Large-scale $R$-matrix-with-pseudostates calculations for electron collisions with argon atoms, using a recently developed parallel version of our B-spline $R$-matrix code, are reported. The calculations were carried out in the semirelativistic $\mathit{jK}$-coupling scheme. They are intended to provide converged (with respect to the number of coupled states) results for electron-impact excitation of individual target states with dominant configurations $3p^{5}4s$, $3p^{5}4p$, $3p^{5}3d$, and $3p^{5}5s$ for incident electron energies from threshold to 300 eV. The close-coupling expansion includes 500 target states, with the lowest 78 states representing the bound spectrum and the remaining 422 the ionization continuum. The results reveal dramatic reductions of the predicted excitation cross sections at intermediate energies due to a strong influence of coupling to the target continuum and the higher-lying Rydberg states. Comparison with available experimental data for excitation raises questions about the absolute normalization in the measurements.

The $B$-spline $R$-matrix-with-pseudostates (BSR) method is employed to treat electron collisions with nitrogen atoms. Predictions for elastic scattering, excitation, and ionization are presented for all transitions between the lowest 21 states of nitrogen in the energy range from threshold to 120 eV. The structure description has been further improved compared to a previous BSR calculation by Tayal and Zatsarinny [ J. Phys. B 38, 3631 (2005)]. This change in the structure model, together with the inclusion of a large number of pseudostates in the close-coupling expansion, has a major influence on the theoretical predictions, especially at intermediate energies, where many of the excitation cross sections are reduced significantly. Ionization cross sections for the ground and metastable initial states are also provided. Finally, we carry out an accurate ab initio treatment of the prominent shape resonance just above the elastic threshold.

The $B$-spline $R$-matrix method with nonorthogonal orbital sets is extended to a fully relativistic version based on the solution of the many-electron Dirac equation. The $B$-spline basis is used to generate both the target description and the $R$-matrix basis functions in the inner region. Using $B$-splines of different orders for the large and small components prevents the appearance of pseudostates in the spectrum of the Dirac equation. Using term-dependent and thus nonorthogonal sets of one-electron functions enables us to generate accurate and flexible representations of the target states and the scattering function. Our method is based upon the all-electron Dirac-Coulomb Hamiltonian and thus may be employed for any complex atom or ion, without the use of phenomenological core potentials. As a first test of the method, we consider elastic electron scattering from Cs atoms in their ground state. Close agreement with experiment is obtained for the total and the angle differential cross sections at various energies between 1 eV to 7 eV, as well as for several spin asymmetry parameters. The results represent a substantial improvement over those obtained in previous Breit-Pauli and Dirac $R$-matrix calculations.

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Electron scattering with atomic oxygen has been studied using the $B$-spline $R$-matrix-with-pseudostates method. Cross sections for elastic scattering, excitation, emission, and ionization processes are presented. The excitation cross sections have been calculated for transitions between the $2s^{2}2p^4$ and $2s^{2}2p^{3}3l$ states of oxygen in the energy range from threshold to 200 eV. The present work differs from numerous previous studies due to the inclusion of a large number of pseudostates in the calculation. We included a total of 1116 spectroscopic bound, core-excited autoionizing, and target continuum states in the close-coupling expansion. The atomic oxygen structure model has been described by combining the multiconfiguration Hartree-Fock and the $B$-spline box-based multichannel methods. The inclusion of a large number of pseudostates representing the target continuum has a major impact, especially on the theoretical prediction of the excitation cross sections for many transitions at intermediate energies. A large reduction in excitation and emission cross sections has been noted due to the inclusion of coupling to the ionization continuum. The calculated cross sections are now in better agreement with available experimental results. The ionization cross sections for the ground $2s^{2}2p^4{}^{3}P$ and metastable $2s^{2}2p^4{}^{1}D$ and ${}^{1}S$ states are also presented. The electron-impact-induced emission cross sections for the $\left(2s^{2}2p^{3}3s\right){}^3{S}^o–\left(2s^{2}2p^4\right){}^{3}P$ (130.4 nm), $\left(2s^{2}2p^{3}3d\right){}^3{D}^o–\left(2s^{2}2p^4\right){}^{3}P$ (102.7 nm), $\left(2s^{2}2p^{3}3s^{\prime }\right){}^3{D}^o–\left(2s^{2}2p^4\right){}^{3}P$ (98.9 nm), and $\left(2s^{2}2p^{3}3s^{\prime \prime }\right){}^3{D}^o–\left(2s^{2}2p^4\right){}^{3}P$ (87.8 nm) transitions have been calculated and compared with the available experimental results.