⇦Chinese Physics Letters, 2020, Vol. 37, No. 2, Article code 023401 Single- and Double-Electron Capture Processes in Low-Energy Collisions of N$^{4+}$ Ions with He * Kun Wang (王堃)1, Xiao-Xia Wang (王小霞)1, Yi-Zhi Qu (屈一至)1**, Chun-Hua Liu (刘春华)2, Ling Liu (刘玲)3, Yong Wu (吴勇)3, Robert J. Buenker4 Affiliations 1College of Optoelectronic Technology, University of Chinese Academy of Sciences, Beijing 100049 2School of Physics, Southeast University, Nanjing 210094 3Data Center for High Energy Density Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088 4Fachbereich C-Mathematik und Naturwissenschaften, Bergische Universitat Wuppertal, D-42097 Wuppertal, Germany Received 13 November 2019, online 18 January 2020 *Supported by the National Natural Science Foundation of China under Grant Nos. 11774344, 11474033 and 11574326, and the National Key Research and Development Program of China under Grant No. 2017YFA0402300.
**Corresponding author. Email: yzqu@ucas.ac.cn Citation Text: Wang K, Wang X X, Qu Y Z, Liu C H and Liu L et al 2020 Chin. Phys. Lett. 37 023401    Abstract We investigate the electron capture processes of N$^{4+}$(1$s^{2}2s$) colliding with He(1$s^{2}$) in the energy range of 10–1700 eV/amu using the quantum-mechanical molecular-orbital close-coupling (QMOCC) method. Total and state-selective single-electron capture and double-electron capture (SEC and DEC) cross sections are obtained and compared with other available studies. The results agree better with the experimental data in both trend and magnitude when the electron translation factor (ETF) effects are included. Our results indicate that both the SEC and DEC processes play important roles in the considered energy region. For the SEC processes, the N$^{3+}$(1$s^{2}2p^{2}$) + He$^{+}$(1$s$) states are the dominant capture states, and the N$^{2+}$(1$s^{2}2s2p^{2}$) + He$^{2+}$ states are the main DEC states. DOI:10.1088/0256-307X/37/2/023401 PACS:34.70.+e, 34.20.-b © 2020 Chinese Physics Society Article Text Electron capture processes of slow nitrogen ions colliding with atomic helium targets have been shown to be important in fusion plasmas and astrophysics. Nitrogen is one of the main impurities, while helium is a product in the fusion reactors, both of which appear at various relative energies in different ionization stages in the plasmas.[1,2] In addition, the solar wind contains many heavy ion species (H, He, C, N, O, Ne, S, Si, Fe, etc) with a range of charge states, the electron capture mechanisms of these ions with neutrals consequently involve the emission of photons in the extreme ultraviolet and x-ray part of the spectrum.[3] The description of the N$^{4+}$ + He collision system is quite challenging because this system contains numerous states that must be dealt with. The electron capture processes in low-energy collisions have so far been experimentally studied in the earlier works,[4–8] which measured the total single-electron capture and double-electron capture (SEC and DEC) cross sections. McLaughlin et al. employed the translational energy spectroscopy method to study the state-selective SEC cross sections in collisions of 4–28 keV ($\sim $285.6–1999.0 eV/amu) N$^{4+}$ ions with helium,[7] it was shown that the N$^{3+}$ (1$s^{2}2p^{2}\,{}^1\!S$) is the dominant product channel. Tergiman et al. theoretically obtained the total and state-selective SEC and DEC cross sections in the 1–50 keV ($\sim $71.4–3569.6 eV/amu) laboratory energy range by using a semiclassical approach.[9,10] However, not only their total SEC cross sections but also the total DEC cross sections have significant differences from the experimental data. The possible reason for this may be that the states they considered are not sufficient and some higher energy-level states, which are necessary to have an accurate interpretation of both single and double electron capture mechanism, are not included. In this work, we study the electron capture processes of the N$^{4+}$ ions colliding with atomic helium using the quantum-mechanical molecular-orbital close-coupling (QMOCC) method in the energy range of 10–1700 eV/amu. The adiabatic potentials and radial and rotational coupling-matrix elements used in the QMOCC calculations have been computed using the ab initio multi-reference single- and double-excitation configuration-interaction (MRD-CI) method.[11,12] First, the ab initio multi-reference configuration interaction (CI) calculations have been carried out for the adiabatic potential energies of 15  $^{2}\!{\it\Sigma}$ states in $A_{1}$ ($C_{2v}$) symmetry and 13  $^{2}\!{\it\Pi}$ states in the $B_{1}$ symmetry of the NHe$^{4+}$ system using the MRD-CI approach.[11,12] The $^{2}{\it\Delta}$ states have been disregard because the entrance channel is a doublet spin  $^{2}\!{\it\Sigma}$ state. The correlation-consistent polarized valence quadruple-zeta (cc-pVQZ) Gaussian basis sets[13,14] have been used for the nitrogen and helium atoms, with (1$s$, 1$p$, 1$d$) diffuse functions added to describe the Rydberg states of the nitrogen atoms. As a consequence, the (12$s$, 6$p$, 3$d$, 2$f$, 1$g$) contracted to [6$s$, 5$p$, 4$d$, 2$f$, 1$g$] basis set[13] is employed for nitrogen, while the (7$s$, 3$p$, 2$d$, 1$f$) basis set contracted to the [4$s$, 3$p$, 2$d$, 1$f$] basis set[14] is employed for helium. In the present CI calculation, all electrons are included. To select the configurations of NHe$^{4+}$ molecular ions, a threshold of 5.0$\times$10$^{-8}$ hartree (1.36$\times$10$^{-6}$ eV) is used[11,15–17] for internuclear distances of 1.0–100.0 a.u. Table 1 displays the excitation energies of the NHe$^{4+}$ molecular ion in the asymptotic region. The errors with respect to the National Institute of Standards and Technology (NIST) data[18] are less than 1795 cm$^{-1}$. This accuracy level should be adequate for the present scattering calculations.[19] The 15 $^{2}\!{\it\Sigma}$ state is the initial state and is shown in bold in Table 1. The calculated adiabatic potentials of the NHe$^{4+}$ molecular ion for internuclear distances $R = 1.0$–16.0 a.u. are shown in Figs. 1(a) and 1(b) with the potential curves for $^{2}\!{\it\Sigma}$ and $^{2}\!{\it\Pi}$ states, respectively. The 15 $^{2}\!{\it\Sigma}$ state represents the initial channel N$^{4+}$(1$s^{2}2s\,{}^{2}\!S$) + He(1$s^{2}$) for this collision system. Note that some sharp and narrow avoided crossings have been replaced by real crossings; i.e., the 15 $^{2}\!{\it\Sigma}$ state crosses the 10–14 $^{2}\!{\it\Sigma}$ states at $R \sim 6.36$, 6.73, 7.89 11.77 and 13.34, respectively. From the figures, it is found that there exist some complicated avoided crossings among the 5–9 and 15 $^{2}\!{\it\Sigma}$ states for internuclear distances $R = 2.0$–6.0 a.u., such as between the entry 15 $^{2}\!{\it\Sigma}$ and 9 $^{2}\!{\it\Sigma}$ ($N^{2+}$(1$s^{2}2s^{2}3s\,{}^{2}\!S$) + He$^{2+}$) states, the very sharp avoided crossing around $R \sim 4.9$ a.u. may drive the transition directly to the 9 $^{2}\!{\it\Sigma}$ exit state, between 9 $^{2}\!{\it\Sigma}$ and 8 $^{2}\!{\it\Sigma}$ ($N^{3+}$(1$s^{2}2p^{2}\,{}^1\!S$) + He$^{+}$(1$s)$) states, there is a strong avoided crossing around $R \sim 3.8$ a.u., which may make the 8 $^{2}\!{\it\Sigma}$ state to be the dominant SEC state as observed experimentally,[7] broader avoided crossings can be found between the SEC 8 $^{2}\!{\it\Sigma}$ and DEC 7 $^{2}\!{\it\Sigma}$ ($N^{2+}$(1$s^{2}2s2p^{2}\,{}^2\!P$) + He$^{2+}$) states around $R \sim 3.2$, 3.4 and 4.6 a.u., between the DEC 7 $^{2}\!{\it\Sigma}$ and SEC 6 $^{2}\!{\it\Sigma}$ ($N^{3+}$(1$s^{2}2p^{2}\,{}^1\!D$) + He$^{+}$(1$s)$) states around $R \sim 3.3$ a.u., and between the SEC 6 $^{2}\!{\it\Sigma}$ and DEC 5 $^{2}\!{\it\Sigma}$ ($N^{2+}$(1$s^{2}2s2p^{2}\,{}^{2}\!D$) + He$^{2+}$) states around $R \sim 2.2$ a.u. These complicated avoided crossings show a very complex electron-capture mechanism and should play a significant role in the collision dynamics. The energy curves of $^{2}\!{\it\Pi}$ states show a relatively simpler behavior. There are less avoided crossings for internuclear distances $R > 3.0$ a.u. It is important to note that for the internuclear distance range of $R < 3.0$ a.u., the potential curves of 5–9 $^{2}\!{\it\Sigma}$ and 4–7 $^{2}\!{\it\Pi}$ become very close, which implies that the radial and rotational couplings between them may be important in high collision energy region.
cpl-37-2-023401-fig1.png
Fig. 1. Potential curves of NHe$^{4+}$ molecular ions referring to Table 1: (a) $^{2}\!{\it\Sigma}$ states and (b) $^{2}\!{\it\Pi}$ states.
Table 1. Asymptotic separated-atom energies for the states of NHe$^{4+}$. Here 15 $^{2}\!{\it\Sigma}$ represents the initial state.
Molecular states Asymptotic atomic states Energy (cm$^{-1}$)
MRD-CI Ref. [18] Error
1 $^{2}\!{\it\Sigma}$ N$^{3+}$(1$s^{2}2sp^{2}\,{}^1\!S$) + He$^{+}$(1$s$) 0 0 0
2 $^{2}\!{\it\Sigma}$, 1 $^{2}\!{\it\Pi}$ N$^{3+}$(1$s^{2}2s2p$ $^{3}\!P^{\rm o})$ + He$^{+}$(1$s$) 67137 67209 $-72$
3 $^{2}\!{\it\Sigma}$, 2 $^{2}\!{\it\Pi}$ N$^{2+}$(1$s^{2}2s^{2}2p \,{}^{2}\!P^{\rm o})$ + He$^{2+}$ 57328 56237 1091
4 $^{2}\!{\it\Sigma}$, 3 $^{2}\!{\it\Pi}$ N$^{3+}$(1$s^{2}2s2p$ $^{1}\!P^{\rm o})$ + He$^{+}$(1$s$) 130856 130694 162
5 $^{2}\!{\it\Sigma}$, 4 $^{2}\!{\it\Pi}$ N$^{2+}$(1$s^{2}2s2p^{2}\, {}^{2}\!D$) + He$^{2+}$ 158207 157268 939
5 $^{2}\!{\it\Pi}$ N$^{3+}$(1$s^{2}2p^{2}\,{}^3\!P$) + He$^{+}$(1$s$) 175183 175535 $-352$
6 $^{2}\!{\it\Sigma}$, 6 $^{2}\!{\it\Pi}$ N$^{3+}$(1$s^{2}2p^{2}\,{}^1\!D$) + He$^{+}$(1$s$) 188733 188883 $-150$
7 $^{2}\!{\it\Sigma}$ N$^{2+}$(1$s^{2}2s2p^{2}\,{}^2\!S$) + He$^{2+}$ 188445 187241 1204
7 $^{2}\!{\it\Pi}$ N$^{2+}$(1$s^{2}2s2p^{2}\,{}^2\!P$) + He$^{2+}$ 203174 202112 1062
8 $^{2}\!{\it\Sigma}$ N$^{3+}$(1$s^{2}2p^{2}\,{}^1\!S$) + He$^{+}$(1$s$) 235637 235369 268
8 $^{2}\!{\it\Pi}$ N$^{2+}$(1$s^{2}2p^{3}\,{}^2\!D^{\rm o})$ + He$^{2+}$ 259945 259326 619
9 $^{2}\!{\it\Sigma}$ N$^{2+}$(1$s^{2}2s^{2}$3$s\,{}^{2}\!S$) + He$^{2+}$ 278377 277539 838
10 $^{2}\!{\it\Sigma}$, 9 $^{2}\!{\it\Pi}$ N$^{2+}$(1$s^{2}2p^{3}\,{}^{2}\!P^{\rm o})$ + He$^{2+}$ 287543 286641 902
11 $^{2}\!{\it\Sigma}$, 10 $^{2}\!{\it\Pi}$ N$^{2+}$(1$s^{2}2s^{2}3p \,{}^{2}\!P^{\rm o})$ + He$^{2+}$ 302793 301902 891
12 $^{2}\!{\it\Sigma}$, 11 $^{2}\!{\it\Pi}$ N$^{2+}$(1$s^{2}2s^{2}3d \,{}^{2}\!D$) + He$^{2+}$ 324448 323475 973
13 $^{2}\!{\it\Sigma}$, 12 $^{2}\!{\it\Pi}$ N$^{2+}$(1$s^{2}2s2p(^{3}\!P^{\rm o}$)3$s\,{}^{2}\!P^{\rm o})$ + He$^{2+}$ 354181 353387 794
13 $^{2}\!{\it\Pi}$ N$^{2+}$(1$s^{2}2s2p(^{3}\!P^{\rm o}$)3$p \,{}^{2}\!P$) + He$^{2+}$ 365875 365368 507
14 $^{2}\!{\it\Sigma}$ N$^{3+}$(1$s^{2}2s3s\,^{3}\!S$) + He$^{+}$(1$s$) 376807 377285 $-478$
15 $^{\mathbf{2}}\!{\it\Sigma}$ N$^{\mathbf{4+}}$(1${\boldsymbol s}^{\mathbf{2}}2{\boldsymbol s}\,^{\mathbf{2}}\!S$) + He(1${\boldsymbol s}^{\mathbf{2}}$) 424760 426555 $-1795$
Compared with the previous theoretical calculations of Tergiman et al.,[9] more Rydberg states have been considered in our work; i.e., 9–14 $^{2}\!{\it\Sigma}$ and 8–13 $^{2}\!{\it\Pi}$. The potentials of these Rydberg states and the more complicated radial and rotational couplings may play a significant role in the collision dynamics. The radial coupling matrix elements between all pairs of states in the same symmetry have been calculated by the finite difference approximation $$ A_{ij}^{R} =\langle \psi_{i} \vert \frac{\partial }{\partial R}\vert \psi_{i} \rangle =\lim\limits_{\Delta R\to 0} \frac{1}{\Delta R} \langle \psi_{i} (R)\vert \psi_{i} (R+\Delta R)\rangle,~~ \tag {1} $$ with a step size of 0.0002 a.u. Figures 2(a)–2(c) display some important radial coupling matrix elements of $^{2}\!{\it\Sigma}$ and $^{2}\!{\it\Pi}$ states for the NHe$^{4+}$ molecular ion. It is evident that the positions of the peaks are consistent with the avoided crossings of the adiabatic potentials observed in Fig. 1. Some important adiabatic rotational coupling matrix elements $A_{ij}^{\theta } = \langle \psi_{i} \vert iL_{y} \vert \psi_{j} \rangle$, which have been calculated analytically from the angular momentum tensor, are presented in Fig. 2(d). These couplings drive the transitions between states of the same spin but of different spatial symmetry.
cpl-37-2-023401-fig2.png
Fig. 2. Coupling matrix elements (CMEs) for NHe$^{4+}$: (a) and (b) radial CME between $^{2}\!{\it\Sigma}$ states, (c) radial CME between $^{2}\!{\it\Pi}$ states, and (d) rotational CME between $^{2}\!{\it\Sigma}$ and $^{2}\!{\it\Pi}$ states.
In the present work, the electron capture processes in ion-atom collisions have been investigated by the QMOCC method,[20–23] which has been mentioned many times in our previous papers.[24–26] The electron translation factors (ETFs),[27] which are often used to modify the molecular eigenfunctions to remove asymptotic couplings between atomic states, are made by introducing appropriate reaction coordinates[28,29] in the present work as they are expected to be important about $E > 1$ keV/amu.[30] Accordingly, the radial and rotational coupling matrix elements between the states $\psi_{K}$ and $\psi_{L}$ are, respectively, transformed into[31] $$ \langle {\psi_{K} \vert \frac{\partial }{\partial R}-\frac{(\varepsilon_{K} -\varepsilon_{L})z^{2}}{2R}\vert \psi_{L} } \rangle, $$ $$ \langle {\psi_{K} \vert iL_{y} +(\varepsilon_{K} -\varepsilon_{L})zx\vert \psi_{L} } \rangle,~~ \tag {2} $$ where $\varepsilon_{K}$ and $\varepsilon_{L}$ are the electronic energies of states $\psi_{K}$ and $\psi_{L}$, and $z^{2}$ and $zx$ are the components of the quadrupole moment tensor. The modification is similar in form to that resulting from the application of the common ETF method.[27]
cpl-37-2-023401-fig3.png
Fig. 3. Comparison between the present total SEC cross-section results for the N$^{4+}$(1$s^{2}2s)$ + He(1$s^{2}$) collision with other theoretical[9] and experimental[4–8] results. The present QMOCC calculation without ETF effects (solid line with filled squares), the present results including ETF effects (solid line with open circles), and the semiclassical results of Tergiman et al.[9] (short dash-dotted line with filled diamonds) are given. The experimental results of Iwai et al.[4] (filled pentagrams with error bars), Hoekstra et al.[5] (filled triangles), McLaughlin et al.[7] (filled circles) and Ishii et al.[8] (filled squares) are presented.
As shown in Fig. 3, when ETF effects are included, our calculations become more consistent with the experimental data in both trend and magnitude. The present total SEC cross sections are around 2 to 3.5$\times$10$^{-16}$ cm$^{2}$ in the energy region from 10 eV/amu to 1700 eV/amu and are compared with the available experimental[4–8] and theoretical[9] results. In the overlapping energy range of $E > 200$ eV/amu, our results are in good agreement with the experimental results of Iwai et al.[4] and are within their error bars. Moreover, in both trend and magnitude, our results are in good agreement with the results of Hoekstra et al.[5] and McLaughlin et al.[7] It seems that our results agree well with those of Ishii et al.[8] for $E < 60$ eV/amu, but are smaller than their results for the collisional energies $E > 80$ eV/amu. However, there is a jump in their experimental data around $E \sim 80$ eV/amu. Compared with the theoretical results of Tergiman et al.[9] including 16 channels by using a semiclassical approach, it can be seen that our results are in better agreement with the experimental data for both trend and magnitude. The possible reason may be: (1) our potential curves agree better with the experiment results—e.g., our error of the initial state energy in the asymptotic region is 1795 cm$^{-1}$ compared to the experimental data from NIST[18] (see Table 1), which is considerably smaller than theirs (about 4000 cm$^{-1}$); and (2) more channels are included in our calculations, i.e., the higher level states (9–14 $^{2}\!{\it\Sigma}$ and 8–13 $^{2}\!{\it\Pi}$), which should not be neglected in the single electron capture mechanism. To check the validity of our results further, the comparisons between the present state-selective SEC cross sections (ETF effects included) with other experimental[7] and theoretical[9] results are shown in Fig. 4. The cross sections to the N$^{3+}$(1$s^{2}2s^{2})$ + He$^{+}$(1$s$) states are not shown since they are too small. Among these SEC processes, the N$^{3+}$(1$s^{2}2p^{2})$ + He$^{+}$(1$s$) states are found to be dominant in the whole energy region considered, the values of the cross sections are nearly constant around 2 to 3$\times$10$^{-16}$ cm$^{2}$. Our results are in better agreement with the experimental data of McLaughlin et al.[7] than the theoretical ones of Tergiman et al.[9] in both trend and magnitude. For $E < 1$ keV/amu, the N$^{3+}$(1$s^{2}2s2p)$ + He$^{+}$(1$s$) states are the sub-dominant states, while the cross sections are more than one order of magnitude smaller than those to the dominant channels. For the energies higher than 1 keV/amu, the cross sections of the N$^{3+}$(1$s^{2}2s3s)$ + He$^{+}$(1$s$) states show an increasing trend and become sub-dominant. This is one reason why our total SEC cross sections (including 28 channels) agree with the experimental results[7] better than those of Tergiman et al.[9] (including only 16 channels without N$^{3+}$(1$s^{2}2s3s)$ + He$^{+}$(1$s)$), in the overlapping energy region as shown in Fig. 3.
cpl-37-2-023401-fig4.png
Fig. 4. Comparison between the present state-selective SEC cross sections (ETF effects considered) with other theoretical[9] and experimental[7] results.
The present total DEC cross sections are displayed in Fig. 5 and compared with available theoretical[9] and experimental[5,8] results. It should be noted that when considering the ETF effects, the results agree better with the experimental[5] data in both trend and magnitude for $E$ larger than $\sim $500 eV/amu, and for the collisional energies around 100 eV/amu, the modified results are also in better agreement with the data of Ishii et al.[8] It can be seen that the present results including 28 channels are around 3 to 5$\times$10$^{-16}$ cm$^{2}$ in the considered energy region and are in the same order of magnitude with the total SEC cross sections, and the trend generally agrees with the experimental results of Hoekstra et al.[5] in the overlapping energy range of $E > 500$ eV/amu. However, it must be noted that all the available experimental[5,8] data for the DEC processes have differences from not only the present but also the other theoretical[9] calculations, e.g., for $E > 1$ keV/amu, the results of the present work and of Tergiman et al.[9] are around 50% larger than the experimental data of Hoekstra et al.[5] Therefore, new experimental measurements are expected, especially in the low energy collision region.
cpl-37-2-023401-fig5.png
Fig. 5. Comparison between the present total DEC cross sections with other available theoretical[9] and experimental[5,8] results. The present QMOCC calculation without ETF effects (solid line with filled squares), the present results considering ETF effects (solid line with open circles), and the semiclassical results of Tergiman et al.[9] (short dash dotted line with filled triangles) are given. The experimental results of Hoekstra et al.[5] (filled triangles) and Ishii et al.[8] (filled squares) are presented.
cpl-37-2-023401-fig6.png
Fig. 6. The present state-selective cross sections for DEC processes (ETF effects considered).
In Fig. 6, the present state-selective cross sections (ETF effects included) for DEC processes are displayed. It can be seen that the dominant states of the DEC processes are the N$^{2+}$(1$s^{2}2s2p^{2})$ + He$^{2+}$ states, the values of the cross sections to the dominant channels are about 3 to 4$\times$10$^{-16}$ cm$^{2}$ and are more than 1 order of magnitude larger than other channels because the broader avoided crossings between 8 $^{2}\!{\it\Sigma}$ and 7 $^{2}\!{\it\Sigma}$ make the major contributions here, and they are consistent with the previous inferences from the molecular structure. In summary, the total and state-selective SEC and DEC cross sections have been obtained by employing the quantum-mechanical molecular-orbital close-coupling (QMOCC) method in the energy range from 10 eV/amu to 1700 eV/amu, where the multi-reference single- and double-excitation configuration interaction (MRD-CI) method is used to compute the ab initio potential curves and nonadiabatic coupling matrix elements. The present results indicate that both the SEC and DEC processes are of same importance in the considered energy region for the N$^{4+}$ + He collision system, and when considering the ETF effects, the results agree better with the experimental data in both trend and magnitude. For the SEC processes, compared with the available experimental[4–8] data, our results including 28 channels are in better agreement than those of Tergiman et al.[9,10] including only 16 channels. The N$^{3+}$(1$s^{2}2p^{2})$ + He$^{+}$(1$s$) states play the dominant role in the whole considered energy region. On the other hand, for the DEC processes, the dominant states are the N$^{2+}$(1$s^{2}2s2p^{2})$ + He$^{2+}$ states, the cross sections are more than 1 order of magnitude larger than those of other channels. However, all of the theoretical DEC cross sections have obvious differences from the available experimental data. New experimental measurements are expected, especially in the low energy collision region. References Chapter 1: Overview and summaryChapter 4: Power and particle controlSolar wind ion compositionCross sections for one-electron capture by highly stripped ions of B, C, N, O, F, Ne, and S from He below 1 keV/amuTwo- and more-electron transitions in slow multicharged ion-He collisionsApplication of mini-EBIS to cross section measurements of single and double electron capture in low energy collisions of C4+, N4+ and O4+ with HeState-selective electron capture by slow N 4+ ions in collisions with heliumElectron-capture cross sections of multiply charged slow ions of carbon, nitrogen, and oxygen in HeState-selective single and double electron capture in the collision of N 4 + with HeA new table‐direct configuration interaction method for the evaluation of Hamiltonian matrix elements in a basis of linear combinations of spin‐adapted functionsImplementation of the table CI method: Matrix elements between configurations with the same number of open-shellsGaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogenGaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response propertiesIndividualized configuration selection in CI calculations with subsequent energy extrapolationEnergy extrapolation in CI calculationsCombining perturbation theory techniques with variational CI calculations to study molecular excited statesStructure and couplings in the quasimoleculeDirect charge transfer of He + in neonThe multichannel log-derivative method for scattering calculationsCharge transfer of multiply charged ions at thermal energiesCharge transfer and excitation in slow proton collisions with sodiumRadiative and nonradiative charge transfer in collisions of Be 2 + and B 3 + ions with H atomsThe influence of pseudo states on the single-electron capture processes in low-energy collisions of N 5+ with HeOn the choice of translation factors for approximate molecular wavefunctionsInfluence of rotational coupling on charge transfer in low-energy C 4+ /H collisionsCommon translation factor methodAb initio molecular treatment of charge transfer by Si 4 + ions in helium
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