Generalizations of the R-Matrix Method to the Treatment of the Interaction of Short-Pulse Electromagnetic Radiation with Atoms

Barry I Schneider,Klaus Bartschat,Kathryn R Hamilton

doi:10.3390/atoms10010026

Barry I Schneider, Klaus Bartschat + Show 1 more

Open Access

https://doi.org/10.3390/atoms10010026

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Abstract

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.

Highlights

The evolution of the R-matrix theory from a useful but largely phenomenological approach for the description of nuclear resonances [1,2] to an accurate computational method in atomic physics in the 1970s is primarily due to Phil Burke and his collaborators at The Queen’s University of Belfast [3,4,5,6]
The remaining small disagreement between the TDBSR and the R-matrix with time dependence (RMT) results is due to the differences in the respective structure descriptions
This was important to obtain accurate ionization potentials as well as the position of the intermediate (3p5 4s)1 P state. No such special effort was devoted to this issue in the TDBSR calculations, but apparently a sufficient number of short-range orbitals were included in this case to obtain accurate results

Summary

Introduction

The evolution of the R-matrix theory from a useful but largely phenomenological approach for the description of nuclear resonances [1,2] to an accurate computational method in atomic physics in the 1970s is primarily due to Phil Burke and his collaborators at The Queen’s University of Belfast [3,4,5,6]. B-splines as the primitive numerical basis, together with their use to expand the non-orthogonal set of physical and pseudo-orbitals in them, provide a potent mix that may improve significantly on the standard versions of the atomic R-matrix codes. In the latter codes, the individual orbitals expanded in this basis are still assumed to be orthogonal, thereby limiting their flexibility to represent the generally existing term dependence. All the key ingredients were available; namely, the Hamiltonian matrix and the dipole length and/or velocity matrix elements required for the coupling of the target system to the external EM field Since these could be “” extracted from the BSR code, this would provide a general ab initio and non-perturbative treatment to the problem that goes beyond quasi-one-electron or quasi-two-electron models.

Solving the TDSE via the R-Matrix Method

Example Results

Summary and Outlook