# Petascale Computations for Atomic and Molecular Collisions

**Principal Investigator:** Alfred Müller, Institut für Atom- und Molekühlphysik, Universität Giessen (Germany)

**HPC Platform:** Hermit of HLRS

Research efforts of an international group of scientists focus on the development of computational methods to obtain quantities that can be measured from the equations of motion that arise for atoms and molecules interacting with electrons or light within a fully quantum description. The theoretical quantum models the researchers use include semi-relativistic or fully relativistic effects in order to obtain accurate results.

Access to leadership-class supercomputers such as those available at the High Performance Computing Center Stuttgart (HLRS) allow one to benchmark the theoretical solutions obtained from these equations against measurable observables determined from dedicated collision experiments performed at leading synchrotron facilities in Europe and the USA. Furthermore, in the absence of experimental measurements, the scientists’s 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].

In order to achieve spectroscopic accuracy for direct comparisons with experiment, in particular for light or heavy systems [3,4] in the computations the scientists include semi-relativistic or fully relativistic effects [5] and a large number of target-coupled states [7,8,9,10]. Computations of such complexity and magnitude could not be attempted without access to high performance computing resources at leadership computational centres in Europe and the USA.

The scientists use a basis set method know 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 the scientists’s work is multi-fold:

(a) Astrophysical Applications

(b) Fusion and plasma modeling

(c) Fundamentally interesting

(d) Support of experimental measurements

(e) Support of Satellite observations.

(f) Provide data for plasma modeling where no experimental data exist

In the case of heavy atomic systems little atomic data exists and the researchers’s work provides results for new frontiers on the application of their parallel suite of codes. These highly efficient codes are widely applicable to the support of dedicated experiments being performed at synchrotron radiations facilities around the world, such as ALS, ASTRID II, SOLEIL, PETRA III, BESSY II.

Examples of the large-scale calculations carried out are shown below to illustrate the predictive nature of the method compared to experimental results from dedicated light sources; ALS and ASTRID.

**Atomic Oxygen K-shell**

Copyright: Queens University Belfast, CTAMOP

*Fig 1: Atomic oxygen photo-absorption cross-sections taken at 124 meV FWHM at the Advanced Light Source (ALS) compared with theoretical estimates. The*

**R**-matrix calculations shown (solid black) are convoluted with a Gaussian profile of 124 meV FWHM.**Valence-shell Photoionization of Kr+**

Copyright: Queens University Belfast, CTAMOP

*Fig 2. An overview of measurements from ASTRID and ALS for the absolute single photoionization measurements of Kr+ ions as a function of the photon energy measured compared with theoretical estimates for cross sections using the R-matrix method.*

**Valence-shell Photoionization of W3+**

Copyright: Queens University Belfast, CTAMOP

*Fig. 3: Photoionization of W3+ ions over the photon energy range 20 eV – 90 eV. Theoretical work (solid red line: DARC) from the 379 level approximation calculations, convoluted with a Gaussian profile of 100 meV FWHM and statistically averaged over the fine structure J =3/2, 5/2, 7/2, and 9/2 levels (see text for details). The solid circles (yellow) are from the experimental measurements made at the ALS using a bandwidth of 100 meV and the solid triangle (black) is the absolute measurement, accurate to within 20%.*

**Valence‐shell Photoionization of Xe+**

Copyright: Queens University Belfast, CTAMOP

*Fig. 4: Xe+ ALS experimental PI cross section data (green circles) for photon energies ranging from 21.84 eV – 22.08 eV at a photon energy resolution of 4 meV. Results are compared with theoretical results from a 326-level Dirac-Coulomb R-matrix calculation (red line) convoluted with a FWHM Gaussian of 4 meV and statistically averaged over the ground and metastable states to simulate the experimental measurements. The bars mark the energies of the [5s*

^{2}5p^{4}(^{3}P_{1})] and resonances obtained with a quantum defect of 0.16.**References:**

[1] B**.** M. McLaughlin, Inner-shell Photoionization, Fluorescence and Auger Yields, Spectroscopic Challenges of Photoionized Plasma, Edited by G. Ferland and D. W. Savin, Astronomical Society of the Pacific, ASP Conference Series 247 pp. 87. San Francisco (2001)

[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 Performance2014, 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. Mueller, in High Performance Computing in Science and Engineering 2014, Chapter 4, Edited by, W. E. Nagel, D. H. Kroener and M. M. Resch, Springer (New York and Berlin) (2014)

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

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

[7] 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)

[8] 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)

[9] 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)

[10] A. Mueller, 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 Xe7+ ions, J. Phys. B: At. Mol. Opt. Phys. 47 215202 (2014)

see also: Springer-Verlag: Sustained Simulation Performance 2014

Springer-Verlag: High Performance Computing in Science and Engineering ‘14

**Scientific Contacts:**

Brendan M McLaughlin,

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

School of Mathematics and Physics

Queens University Belfast

The Sir David Bates Building

7 College Park, Belfast BT7 1NN/UK

b.mclaughlin@qub.ac.uk

Connor P Ballance and Mitch S Pindzola

Department of Physics

206 Allison Laboratory,

Auburn University,

Auburn, AL 36849/USA

Stefan Schippers and Alfred Mueller (PI)

Institut für Atom- und Molekülphysik,

Justus-Liebig-Universität

Leihgesterner Weg 217, D-35392 Giessen/Germany

*November 2014*