The international collaboration on Computation Atomic Structure

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The members of the CompAS group perform research within the domain of computational atomic structure utilizing primarily the ATSP2K and GRASP2K program packages. CompAS researchers are involved in studies and state-of-the-art calculations on the many interesting aspects of complex atomic systems. In addition, code development is an always on-going activity aiming at extending the capabilities and efficiency of the software. A few examples of current research are given below.

Information about physical processes in astrophysical and fusion plasmas can be inferred from high resolution spectra. However, the subsequent analysis requires knowledge of highly accurate level and transition data to identify spectral lines, perform collisional and radiative modeling etc. To meet this demand we are performing extensive spectroscopic calculations of relevant atomic systems covering ions in the Be-like to Cl-sequences, but also other systems like W ions in different ionization stages. Many of the calculations attain “spectroscopic accuracy”, i.e. the computed transition energies are of comparable accuracy as the energies from observation, and thus the calculations aid analysis in a very direct way.

- P.Jönsson, G. Gaigalas, P. Rynkun, L. Radziute, J. Ekman, S. Gustafsson, H. Hartman, K. Wang, M. Godefroid, C. Froese Fischer, I.P. Grant, T. Brage, G. Del Zanna, Multiconfiguration Dirac-Hartree-Fock calculations with spectroscopic accuracy: applications to astrophysics, Atoms 5(2), 16 (2017).

Hyperfine structures splits and broadens atomic lines in high resolution spectra and must be included in detailed modeling of lines in astrophysical spectra to derive element abundances, and to determine rotational, micro-turbulent, and macro-turbulent velocities. Hyperfine structure is directly connected to nuclear properties and calculated coupling constants together with accurate experimental splittings can be used to infer nuclear quadrupole moments and also magnetization distributions. The hyperfine codes of the ATSP2K and GRASP2K packages have been used to compute hyperfine coupling constants for a range of elements from few electron systems to superheavy elements. The current activities within this field support studies on radioactive beams at the ISOLDE facility.

- T. Carette, M. Nemouchi, P. Jönsson, and M. Godefroid, Saturation spectra of low lying states of Nitrogen: reconciling experiment with theory, Eur. Phys. J. D 60, 231 (2010).
- J. Bieron, C. Froese Fischer, S. Fritzsche, G. Gaigalas, I.P. Grant, P. Indelicato P. Jönsson, P. Pyykkö, Ab initio MCDHF calculations of electron-nucleus interactions, Phys. Scr. 90 054011 (2015).

Isotopic ratios can be derived from high resolution astrophysical spectra, giving important insight in cosmic nucleosynthesis. The needed data of the shifts of the atomic lines are often calculated. Combining measured isotope shifts with accurate calculations of mass shift parameters, nuclear properties such as difference in nuclear square radii along isotope chains can be derived. The CompAS group provides codes for these types of calculations based on the most accurate operators for the mass- and field shift, the latter accounting for higher order effects that are normally left out. There are developed collaborations with experimental groups such as the ones at ISOLDE.

- C. Nazé, E. Gaidamauskas, G. Gaigalas, M. Godefroid and P. Jönsson, RIS3: A program for relativistic isotope shift calculations, Comput. Phys. Commun. 184, 2187 (2013).
- A. Papoulia, B. G. Carlsson, and J. Ekman, Effect of realistic nuclear charge distributions on isotope shifts and progress towards the extraction of higher-order nuclear radial moments, Phys. Rev. A94, 042502 (2016).
- L. Filippin, R. Beerwerth, J. Ekman, S. Fritzsche, M. Godefroid and P. Jönsson, Multiconfiguration calculations of electronic isotope shift factors in Al I, Phys. Rev. A94, 062508 (2016).

It was believed for a long time that alkaline earth elements could not form stable anions. C. Froese Fischer et al (1987) predicted that this assumption was not correct for both Ca. A few months later, experimental evidence for a stable negative calcium ion was demonstrated by photo-detachment spectroscopy. This result illustrated the predictive value of ab initio calculations. Electron affinities are energy differences and the issue of balance between N and N+1 electron systems needs to be addressed to find appropriate correlation models. On the way to heavy elements, theoretical relativistic calculations of the Astatine electron affinity are considered while measurements of it are currently in progress at ISOLDE.

Isotope shifts on electron affinities combine two observables that are both highly sensitive to electron correlation. They can be obtained by measuring electron affinities for different isotopes using photo-detachment microscopy or the laser photo-detachment threshold method. In the last decade, multiconfiguration calculations have been performed to investigate the normal or anomalous character of the mass isotope shift in the EA for a series of light systems, from Be up to Cl. The longstanding theory-observation discrepancy problem encountered in chlorine is solved and a recent photodetachment microscopy experiment confirms our theoretical prediction for carbon.

- C. Froese Fischer, J.B. Lagowski, S.H. Vosko, Ground States of Ca- and Sc- from two theoretical points of view, Phys. Rev. Lett. 59, 2263 (1987).
- M. Godefroid and C. Froese Fischer, Isotope shift in the oxygen electron, Phys. Rev. A, 60, R2637 (1999).
- T. Carette and M. Godefroid, Isotope shift on the chlorine electron affinity revisited by a MCHF/CI approach, J. Phys. B: At. Mol. Opt. Phys. 46, 095003 (2013).

Unexpected transitions are due to a symmetry breaking, either an internal due to off-diagonal hyperfine interaction or external due to magnetic of electric fields of the surrounding plasma. Unexpected transitions have very high diagnostic potentials, serving as probes of electron densities in thin plasma as well as magnetic fields in coronal plasma. Codes are available in the GRASP2K package to study these exotic processes and the CompAS group is actively pursuing this field to develop operational space based methods to study magnetic fields in the coronal plasma.

- T. Brage, P. Judge, A. Aboussaid, M. Godefroid, P. Jönsson, A. Ynnerman, D. Leckrone and C. Froese Fischer Hyperfine induced transitions as diagnostics of low density plasmas Astrophysical Journal, 500, 507 (1998).
- J. Grumer, T. Brage, M. Andersson, J. Li, P. Jönsson, W. Li, Y. Yang, R. Hutton, and Y. Zou, Unexpected transitions induced by spin-dependent, hyperfine, and magnetic Interactions Physica Scripta 89 114002 (2014).

Methods and codes need to constantly improve to meet the challenges of experiments with unprecedented accuracy. Within the CompAS group we are actively working on utilizing non-orthogonal orbital sets in the framework of the portioned correlation function interaction (PCFI) method to more efficiently describe correlation effects also in larger and more complex systems. The PCFI method can be combined with perturbative corrections. The method can also be used to handle non-orthogonal orbital sets in for example calculations of Auger rates. The results are promising.

- S. Verdebout, P. Rynkun, P. Jönsson, G. Gaigalas, C. Froese Fischer, M. Godefroid, A Partitioned Correlation Function Interaction approach for describing electron correlation in atoms, Journal of Physics B 46, 085003 (2013).
- C. Froese Fischer, S. Verdebout, M. Godefroid, P. Rynkun, P. Jönsson, and G. Gaigalas, Doublet-quartet energy separation in boron: A partitioned-correlation-function-interaction method, Physical Review A 88, 062506 (2013).

Both Lanthanides and “heavy” elements (actinides and beyond) present a number of challenges for atomic structure calculations. The finite volume of the nucleus (always modelled as having spherical symmetry) affects the spectrum , quantum electrodynamic effects (QED) cannot be ignored and, unlike the super-heavy elements, the effect of correlation in the motion of the electrons is still important. The shell structure is no longer strictly followed and open f-shells are frequently present. At the same time, when an atom is modelled as a core plus valence electrons, the number of filled subshells defining the core (in jj-coupling), may well be more than 20. An important question relates to the single- and double- excitation (SD) process. There is a strong interaction between states from a d2 => f2 excitation which might require an SDTQ process for accurate spectra. Many angular symmetries are associated with open f-shells leading rapidly to large expansions and calculations requiring high-performance computing methods and resources. GRASP codes are being modified for research in nuclear physics and nuclear astrophysics involving these atoms. The electron affinity of astatine (At, Z=85), for example, is a radioactive element of interest in the treatment of cancer.

Over the past decade, the number of properties that can be studied by the RATIP program has been increased continuously and has made this code a powerful tool for rather a broad community in physics, from atomic photoionization and electron spectroscopy to the study of highly-charged ions, the spectroscopy of heavy and superheavy elements, the generation of atomic data for astro and plasma physics, and up to the search for time-reversal violating interactions in atomic systems. Based on Fortran 90 and its subsequent standards, RATIP combines the numerical strength of Fortran with an object-oriented approach in dealing, for example, with quantum numbers, atomic and configuration states, or many-electron transition amplitudes.

Much of the present interest in studying the excitation and ionization dynamics of atoms focus on second- and higher-order processes that formally include a summation of transition amplitudes over the (complete) spectrum of the system. Apart from the discrete bound states, this generally requires an integration over the continuum part of the many-electron spectrum. Obviously, this is a highly non-trivial task, especially for multi-electron systems, since it requires to generate the continuum and to evaluate the free-free transition amplitudes. Examples of such second-order processes are the (single-photon) double ionization of atoms, the two-photon excitation and decay, sequential two-photon processes, double Auger processes, and several others. Therefore, any implementation of these physical properties requires first of all a good “physical insight” into the relevant part of the many-electron spectrum in order to reduce it to a finite and well feasible set of intermediate states. In RATIP, we will continue to developing the SPECTRUM component in order to generate an intermediate set of atomic states independently and before these states are utilized to compute transition amplitudes. We hope this will make RATIP ready for a new generation of experiments that are performed at present or in the near future at free-electron lasers or some other high-intense light sources.

- S. Fritzsche, A. N. Grum-Grzhimailo, E. V. Gryzlova and N. M. Kabachnik, Sequential two-photon double ionization of the 4d shell in xenon, J. Phys. B: At. Mol. Opt. Phys. B44, 175602:1-10 (2011), selected also for the “2011 Highlights” collection of this journal.
- S. Fritzsche, A. Surzhykov, A. Gumberidze and T. Stöhlker, Electron emission from highly-charged ions: signatures of magnetic interactions and retardation in strong fields New J. Phys. 14, 083018:1-13 (2012). P. Linusson, S. Fritzsche, J.H.D. Eland, M. Mucke and R. Feifel, Single photon double ion-ization forming double vacancies in the 2p sub-shell of argon, Phys. Rev. A87, 043409:1-6 (2013).