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Open Physics

formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

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Volume 12, Issue 5

Issues

Volume 13 (2015)

Angular dependence of resonant inelastic x-ray scattering: a spherical tensor expansion

Amélie Juhin
  • Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Universités, UMR CNRS 7590, UPMC Univ. Paris 06, Muséum National d’Histoire Naturelle, IRD UMR 206, 4 place Jussieu, F-75005, Paris, France
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/ Christian Brouder
  • Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Universités, UMR CNRS 7590, UPMC Univ. Paris 06, Muséum National d’Histoire Naturelle, IRD UMR 206, 4 place Jussieu, F-75005, Paris, France
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/ Frank Groot
  • Inorganic Chemistry and Catalysis, Department of Chemistry, Utrecht University, Universiteitsweg 99, 3584 CG, Utrecht, The Netherlands
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Published Online: 2014-05-08 | DOI: https://doi.org/10.2478/s11534-014-0450-2

Abstract

A spherical tensor expansion is carried out to express the resonant inelastic scattering cross-section as a sum of products of fundamental spectra with tensors involving wavevectors and polarization vectors of incident and scattered photons. The expression presented in this paper differs from that of the influential article by Carra et al. (Phys. Rev. Lett. 74, 3700, 1995) because it does not omit interference terms between electric dipole and quadrupole contributions when coupling each photon to itself. Some specific cases of the spherical tensor expansion are discussed. For example the case of isotropic samples is considered and the cross-section is expressed as a combination of only three fundamental spectra for the situation where electric dipole or electric quadrupole transitions in the absorption process are followed by electric dipole transitions in the emission. This situation includes the case of untextured powder samples, which corresponds to the most frequent situation met experimentally. Finally, it is predicted that some circular dichroism may be observed on isotropic samples provided that the circular polarization of the scattered beam can be detected.

Keywords: Resonant Inelastic Scattering; angular dependence; dichroism

  • [1] L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, J. van den Brink, Rev. Mod. Phys 83, 705 (2011) http://dx.doi.org/10.1103/RevModPhys.83.705CrossrefGoogle Scholar

  • [2] J.-Ph. Schillé, J.-P. Kappler, Ph. Sainctavit, C. Cartier dit Moulin, Ch. Brouder, G. Krill, Phys. Rev. B 48, 9491 (1993) http://dx.doi.org/10.1103/PhysRevB.48.9491CrossrefGoogle Scholar

  • [3] M. Blume, D. Gibbs, Phys. Rev. B 37, 1779–1789 (1988) http://dx.doi.org/10.1103/PhysRevB.37.1779CrossrefGoogle Scholar

  • [4] B. T. Thole, P. Carra, F. Sette, G. van der Laan, Phys. Rev. Lett. 68, 1943–1946 (1992) http://dx.doi.org/10.1103/PhysRevLett.68.1943CrossrefGoogle Scholar

  • [5] B. T. Thole, G. van der Laan, M. Fabrizio, Phys. Rev. B 50, 11466 (1994) http://dx.doi.org/10.1103/PhysRevB.50.11466CrossrefGoogle Scholar

  • [6] B. T. Thole, G. van der Laan, Phys. Rev. B 44, 12424 (1991) http://dx.doi.org/10.1103/PhysRevB.44.12424CrossrefGoogle Scholar

  • [7] P. Carra, B. T. Thole, M. Altarelli, X. D. Wang, Phys. Rev. Lett. 70, 694–697 (1993). http://dx.doi.org/10.1103/PhysRevLett.70.694CrossrefGoogle Scholar

  • [8] G. van der Laan, B. T. Thole, Phys. Rev. B 48, 210 (1993) http://dx.doi.org/10.1103/PhysRevB.48.210CrossrefGoogle Scholar

  • [9] B. T. Thole, G. van der Laan, Phys. Rev. B 49, 9613 (1994) http://dx.doi.org/10.1103/PhysRevB.49.9613CrossrefGoogle Scholar

  • [10] G. van der Laan, B. T. Thole, Phys. Rev. B 52, 15355 (1995) http://dx.doi.org/10.1103/PhysRevB.52.15355CrossrefGoogle Scholar

  • [11] G. van der Laan, B. T. Thole, J. Phys. Condens. Matter 7, 9947 (1995) http://dx.doi.org/10.1088/0953-8984/7/50/028CrossrefGoogle Scholar

  • [12] Ch. Brouder, A. Juhin, A. Bordage, M.-A. Arrio, J. Phys.: Condens. Matt. 20, 455205 (2009) Google Scholar

  • [13] A. P. Jucys, I. B. Levinson, V. V. Vanagas, Mathematical Apparatus of the Angular Momentum Theory, (Gordon and Breach, New York, 1963) Google Scholar

  • [14] Z. Rudzikas, Theoretical Atomic Spectroscopy, (Cambridge University Press, Cambridge, 1997) http://dx.doi.org/10.1017/CBO9780511524554CrossrefGoogle Scholar

  • [15] H. A. Kramers, W. Heisenberg, Zeit. f. Physik 31, 681 (1925) http://dx.doi.org/10.1007/BF02980624CrossrefGoogle Scholar

  • [16] H. A. Kramers, W. Heisenberg, On the scattering of radiation by atoms, In: D. ter Haar (Ed.) Master of Modern Physics, Princeton Series in Physics (Princeton University Press, Princeton, 1998), 121 Google Scholar

  • [17] L. A. Wray, Wanli Yang, H. Eisaki, Z. Hussain, Y.-D. Chuang, Phys. Rev. B 86, 195130 (2012) http://dx.doi.org/10.1103/PhysRevB.86.195130CrossrefGoogle Scholar

  • [18] S. Rossano, Ch. Brouder, M. Alouani, M.-A. Arrio, Phys. Chem. Minerals, 27, 170 (2000) http://dx.doi.org/10.1007/s002690050005CrossrefGoogle Scholar

  • [19] Ch. Brouder, J. Phys.: Condens. Matter 2, 701 (1990) Google Scholar

  • [20] M. van Veenendaal, R. Benoist, Phys. Rev. B 58, 3741 (1998) http://dx.doi.org/10.1103/PhysRevB.58.3741CrossrefGoogle Scholar

  • [21] P. Ferriani, Ph.D. thesis, University of Modena (Modena, Italy, 2003) Google Scholar

  • [22] I. Marri, Ph.D. thesis, University of Modena (Modena, Italy, 2003) Google Scholar

  • [23] I. Marri, P. Carra, Phys. Rev. B 69, 113101 (2004) http://dx.doi.org/10.1103/PhysRevB.69.113101CrossrefGoogle Scholar

  • [24] I. Marri, C. M. Bertoni, P. Ferriani, Y. Joly, Phys. Rev. B 74, 212410 (2006) http://dx.doi.org/10.1103/PhysRevB.74.212410CrossrefGoogle Scholar

  • [25] P. Ferriani, C. M. Bertoni, J. Magn. Magn. Mater. 272, 1613 (2004) http://dx.doi.org/10.1016/j.jmmm.2003.12.1071CrossrefGoogle Scholar

  • [26] L. Braicovich, G. van der Laan, G. Ghiringhelli, A. Tagliaferri, N. B. Brookes, Phys. Rev. B 66, 174435 (2002) http://dx.doi.org/10.1103/PhysRevB.66.174435CrossrefGoogle Scholar

  • [27] L. Braicovich et al., Phys. Rev. Lett. 82, 1566 (1999) http://dx.doi.org/10.1103/PhysRevLett.82.1566CrossrefGoogle Scholar

  • [28] K. Fukui, H. Ogasawara, A. Kotani, T. Iwazumi, H. Shoji, T. Nakamura, J. Phys. Soc. Japan 70, 1230 (2001) http://dx.doi.org/10.1143/JPSJ.70.1230CrossrefGoogle Scholar

  • [29] K. Fukui, H. Ogasawara, A. Kotani, T. Iwazumi, H. Shoji, T. Nakamura, J. Phys. Soc. Japan 70, 3457(2001) http://dx.doi.org/10.1143/JPSJ.70.3457CrossrefGoogle Scholar

  • [30] H. Ogasawara, K. Fukui, M. Matsubara, J. Elect. Spect. Relat. Phenom. 136, 161 (2004) http://dx.doi.org/10.1016/j.elspec.2004.02.143CrossrefGoogle Scholar

  • [31] P. Carra, M. Fabrizio, B. T. Thole, Phys. Rev. Lett. 74, 3700 (1995) http://dx.doi.org/10.1103/PhysRevLett.74.3700CrossrefGoogle Scholar

  • [32] L. Alagna et al., Phys. Rev. Lett 80, 4799 (1998) http://dx.doi.org/10.1103/PhysRevLett.80.4799CrossrefGoogle Scholar

  • [33] C.R. Natoli, Ch. Brouder, Ph. Sainctavit, J. Goulon, Ch. Goulon-Ginet, A. Rogalev, Europ. Phys. J. B 4, 1 (1998) http://dx.doi.org/10.1007/s100510050344CrossrefGoogle Scholar

  • [34] P. A. M. Dirac, Proc. R. Soc. Lond. A 114, 710 (1927) http://dx.doi.org/10.1098/rspa.1927.0071CrossrefGoogle Scholar

  • [35] J. Tulkki and T. Åberg, J. Phys. B: Mol. Phys. 15, L435 (1982) http://dx.doi.org/10.1088/0022-3700/15/13/004CrossrefGoogle Scholar

  • [36] S. M. Blinder, Foundations of Quantum Dynamics, (Academic Press, London, 1974) Google Scholar

  • [37] M. van Veenendaal, P. Carra, B. T. Thole, Phys. Rev. B 54, 16010 (1996). http://dx.doi.org/10.1103/PhysRevB.54.16010CrossrefGoogle Scholar

  • [38] J. Goulon et al., Phys. Rev. Lett. 85, 4385 (2000) http://dx.doi.org/10.1103/PhysRevLett.85.4385CrossrefGoogle Scholar

  • [39] J. Goulon et al., Phys. Rev. Lett. 88, 237401 (2002) http://dx.doi.org/10.1103/PhysRevLett.88.237401CrossrefGoogle Scholar

  • [40] M. van Veenendaal, J. B. Goedkoop, B. T. Thole, Phys. Rev. Lett. 77, 1508 (1996) http://dx.doi.org/10.1103/PhysRevLett.77.1508CrossrefGoogle Scholar

  • [41] P. Carra. In: D. S. Gemmell, S. H. Southworth, R. W. Dunford, E. P. Kanter, L. Young (Eds.), X-ray and Inner-Shell Processes: 18th International Conference, (AIP Conference Proceedings, AIP, 2000), 506, 273 Google Scholar

  • [42] K. Ishii et al., Phys. Rev. B 83, 241101 (2011) http://dx.doi.org/10.1103/PhysRevB.83.241101CrossrefGoogle Scholar

  • [43] D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii, Quantum Theory of Angular Momentum, (World Scientific, Singapore, 1988). http://dx.doi.org/10.1142/0270CrossrefGoogle Scholar

  • [44] H. Weyl, The Classical Groups. Their Invariants and Representations, (Princeton University Press, Princeton, 1946). Google Scholar

  • [45] D. R. Lehman, W. C. Parke, J. Math. Phys. 30, 2797 (1989) http://dx.doi.org/10.1063/1.528515CrossrefGoogle Scholar

About the article

Published Online: 2014-05-08

Published in Print: 2014-05-01


Citation Information: Open Physics, Volume 12, Issue 5, Pages 323–340, ISSN (Online) 2391-5471, DOI: https://doi.org/10.2478/s11534-014-0450-2.

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© 2014 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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