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Astrophysics Research Centre

School of Mathematics and Physics

Relativistic R-Matrix Calculations in the EUV/soft X-ray energy regime


Cosmic x-ray and EUV spectroscopy has entered a Golden Era, with a wide range of high resolution spectrometers observing the Sun, the solar system, and distant astrophysical sources as well as new facilities in development for launch [1]. Placing the spectrometer beyond the Earths atmosphere, each mission represents a major investment by NASA, ESA, or JAXA, typically requiring at least an order of magnitude improvement over previous mission. Upcoming missions, such as XRism or Athena, will further push bandpass accuracy down to 0.1 − 6.2 nm which demands a similar upgrade in the theoretical calculations that underpin the interpretation of this observed spectra.

Objectives & Methodology

Within the collision group of CTAMOP, we develop relativistic scattering and photoionisation codes that need theoretical refinement if we are to address these problems. The R-matrix method, DARC (Dirac Atomic R-matrix Codes) although already a level-resolved scattering code, does not fully account for the relativistic properties of the incident electron if its energy exceeds 1000-1500 Rydbergs i.e.a significant fraction of the speed of light. Therefore, this project would involve an extension of both the theory and its implementation within the current suite of codes, by solving equations of the form

where P and Q are continuum radial orbitals, κi the angular momentum of the incident electron, εi relates the channel energies, and V_ii0 a potential matrix coupling channels together[2].


These developments align well with the goals our colleagues from ARC, whose kilanova simulations under certain conditions may benefit from the inclusion of higher order relativistic cross sections and rates. We also have ongoing collaborations locally, with Prof. Simon Jeffries at Armagh Planetarium(N.I), with Dr Franck Delahaye at the Observatoire de Paris (EU) concerning stellar opacities, as well as colleagues at Auburn University (US) and the Harvard Centre for Astrophysics (US) where they build and develop spectrometers.

Required skills

  • At least an introductory course in Quantum Mechanics.
  • Taking the lead in implementing these additions to the existing code-base.
  • An interest in High Performance Computing as these simulations will require the use of

our parallelized suite of codes

  • An interest in visiting other institutions for short periods of time, as well as presenting

your work at conferences and workshops

Further information

Please contact the project supervisor, Dr. Connor Ballance (c.ballance@qub.ac.uk) if you have further questions or require more details.


[1] Randall Smith it et al J. Phys. B: At Mol Opt. Phys 53 092001 (2020).

[2] ’R-matrix Theory of Atomic Collisions’, Phillip Burke, Springer Publishing, ISBN 978-3-642-15930-5, pp.284-285 (2011)

public/phds2021/2021_ballance.txt · Last modified: 2021/02/03 11:05 by edemooij

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