R-matrix with pseudo-states for electron collisions with atoms and ions: theory, calculations, and applications of the data

Accurate data for charged-particle collisions with atoms, ions, and molecules are required for many modelling applications in plasma science. Since it is virtually impossible to measure all the data needed for state-of-the-art collisional radiative models (CRMs), much of the responsibility for generating sufficiently comprehensive datasets has been put on theory. There is a vast variety of methods available to generate the data, ranging from classical to semi-classical to fully quantal approaches.

Here I will concentrate on one of those widely-used approaches, which is based on the R-matrix approach to solve the close-coupling equations for electron collisions with atoms and ions. In recent years, rapid advances in available hardware, hand-in-hand with sophisticated software development, have made it possible to solve the collision problem for quasi-one- and quasi-two electron systems with very high accuracy. The key idea is to enhance the usual close-coupling expansion containing a few physical discrete target states by adding a large number of so-called pseudo-states to account for the coupling to the high-lying Rydberg states as well as the ionization continuum. Accurate predictions for state-to-state elastic, momentum-transfer, and excitation cross sections between the physical target states can now be made, and ionization cross sections can be obtained fully ab initio. More complex, open-shell targets remain a challenge, but much progress has been made on those as well. Many results are publicly available on data bases such as LXCAT [1].

I will discuss the basic ideas behind the R-matrix with pseudo-states approach and their implementation in the Belfast package [2] and Zatsarinny's B-spline R-matrix code [3], which has been very successful for both structure and collision problems [4]. I will also illustrate how fundamental research can empower technological advancements [5].

[1] https://us.lxcat.net/home/

[2] K. A. Berrington et al., Comp. Phys. Commun. 92 (1995) 290

[3] O. Zatsarinny, Comp. Phys. Commun. 174 (2006) 273

[4] O. Zatsarinny and K. Bartschat, J. Phys. B 46 (2013) 112001

[5] K. Bartschat and M. J. Kushner, Proc. Nat. Acad. Sci. 113 (2016) 7026