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Since its initial development in the 1970s by Phil Burke and his collaborators, the R-matrix theory and associated computer codes have become the method of choice for the calculation of accurate data for general electron–atom/ion/molecule collision and photoionization processes. The use of a non-orthogonal set of orbitals based on B-splines, now called the B-spline R-matrix (BSR) approach, was pioneered by Zatsarinny. It has considerably extended the flexibility of the approach and improved particularly the treatment of complex many-electron atomic and ionic targets, for which accurate data are needed in many modelling applications for processes involving low-temperature plasmas. Both the original R-matrix approach and the BSR method have been extended to the interaction of short, intense electromagnetic (EM) radiation with atoms and molecules. Here, we provide an overview of the theoretical tools that were required to facilitate the extension of the theory to the time domain. As an example of a practical application, we show results for two-photon ionization of argon by intense short-pulse extreme ultraviolet radiation. 

We reinvestigate a key process in electron-atom collision physics, the elastic scattering of electrons from helium atoms. Specifically, results from a special-purpose relativistic polarized-orbital method, which is designed to treat elastic scattering only, are compared with those from a very extensive, fully ab initio, general-purpose B-spline R-matrix (close-coupling) code. 

We have applied the full-relativistic Dirac B-Spline R-matrix method to obtain cross sections for electron scattering from ytterbium atoms. The results are compared with those obtained from a semi-relativistic (Breit-Pauli) model-potential approach and the few available experimental data. 

Cross sections for electron scattering from atomic and molecular iodine are calculated based on the R-matrix (close-coupling) method. Elastic and electronic excitation cross sections are presented for both I and I2. The dissociative electron attachment and vibrational excitation cross sections of the iodine molecule are obtained using the local complex potential approximation. Ionization cross sections are also computed for I2 using the BEB model. 

The Quantemol database (QDB) provides cross sections and rates of processes important for plasma models; heavy particle collisions (chemical reactions) and electron collision processes are considered. The current version of QDB has data on 28 917 processes between 2485 distinct species plus data for surface processes. These data are available via a web interface or can be delivered directly to plasma models using an application program interface; data are available in formats suitable for direct input into a variety of popular plasma modeling codes including HPEM, COMSOL, ChemKIN, CFD-ACE+, and VisGlow. QDB provides ready assembled plasma chemistries plus the ability to build bespoke chemistries. The database also provides a Boltzmann solver for electron dynamics and a zero-dimensional model. Thesedevelopments, use cases involving O₂, Ar/NF₃, Ar/NF₃/O₂, and He/H₂O/O₂chemistries, and plans for the future are presented.