frequency CO plasmas since excited neutrals exhibit greater chemical reactivity than neutrals in ground electronic state, hence altering many properties of plasma.

Calculation of fully relativistic cross sections for electron excitation of cesium atom and its application to the diagnostics of hydrogen-cesium plasma

Electron impact excitation cross-sections and rate coefficients have been calculated using fully relativistic distorted wave theory for several fine-structure transitions from the ground as well as excited states of cesium atom in the wide range of incident electron energy. These processes play dominant role in low pressure hydrogen-cesium plasma, which is relevant to the negative ion based neutral beam injectors for the ITER project. As an application, the calculated detailed cross-sections are used to construct a reliable collisional radiative (CR) model to characterize the hydrogen-cesium plasma. Other processes such as radiative population transfer, electron impact ionization and mutual neutralization of Cs+ ion with negative hydrogen ion along with their reverse processes are also taken into account. The calculated cross-sections and the extracted plasma parameters from the present model are compared with the available experimental and theoretical results.

Laser gain calculations for soft X-ray and XUV radiation emitted from copper-like ions by electron collisional pumping

Electron impact excitation rate coefficients, level population densities, and gain coefficients for six excited ions with Z = 51, 52, 53, 54, 55, 56 in the copper isoelectronic sequence have been calculated. The electron collisional excitation rate coefficients are calculated according to the analytical formulas of Vriens and Smeets. Fine structure energy levels, transition probabilities, and oscillator strengths needed in the calculations have been calculated using Cowan atomic structure code with relativistic corrections for [Ar]3d10nl with n = 4–7 and l = 0–6. The level population densities are calculated by solving the coupled rate equations involving 30 levels. Positive gain coefficients of the possible emitted lines are obtained at three selected electron temperatures, namely 1/4, 1/2, and 3/4 of the ionization energy. The present calculated data show promising values for the production of soft X-ray and XUV laser by collisional pumping for the transitions 5p–5s and 6d–5f with wavelengths between 108 and 571 Å. The values of the maximum gain coefficient are found to increase with atomic number and their order of magnitude ranges from102to 104cm−1.

Electron-impact excitation rate-coefficients and polarization of subsequent emission for Ar+ ion

Electron impact excitation in Ar+ ions has been studied by using fully relativistic distorted wave theory. Calculations are performed to obtain the excitation cross-sections and rate-coefficients for the transitions from the ground state 3p5 (J=3/2) to fine-structure levels of excited states 3p44s, 3p44p, 3p45s, 3p45p, 3p43d and 3p44d. Polarization of the radiation following the excitation has been calculated using the obtained magnetic sub-level cross-sections. Comparison of the present rate-coefficients is also done with the previously reported theoretical results for some unresolved fine structure transitions.

Measurement of the electron-impact excitation rate coefficients from argon 1s states to 3p states

The apparent rate coefficients for the electron-impact excitation from argon 1s to 3p states are determined in the electron temperature (Te) range of 0.8 to 1.2 eV, in the afterglow of a capacitive argon discharge by using the temporal behavior of different state densities. The measured parameters include the densities of the 3p states (by optical emission), the densities of the four argon 1s states (by diode laser absorption) and Te (by a Langmuir probe and a line-ratio technique). Among the 24 rate coefficients obtained in this work, the results for excitation from the two resonance states (1s2 and 1s4) are reported here for the first time. As for the excitation from the two metastable states (1s3 and 1s5), the measured rate coefficients are compared with the available values from the distorted wave method and the electron beam experiment.

Generalized collisional radiative model for light elements: C: Data for the B isonuclear sequence

A first stage collision database is assembled which contains electron-impact excitation, ionization, and recombination rate coefficients for B, B+, B2+, B3+, and B4+. The first stage database is constructed using the R-matrix with pseudostates, time-dependent close-coupling, and perturbative distorted-wave methods. A second stage collision database is then assembled which contains generalized collisional-radiative ionization, recombination, and power loss rate coefficients as a function of both temperature and density. The second stage database is constructed by solution of the collisional-radiative equations in the quasi-static equilibrium approximation using the first stage database. Both collision database stages reside in electronic form at the IAEA Labeled Atomic Data Interface (ALADDIN) database and the Atomic Data Analysis Structure (ADAS) open database.

Determination of the rate coefficients of the electron-impact excitation from the metastable states to 2p states of argon by the emission line ratios in an afterglow plasma

The rate coefficients of electron-impact excitation from the argon metastable to 2p states are measured in the afterglow of an rf pulsed capacitive discharge. In the afterglow, the 2p state densities are measured by optical emission spectroscopy, the time-resolved 1s state densities are measured by laser absorption, the time-resolved electron temperature (Te) and electron density are measured by a Langmuir probe. By employing these measured parameters, the electron-impact excitation rate coefficients are obtained from the rate balance equations of 2p states in the Te range from 0.7 to 1.2 eV. The measured rate coefficients are in good agreement with those obtained from the cross sections measured by Boffard et al. In addition, we obtain rate coefficients of the transitions from the metastable states to 2p1,7,10, whose measured values have not been reported before. These rate coefficients are also compared with the calculated ones (Zatsarinny et al with the R-matrix method, Srivastava et al with the Distorted wave method).

Emission spectroscopy of Ar + H2 + C7H8 plasmas: C7H8 flow rate dependence and pressure dependence

We have studied toluene flow rate dependence and pressure dependence of Ar emission intensities at 425.9 nm, 750.4 nm and 811.5 nm for Ar + H2 + C7H8 plasmas. Electron density and the electron impact excitation rate coefficients are nearly the same for Ar(100%) and Ar+H2(33%) plasmas. Toluene addition leads to a decrease in the high energy electron density, whereas the effective electron temperature and low energy electron density remain almost the same. The effective electron temperature, and Ar metastable density and/or low energy electron density decrease significantly with increasing the total pressure from 0.1 to 5 Torr.

Atomic and Molecular Databases and Data Evaluation Activities at the National Institute for Fusion Science

We have constructed and opened atomic and molecular (AM) numerical databases for collision processes important for fusion research. Our databases are accessible through the Internet; the data are retrievable and are displayed as a table or a graph. The databases have been used for data evaluation. Critical assessments of AM data have been carried out since 1978 for electron impact ionization and excitation cross sections, rate coefficients, and charge-transfer cross sections of atom-ion collisions, for helium, carbon, oxygen, etc. Evaluated data are fitted to analytic formulas that have physically correct asymptotic behavior. As another type of evaluation, recommended data sets were selected for electron impact excitation rate coefficients of Fe atoms and ions. Because a large amount of data exists, recommended data are not fitted to analytic formulas, but all data are available as electronic files via the Internet. In addition to AM data, physical sputtering yields and backscattering coefficients are also stored as databases, and empirical formulas have been obtained since the 1980s. All evaluated data are published as research reports of the Institute for Plasma Physics of Nagoya University and the National Institute for Fusion Science of Japan. It is important to establish a systematic way for data evaluation by international collaborations to develop an evaluated AM database required for fusion research.

Electron-impact excitation and ionization of W3+ for the determination of tungsten influx in a fusion plasma

Tungsten will be employed as a plasma facing material in the ITER fusion reactor under construction in Cadarache, France; therefore, there is a significant need for accurate electron-impact excitation and ionization data for the ions of tungsten. We report on the results of extensive calculations of ionization and excitation for W3+ that are intended to provide the atomic data needed for the determination of impurity influx diagnostics of tungsten in several existing tokamak reactors. The electron-impact excitation rate coefficients for this study were determined using the relativistic R-matrix method. The contribution to direct electron-impact ionization was determined using the distorted-wave approximation, the accuracy of which was verified by an R-matrix with pseudo states calculation. Contributions to total ionization from excitation autoionization were also generated from the relativistic R-matrix method. These results were then employed to calculate values of ionization per emitted photon, or SXB ratios, for four carefully selected spectral lines; these data will allow the determination of impurity influx from tungsten facing surfaces. For the range of densities of importance in the edge region of a tokamak reactor, these SXB ratios are found to be nearly independent of electron density but vary significantly with electron temperature.

Electron-impact resonant vibration excitation cross sections and rate coefficients for carbon monoxide

Resonant vibrational and rotation–vibration excitation cross sections for electron–CO scattering are calculated in the 0–10 eV energy range for all 81 vibrational states of CO, assuming that the excitation occurs via the 2Π shape resonance. Static exchange plus polarization calculations performed using the R-matrix method are used to estimate resonance positions and widths as functions of internuclear separation. The effects of nuclear motion are considered using a local-complex-potential model. Good agreement is obtained with available experimental data on excitation from the vibrational ground state. Excitation rates and cross sections are provided as a function of the initial CO vibrational state for all ground state vibrational levels.