Advertisement

The Density Matrix Theory for Polarized Radiation Redistribution

Extensions for Multilevel Atom model and Quantum Doppler effect
  • Véronique Bommier
Part of the Astrophysics and Space Science Library book series (ASSL, volume 243)

Abstract

The density matrix theory is a powerful tool to investigate non-equilibrium phenomena connected with atomic and radiation polarization, particularly in the presence of a magnetic field. In this formalism, the atom-radiation interaction is described through the two basic sets of coupled equations: the statistical equilibrium equations for the density matrix elements, and the radiative transfer equations for the Stokes parameters. These are the basic equations of the NLTE problem. In Bommier (1997a, 1997b), radiation redistribution has been introduced in the formalism through a new formulation of this problem: Rayleigh scattering is taken into account by an additional term in the emissivity coefficient of the transfer equation, which could be applied to new iterative numerical schemes for PRD codes. Alternatively, Landi Degl’Innocenti et al. (1997) take advantage of the metalevels concept to introduce coherent scattering in the formalism, leading thus to possible multilevel applications. The present work has been devoted to investigate the extension of the work of Bommier (1997a, 1997b) on PRD to multilevel atoms: this requires considering Raman scattering, which can be done in the same way as for Rayleigh scattering, i. e., by introducing additional terms in the emissivity coefficient of the transfer equation. Transition from the atomic rest frame to the laboratory frame has also been investigated, and atomic velocity effects have been introduced, leading thus to velocitydependent density matrix elements in the laboratory frame. With these last extensions, the two basic sets of equations of the NLTE problem can now handle complicated problems involving PRD effects, multilevel atoms, polarization and magnetic field.

Key words

atomic processes line: formation line: profiles magnetic fields polarization radiative transfer 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bommier, V.: 1977, Étude théorique de l’effet Hanle; traitement du cas de la raie D3 de l’Hélium en vue de la détermination du champ magnétique des protubérances solaires, Thèse de 3ème cycle, Paris VI University.Google Scholar
  2. Bommier, V.: 1980, Astron. Astrophys. 87, 109.ADSGoogle Scholar
  3. Bommier, V.: 1991, Ann. Phys. Fr. 16, 599.ADSCrossRefGoogle Scholar
  4. Bommier, V.: 1996, in J.O. Stenflo and K.N. Nagendra (eds.), Solar Polarization, Proc. 1st SPW, Kluwer, Dordrecht, p. 29 (also Solar Phys. 164, 29).CrossRefGoogle Scholar
  5. Bommier, V.: 1997a, Astron. Astrophys. 328, 706.ADSGoogle Scholar
  6. Bommier, V.: 1997b, Astron. Astrophys. 328, 726.ADSGoogle Scholar
  7. Bommier, V. and Sahal-Bréchot, S.: 1978, Astron. Astrophys. 69, 57.ADSGoogle Scholar
  8. Bommier, V. and Sahal-Bréchot, S.: 1982, Solar Phys. 78, 157.ADSCrossRefGoogle Scholar
  9. Bommier, V. and Sahal-Bréchot, S.: 1991, Ann. Phys. Fr. 16, 555.ADSCrossRefGoogle Scholar
  10. Brink, D.M. and Satchler, G.R.: 1968, Angular Momentum, 2nd edition, Clarendon Press, Oxford.Google Scholar
  11. Cohen-Tannoudji, C.: 1977, in R. Balian, S. Haroche, and S. Liberman (eds.), Frontiers in Laser spectroscopy, Les Houches, Session XXVII, 1975, North-Holland, Amsterdam, p. 3.Google Scholar
  12. Fano, U.: 1957, Rev. Mod. Phys. 29, 74.MathSciNetADSzbMATHCrossRefGoogle Scholar
  13. Faurobert, M.: 1987, Astron. Astrophys. 178, 269.ADSGoogle Scholar
  14. Faurobert, M.: 1988, Astron. Astrophys. 194, 268.ADSGoogle Scholar
  15. Finn, G.: 1967, Astrophys. J. 147, 1085.ADSCrossRefGoogle Scholar
  16. Frisch, H.: 1998, Astron. Astrophys. 338, 683.ADSGoogle Scholar
  17. Frisch, H.: 1999, in K.N. Nagendra and J.O. Stenflo (eds.), Solar Polarization, Proc. 2nd SPW, Kluwer, Dordrecht (this volume)Google Scholar
  18. Hubený, I. and Oxenius, J.: 1987, JQSRT 37, 65.ADSCrossRefGoogle Scholar
  19. Hummer, D.G.: 1962, M.N.R.A.S. 125, 21.ADSGoogle Scholar
  20. Isliker, H., Nussbaumer, H., and Vogel, M.: 1989, Astron. Astrophys. 219, 271.ADSGoogle Scholar
  21. de Kertanguy, A.: 1998, Astron. Astrophys. 333, 1130.ADSGoogle Scholar
  22. Landi Degl’Innocenti, E.: 1983, Solar Phys. 85, 3.ADSCrossRefGoogle Scholar
  23. Landi Degl’Innocenti, E.: 1984, Solar Phys. 91, 1.ADSGoogle Scholar
  24. Landi Degl’Innocenti, E.: 1985, Solar Phys. 102, 1.ADSCrossRefGoogle Scholar
  25. Landi Degl’Innocenti, E.: 1996, in J.O. Stenflo and K.N. Nagendra (eds.), Solar Polarization, Proc. 1st SPW, Kluwer, Dordrecht, p. 21 (also Solar Phys. 164, 21).Google Scholar
  26. Landi Degl’Innocenti, E.: 1998, Nature 392, 256.ADSCrossRefGoogle Scholar
  27. Landi Degl’Innocenti, E.: 1999, in K.N. Nagendra and J.O. Stenflo (eds.), Solar Polarization, Proc. 2nd SPW, Kluwer, Dordrecht (this volume).Google Scholar
  28. Landi Degl’Innocenti, M. and Landi Degl’Innocenti, E.: 1988, Astron. Astrophys. 192, 374.ADSGoogle Scholar
  29. Landi Degl’Innocenti, E., Bommier, V., and Sahal-Bréchot, S.: 1991, Astron. Astrophys. 244, 391.ADSGoogle Scholar
  30. Landi Degl’Innocenti, E. and Bommier, V.: 1994, Astron. Astrophys. 284, 865.ADSGoogle Scholar
  31. Landi Degl’Innocenti, E., Landi Degl’Innocenti, M., and Landolfi, M.: 1997, in N. Mein and S. Sahal-Bréchot (eds.), Forum THEMIS, Science with THEMIS, proceedings of a Forum held in Paris-Meudon Observatory, 14–15 November, 1996, Paris Observatory Publ., p. 59.Google Scholar
  32. Loudon, R.: 1973, The quantum theory of light, Clarendon Press, Oxford.Google Scholar
  33. Louisell, W.H.: 1973, Quantum Statistical Properties of Radiation, Wiley, New-York.Google Scholar
  34. von Neumann, J.: 1927, Göttingen Nachrichten 245.Google Scholar
  35. Oxenius, J. and Simonneau, E.: 1994, Annals of Physics 234, 60.ADSCrossRefGoogle Scholar
  36. Raouafi, N., Sahal-Bréchot, S., Lemaire, P., and Bommier, V.: 1999, in K.N. Nagendra and J.O. Stenflo (eds.), Solar Polarization, Proc. 2nd SPW, Kluwer, Dordrecht (this volume) .Google Scholar
  37. Reynaud, S. and Cohen-Tannoudji, C.: 1982, J. Physique 43, 1021.CrossRefGoogle Scholar
  38. Sahal-Bréchot, S., Bommier, V., and Feautrier, N.: 1998, Astron. Astrophys. 340, 579.ADSGoogle Scholar
  39. Stenflo, J.O.: 1996, in J.O. Stenflo and K.N. Nagendra (eds.), Solar Polarization, Proc. 1st SPW, Kluwer, Dordrecht, p. 1 (also Solar Phys. 164, 1).CrossRefGoogle Scholar
  40. Stenflo, J.O.: 1998, Astron. Astrophys. 338, 301.ADSGoogle Scholar
  41. Stokes, G.: 1852, Trans. Cambridge Phil. Soc. 9, 399.ADSGoogle Scholar
  42. Weissbluth, M.: 1978, Atoms and Molecules, Student Edition, Academic Press, New York.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Véronique Bommier
    • 1
  1. 1.CNRS URA812 - DAMApObservatoire de Paris, Section de MeudonMeudonFrance

Personalised recommendations