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Self-consistent screened hydrogenic model based on the average-atom model: comparisons with atomic codes and plasma experiments

  • Regular Article – Plasma Physics
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Abstract

Here we present a self-consistent relativistic screened-hydrogenic model (SHM) based on the average-atom model (AAM) for effective calculation of the energy levels of many-electron atoms immersed in plasmas. In addition, we use diverse atomic codes using the configuration interaction method, to calculate the influence of electron density and temperature on the spectra of the diverse ionic states present in a plasma focus device, as well as in other dense plasma systems. The parameters of the AAM are introduced in a coupled system of Saha equations to find the densities and abundances of the different ions to obtain the effective charges and eigenenergies of hydrogenic bound states within the framework of a self-consistent Ion Sphere Model. The results of our calculations are compared with experimental data obtained by different authors and some discrepancies between theoretical and experimental spectra are explained.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The datasets generated during the current study are available under request.]

References

  1. R.P. Feynman, N. Metropolis, E. Teller, Equations of state of elements based on the generalized fermi-thomas theory. Phys. Rev. 75, 1561–1573 (1949). https://doi.org/10.1103/PhysRev.75.1561

    Article  ADS  MATH  Google Scholar 

  2. R.D. Cowan, J. Ashkin, Extension of the Thomas-Fermi-Dirac statistical theory of the atom to finite temperatures. Phys. Rev. 105, 144–157 (1957). https://doi.org/10.1103/PhysRev.105.144

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. B.F. Rozsnyai, Relativistic hartree-fock-slater calculations for arbitrary temperature and matter density. Phys. Rev. A 5, 1137–1149 (1972). https://doi.org/10.1103/PhysRevA.5.1137

    Article  ADS  Google Scholar 

  4. F. Lanzini, H.O. Di Rocco, An implementation of the average atom model using the thermodynamic consistency condition: Application to Ar. Acta Phys. Pol. A 134, 1126–1133 (2018)

    Article  ADS  Google Scholar 

  5. H.O. Di Rocco, F. Lanzini, The influence of the continuum lowering on transition probabilites: competition between cancellation and opacity effects. High Energy Density Phys. 33, 100702 (2019). https://doi.org/10.1016/j.hedp.2019.100702

    Article  Google Scholar 

  6. A.F. Nikiforov, V.G. Novikov, V.B. Uvarov, Quantum-Statistical Models of Hot Dense Matter. Methods for Computation Opacity and Equation of State (Birkhä, Bael, Switzerland, 2005)

    MATH  Google Scholar 

  7. I.I. Sobelman, L.A. Vainshtein, E.A. Yukov, Excitation of Atoms and Broadening of Spectral Lines, 2nd edn. (Springer, Berlin, 1995)

    Book  Google Scholar 

  8. D. Salzmann, H. Szichman, Density dependence of the atomic transition probabilities in hot, dense plasmas. Phys. Rev. A 35, 807–814 (1987). https://doi.org/10.1103/PhysRevA.35.807

    Article  ADS  Google Scholar 

  9. D. Salzmann, Atomic Physics in Hot Plasmas (Oxford University Press, New York, USA, 1998)

    Google Scholar 

  10. J. Abdallah, R.E.H. Clark, A.Y. Faenov, L. Karpinski, S.A. Pikuz, V.M. Romanova, A. Szydlowski, Electron beam effects on the spectroscopy of multiply charged ions in plasma focus experiments. J. Quant. Spectrosc. Radiat. Transfer 62, 85–96 (1999). https://doi.org/10.1016/S0022-4073(98)00073-9

    Article  ADS  Google Scholar 

  11. M. Fatih Yilmaz, A. Eleyan, L.E. Aranchuk, J. Larour, Spectroscopic analysis of X-pinch plasma produced on the compact LC-generator of Ecole Polytechnique using artificial neural networks. High Energy Density Phys. 12, 1–4 (2014). https://doi.org/10.1016/j.hedp.2014.04.001

    Article  ADS  Google Scholar 

  12. R.D. Cowan, The Theory of Atomic Structure and Spectra (University of California Press, Berkeley, 2001)

    Google Scholar 

  13. W. Eissner, M. Jones, H. Nussbaumer, Techniques for the calculation of atomic structures and radiative data including relativistic corrections. Comput. Phys. Commun. 8, 270–306 (1974). https://doi.org/10.1016/0010-4655(74)90019-8

    Article  ADS  Google Scholar 

  14. N.R. Badnell, Dielectronic recombination of Fe22+ and Fe21+. J. Phys. B: At. Mol. Phys. 19, 3827–3835 (1986). https://doi.org/10.1088/0022-3700/19/22/023

    Article  ADS  Google Scholar 

  15. V.V. Karasiev, L. Calderín, S.B. Trickey, Phys. Rev. E 93, 063207 (2016). https://doi.org/10.1103/PhysRevE.93.063207

    Article  ADS  Google Scholar 

  16. I.P. Grant, Relativistic Quantum Theory of Atoms and Molecules (Springer, Berlin, 2007)

    Book  Google Scholar 

  17. A.F. Nikiforov, V.G. Novikov, V.B. Uvarov, A modified Hartree-Fock-Slater model for matter with given temperature and density, problems of atomic science and technology. Methods Codes Numer. Sol. Probl. Math. Phys. 4(6), 16–26 (1979)

    Google Scholar 

  18. S.M. De Carvalho, M. Rotondo, J.A. Rueda, R. Ruffini, Relativistic Feynman-Metropolis-teller treatment at finite temperatures. Phys. Rev. C 89(1), 015801 (2014). https://doi.org/10.1103/physrevc.89.015801

    Article  ADS  Google Scholar 

  19. G. Faussurier, Relativistic finite-temperature Thomas-Fermi model. Phys. Plasmas 24, 112901 (2017). https://doi.org/10.1063/1.5003727

    Article  ADS  Google Scholar 

  20. A. Sherar, G. Bertuccelli, H.O. Di Rocco, Experimental and numerical study of a pulsed cold discharge. Phys. Scripta 47, 579–584 (1993). https://doi.org/10.1088/0031-8949/47/4/019

    Article  ADS  Google Scholar 

  21. A. Kramida, Yu. Ralchenko, J. Reader and NIST ASD Team (2018). NIST Atomic Spectra Database (version 5.1), [Online]. Available: http://physics.nist.gov/asd. National Institute of Standards and Technology, Gaithersburg, MD, USA

  22. G.C. Rodrigues, P. Indelicato, J.P. Santos, P. Patté, F. Parente, Systematic calculation of total atomic energies of ground state configurations. Atom. Data Nucl. Data Tables 86, 117–233 (2004). https://doi.org/10.1016/j.adt.2003.11.005

    Article  ADS  Google Scholar 

  23. A. Poquérusse, Can. J. Phys. 85, 295–305 (2007)

    Article  ADS  Google Scholar 

  24. Q. Porcherot, J.-C. Pain, F. Gilleron, T. Blenski, High Energy Density Phys. 7, 234 (2011)

    Article  ADS  Google Scholar 

  25. J.-C. Pain, F. Gilleron, High Energy Density Phys. 15, 30 (2015)

    Article  ADS  Google Scholar 

  26. N.V. Filippov, T.I. Filippova, A.N. Filippov, M.A. Karakin, E.Y. Khautiev, V.I. Krauz, J. Vierne, Experimental simulation of the collisionless shock wave by plasma focus. Czech. J. Phys. 50, 127–135 (2000). https://doi.org/10.1007/BF03165868

    Article  Google Scholar 

  27. Y. Ralchenko (ed.), Modern Methods in Collisional-Radiative Modeling of Plasmas (Springer, Berlin, 2016)

    Google Scholar 

  28. M. Mizushima, Quantum Mechanics of Atomic Structure and Atomic Spectra (W. A. Benjamin, New York, 1970)

    Google Scholar 

  29. J. Bauche, C. Bauche-Arnoult, E. Luc-Koenig, M. Klapisch, Non-relative energies from relativistic radial integrals in atoms and ions. J. Phys. B At. Mol. Phys. 15, 2325–2338 (1982). https://doi.org/10.1088/0022-3700/15/15/009

    Article  ADS  Google Scholar 

  30. J. Bauche, C. Bauche-Arnoult, O. Peyrusse, Atomic Properties in Hot Plasmas: From Levels to Superconfigurations (Springer International Publishing, Switzerland, 2015)

    Book  Google Scholar 

  31. M.A. Mendoza, J.G. Rubiano, J.M. Gil, M. Rodríguez, R. Florido, P. Martel, E. Mínguez, A new set of relativistic screening constants for the screened hydrogenic model. High Energy Density Phys. 7, 169–179 (2011)

    Article  ADS  Google Scholar 

  32. G.J. Bastiaans, R.A. Mangold, The calculation of electron density and temperature in Ar spectroscopic plasmas from continuum and line spectra. Spectrochim. Acta B At. Spectrosc. 40, 885–892 (1985). https://doi.org/10.1016/0584-8547(85)80059-8

    Article  ADS  Google Scholar 

  33. P. Neumayer, B. Aurand, R. A. Costa Fraga, B. Ecker, R. E. Grisenti, A. Gumberidze, D. C. Hochhaus, A. Kalinin, M. C. Kaluza, T. Kühl, J. Polz, R. Reuschl, T. Stöhlker, D. Winters, N. Winters, Z. Yin, Evidence for ultra-fast heating in intense-laser irradiated reduced-mass targets. Phys. Plasmas, 19, 122708 (2012). https://doi.org/10.1063/1.4772773

  34. A. Sengebusch, H. Reinholz, G. Röpke. arXiv:1709.08493v1 [physics.plasm-ph], (2017)

  35. H.K. Chung, M.H. Chen, W.L. Morgan, Y. Ralchenko, R.W. Lee, FLYCHK: generalized population kinetics and spectral model for rapid spectroscopic analysis for all elements. High Energy Density Phys. 1, 3–12 (2005). https://doi.org/10.1016/j.hedp.2005.07.001

    Article  ADS  Google Scholar 

  36. M. M. Bluteau, Thesis submitted to the Department of Physics of the University of Strathclyde for the Degree of Doctor of Philosophy (2019)

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Authors and Affiliations

  1. Autoridad Regulatoria Nuclear, Av. Del Libertador 8250 (1429) CABA, Buenos Aires, Argentina

    Julio C. Aguiar

  2. Departamento de Cs. Físicas y Ambientales, Fac. Cs. Exactas, Universidad Nacional del Centro, Pinto 399 (7000), Tandil, Argentina

    Héctor O. Di Rocco

  3. Instituto de Física de Materiales Tandil (IFIMAT), Universidad Nacional del Centro de la Provincia de Buenos Aires, Pinto 399, 7000, Tandil, Argentina

    Fernando Lanzini

  4. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Godoy Cruz 2290, Buenos Aires, Argentina

    Fernando Lanzini

Authors
  1. Julio C. Aguiar
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  2. Héctor O. Di Rocco
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  3. Fernando Lanzini
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Contributions

Di Rocco conceived of the presented idea. Lanzini developed the theory and performed the average-atom model code. Aguiar verified the analytical methods and performed the numerical simulations with different codes. All authors provided critical feedback and helped shape the research, analysis and manuscript.

Corresponding author

Correspondence to Julio C. Aguiar.

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Aguiar, J.C., Rocco, H.O.D. & Lanzini, F. Self-consistent screened hydrogenic model based on the average-atom model: comparisons with atomic codes and plasma experiments. Eur. Phys. J. D 75, 272 (2021). https://doi.org/10.1140/epjd/s10053-021-00277-3

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  • DOI: https://doi.org/10.1140/epjd/s10053-021-00277-3

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