**Principal Investigator:**

Alfred Müller

**Affiliation:**

Institut für Atom- und Molekülphysik, Universität Giessen (Germany)

**Local Project ID:**

PAMOP and PAMOP2

**HPC Platform used:**

Hazel Hen of HLRS

**Date published:**

**An international group of scientists leverages high-performance computing to support current and future measurements of atomic photoionization cross-sections at various synchrotron radiation facilities, ion-atom collision experiments, together with plasma, fusion and astrophysical applications. In their work they solve the Schrödinger or Dirac equation using the R-matrix or R-matrix with pseudo-states approach from first principles. Cross-sections and rates for radiative charge transfer, radiative association, and photodissociation collision processes between atoms and ions of interest for several astrophysical applications are presented.**

Research efforts of an international group of scientists focus on the development of computational methods to obtain quantities that are required to understand and to model complex laboratory-based and astrophysical environments. Theory starts from the equations of motion that arise for atoms and molecules interacting with electrons or photons within a full quantum-mechanics description.

Access to leadership-class supercomputers available at the High Performance Computing Center Stuttgart (HLRS) allows us to benchmark the theoretical solutions obtained from these equations against measurable observables determined from dedicated collision experiments performed at leading large-scale experimental facilities in Europe and the USA. Furthermore, in the absence of experimental measurements, the highly effective and accurate method for obtaining theoretical results from this research provides atomic and molecular data for ongoing plasma modeling in research in laboratory and astrophysical plasma science [1,2]. This work could not even be attempted with access to leadership computational facilities like those at HLRS.

In order to achieve spectroscopic accuracy for direct comparisons with experiment, in particular for light or heavy systems [3 - 7] the computations include semi-relativistic or fully relativistic effects [8,9] and include an exponentially increasing number of target-coupled states. Computations of such complexity and magnitude could not be attempted without access to high performance computing resources at leadership computational facilities in Europe and the USA.

The scientists use a basis set method known as the R-matrix method [6], to solve the equations of motion to obtain the observables for the interaction of an electron or photon with atoms, molecules and their ions. The motivation for this work is multi-fold:

(a) Astrophysical applications

(b) Fusion and plasma modeling

(c) Fundamentally interesting

(d) Interpretation of experimental measurements at leading Light Source facilities

(e) Interpretation of Satellite observations.

(f) Provision of data for plasma diagnostics and modeling where no experimental data exist

For the heavy atomic systems we study, little atomic data exists and our current work provides insight into the collision and radiative processes necessary in fusion physics and provide urgently needed data for applications for plasma diagnostics and interpretation of gravity waves. Access to leadership computers available at HLRS allows us to refine and enhance our state-of-the-art codes. Examples of our work are illustrated below for both valence and inner-shell photoionization studies to illustrate the predictive nature of the methods employed and the insight gained from our work. Interpretation of experimental data is made possible using our calculations. We are able to trace the contributions from different initial states in the ion beam and determine the metastable fractions in the experiment. Our theoretical efforts continue to focus on the development of computational methods to solve the equations of motion for electron and photon interacting with atomic and molecular systems. With the trend towards exascale computing power, such as the new Summit the 200-petaflop IBM 922AC architecture at Oak Ridge National Laboratory our codes continue to evolve taking advantage of existing architectures at HLRS to develop, exploit and enhance our codes in preparation for these new machines.

**Atomic Oxygen K-shell**

**Atomic O ^{5+} K-shell**

**Comparison of Satellite observations, and experimental studies**

**Valence-shell Photoionization of W ^{4+}**

**Valence‐shell Photoionization of Zn+**

**Valence‐shell Photoionization of Ca+**

**References:**

[1] B. M. McLaughlin, C. P. Balance, K. P. Bowen, D. J. Gardenghi, and W. C. Stolte, High-Precision K-shell Photoabsorption Cross Sections for Atomic Oxygen: Experiment and Theory, Astrophysical Journal, 771, L8 (2013)

[2] B. M. McLaughlin and C. P. Ballance, Photoionization, fluorescence and inner-shell processes, in McGraw-Hill Science and Technology Yearbook 2013, Edited by McGraw-Hill (New York and London) (2013), 281.

[3] Petascale computations for Large-scale Atomic and Molecular collisions, B. M. McLaughlin and C. P. Ballance, in Sustained Simulated Performance 2014, Chapter 15, Edited by, M. M. Resch, Y, Kovalenko, E. Focht, W. Bez and H. Kobaysahi, Springer (New York and Berlin) (2014)

[4] PAMOP: Petascale Atomic, Molecular and Optical Collision Calculations, B. M. McLaughlin, C. P. Ballance, M. S. Pindzola and A. Müller, in High Performance Computing in Science and Engineering 2015, Chapter 4, Edited by, W. E. Nagel, D. H. Kroener and M. M. Resch, Springer (New York and Berlin) (2015)

[5] PAMOP: Petascale Computations in Suport of Experiments, B. M. McLaughlin, C. P. Ballance, M. S. Pindzola S. Schippers, and A. Müller, in High Performance Computing in Science and Engineering 2015, Chapter 4, Edited by, W. E. Nagel, D. H. Kroener and M. M. Resch, Springer (New York and Berlin) (2016)

[6] PAMOP project: Computations in Suport of Experiments and Astrophysical Applications, B. M. McLaughlin, C. P. Ballance, M. S. Pindzola, P. C. Stancil, S. Schippers, and A. Müller, in High Performance Computing in Science and Engineering 2016, Chapter 4, Edited by, W. E. Nagel, D. H. Kroener and M. M. Resch, Springer (New York and Berlin) (2017)

[7] PAMOP: Large-scale Computations in Support of Experiments and Astrophysics Applications, B. M. McLaughlin, C. P. Ballance, M. S. Pindzola, P. C. Stancil, J. F. Babb, S. Schippers and A. Müller, in High Performance Computing in Science and Engineering 2017, Chapter 4, Edited by, W. E. Nagel, D. H. Kroener and M. M. Resch, Springer (New York and Berlin) (2018)

[8] I. P. Grant, Quantum Theory of Atoms and Molecules: Theory and Computation, Springer (New York, USA) 2007

[9] P. G. Burke, R-Matrix Theory of Atomic Collisions: Application to Atomic, Molecular and Optical Processes, Springer (New York, USA) (2011)

[10] B. M. McLaughlin and C. P. Ballance, Photoionization cross section calculations for the halogen-like ions Kr^{+} and Xe^{+}, J. Phys. B: At. Mol. Opt. Phys. 45 095202 (2012)

[11] B. M. McLaughlin and C. P. Ballance, Photoionization cross section calculations for the tran-iron element Se^{+} from 18 to 31 eV, J. Phys. B: At. Mol. Opt. Phys. 45 085701 (2012)

[12] G. Hinojosa, A. M. Covington, G. Alna-Washi, M. Liu, R. A. Phaneuf, M. M. Sant'Anna, C. Cisneros, I. A'lvarez, A. Aguilar, A. L. D. Kilcoyne, A. S. Schlachter, C. P. Ballance and B. M. McLaughlin, Valence-shell photoionization of Kr^{+} ions: experiment and theory, Phys. Rev. A 86 063402 (2012)

[13] A. Müller, S. Schipper, D. Esteves-Macaluso, M. Habbi, A. Aguilar, A. L. D. Kilcoyne, R. A . Phaneuf, C. P. Ballance and B. M. McLaughlin, Valence-shell photoionization of Ag-like Xe^{7+} ions, J. Phys. B: At. Mol. Opt. Phys. 47 215202 (2014)

[14] E.T Kennedy et al, Photoionization of aluminumlike Si+ ion the region of the 2p threshold (94 – 137 eV) Phys Rev A 90 063409 (2014).

[15] M. Barthel, et al., Photoionization of 3s^{2}3p^{4 3}P and the 3s^{2}3p^{4 1}D, ^{1}S states of sulfur: experiment and theory, Phys. Rev A 91 013406 (2015)

[16] B. M. McLaughlin, Photoionization of C*l*^{+} from the 3s^{2}3p^{4 3}P_{2,1,0} and the 3s^{2}3p^{4 1}D_{2}, ^{1}S_{0} states in the energy range 19 – 28 eV, MNRAS 464, 1990 (2017)

[17] D. Macaluso, et al., Absolute single-photoionization cross sections of Se^{2+}: experiment and theory, Phys. Rev. A 92 063424 (2015)

[18] A. Müller, et al., Single-photon single ionization of W^{+} ions: experiment and theory, J. Phys. B: At. Mol. Opt. Phys. 48 2352033 (2015)

[19] B. M. McLaughlin, et al., Photoionization of tungsten ions: experiment and theory for W^{2+} and W^{3+}, J. Phys. B: At. Mol. Opt. Phys. 49 065201 (2016)

[20] J.-M. Bizau, et al., K-shell photoionization of O^{+} and O^{2+} ions: experiment and theory, Phys. Rev. A 92 023401 (2015)

[21] A. Müller, et al., Photoionization of tungsten ions: experiment and theory for W^{4+}, J. Phys. B: At. Mol. Opt. Phys. 50 085007 (2017)

[22] B. M. McLaughlin, et al., K-shell photoionization of O^{4+} and O^{5+} ions: experiment and theory, MNRAS 465, 4690 (2017)

[23] B. M. McLaughlin, et al., Single photoionization of the Zn II ion in the photon energy range 17.5 – 90 eV: experiment and theory, MNRAS, 470, 4048 (2017).

[24] A. Müller, et al., Photoionization of Ca^{+} ions in the valence energy region 20 – 56 eV: experiment and theory, J. Phys. B: At. Mol. Opt. Phys. 50 205001 (2017)

**Scientific Contacts:**

Brendan M McLaughlin and Connor P Balance

Centre for Theoretical Atomic, Molecular and Optical Physics (CTAMOP)

School of Mathematics and Physics

Queens University Belfast

The Old Physics Building

Belfast BT7 1NN/UK

e-mail: b.mclaughlin [@] qub.ac.uk or c.ballance [@] qub.ac.uk

Mitch S Pindzola

Department of Physics

206 Allison Laboratory

Auburn University,

Auburn, AL 36849/USA

Phillip C Stancil

Department of Physics and Astronomy

Center for Simulation Physics

University of Georgia

Athens, GA 030602-2451/USAInstitute for Theoretical Atomic, Molecular and Optical Physics (ITAMP)

James F Babb

Institute for Theoretical Atomic, Molecular and Optical Physics (ITAMP)

60 Garden Street, MS-14

Harvard Smithsonian Center for Astrophysics

Cambridge, MA 02138/USA

Stefan Schippers and Alfred Müller (PI)

Institut für Atom- und Molekülphysik,

Justus-Liebig-Universität

Leihgesterner Weg 217, D-35392 Giessen/Germany

**Project IDs:** PAMOP and PAMOP2

**Date published: **May 2018