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

• Autorzy: Amélie Juhin , Christian Brouder , Frank Groot
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Resonant Inelastic Scattering; angular dependence; dichroism

• Czasopismo: Open Physics
• Rocznik: 2014
• Tom: 12
• Numer: 5
• Strony: 323-340

Daty

wydano

2014-05-01

online

2014-05-08

Twórcy

autor

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,

autor

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,

autor

Frank Groot

• Inorganic Chemistry and Catalysis, Department of Chemistry, Utrecht University, Universiteitsweg 99, 3584 CG, Utrecht, The Netherlands,

Bibliografia

• [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.83.705[Crossref]
• [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.48.9491[Crossref]
• [3] M. Blume, D. Gibbs, Phys. Rev. B 37, 1779–1789 (1988) http://dx.doi.org/10.1103/PhysRevB.37.1779[Crossref]
• [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.68.1943[Crossref]
• [5] B. T. Thole, G. van der Laan, M. Fabrizio, Phys. Rev. B 50, 11466 (1994) http://dx.doi.org/10.1103/PhysRevB.50.11466[Crossref]
• [6] B. T. Thole, G. van der Laan, Phys. Rev. B 44, 12424 (1991) http://dx.doi.org/10.1103/PhysRevB.44.12424[Crossref]
• [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.70.694[Crossref]
• [8] G. van der Laan, B. T. Thole, Phys. Rev. B 48, 210 (1993) http://dx.doi.org/10.1103/PhysRevB.48.210[Crossref]
• [9] B. T. Thole, G. van der Laan, Phys. Rev. B 49, 9613 (1994) http://dx.doi.org/10.1103/PhysRevB.49.9613[Crossref]
• [10] G. van der Laan, B. T. Thole, Phys. Rev. B 52, 15355 (1995) http://dx.doi.org/10.1103/PhysRevB.52.15355[Crossref]
• [11] G. van der Laan, B. T. Thole, J. Phys. Condens. Matter 7, 9947 (1995) http://dx.doi.org/10.1088/0953-8984/7/50/028[Crossref]
• [12] Ch. Brouder, A. Juhin, A. Bordage, M.-A. Arrio, J. Phys.: Condens. Matt. 20, 455205 (2009)
• [13] A. P. Jucys, I. B. Levinson, V. V. Vanagas, Mathematical Apparatus of the Angular Momentum Theory, (Gordon and Breach, New York, 1963)
• [14] Z. Rudzikas, Theoretical Atomic Spectroscopy, (Cambridge University Press, Cambridge, 1997) http://dx.doi.org/10.1017/CBO9780511524554[Crossref]
• [15] H. A. Kramers, W. Heisenberg, Zeit. f. Physik 31, 681 (1925) http://dx.doi.org/10.1007/BF02980624[Crossref]
• [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
• [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.86.195130[Crossref]
• [18] S. Rossano, Ch. Brouder, M. Alouani, M.-A. Arrio, Phys. Chem. Minerals, 27, 170 (2000) http://dx.doi.org/10.1007/s002690050005[Crossref]
• [19] Ch. Brouder, J. Phys.: Condens. Matter 2, 701 (1990)
• [20] M. van Veenendaal, R. Benoist, Phys. Rev. B 58, 3741 (1998) http://dx.doi.org/10.1103/PhysRevB.58.3741[Crossref]
• [21] P. Ferriani, Ph.D. thesis, University of Modena (Modena, Italy, 2003)
• [22] I. Marri, Ph.D. thesis, University of Modena (Modena, Italy, 2003)
• [23] I. Marri, P. Carra, Phys. Rev. B 69, 113101 (2004) http://dx.doi.org/10.1103/PhysRevB.69.113101[Crossref]
• [24] I. Marri, C. M. Bertoni, P. Ferriani, Y. Joly, Phys. Rev. B 74, 212410 (2006) http://dx.doi.org/10.1103/PhysRevB.74.212410[Crossref]
• [25] P. Ferriani, C. M. Bertoni, J. Magn. Magn. Mater. 272, 1613 (2004) http://dx.doi.org/10.1016/j.jmmm.2003.12.1071[Crossref]
• [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.66.174435[Crossref]
• [27] L. Braicovich et al., Phys. Rev. Lett. 82, 1566 (1999) http://dx.doi.org/10.1103/PhysRevLett.82.1566[Crossref]
• [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.70.1230[Crossref]
• [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.70.3457[Crossref]
• [30] H. Ogasawara, K. Fukui, M. Matsubara, J. Elect. Spect. Relat. Phenom. 136, 161 (2004) http://dx.doi.org/10.1016/j.elspec.2004.02.143[Crossref]
• [31] P. Carra, M. Fabrizio, B. T. Thole, Phys. Rev. Lett. 74, 3700 (1995) http://dx.doi.org/10.1103/PhysRevLett.74.3700[Crossref]
• [32] L. Alagna et al., Phys. Rev. Lett 80, 4799 (1998) http://dx.doi.org/10.1103/PhysRevLett.80.4799[Crossref]
• [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/s100510050344[Crossref]
• [34] P. A. M. Dirac, Proc. R. Soc. Lond. A 114, 710 (1927) http://dx.doi.org/10.1098/rspa.1927.0071[Crossref]
• [35] J. Tulkki and T. Åberg, J. Phys. B: Mol. Phys. 15, L435 (1982) http://dx.doi.org/10.1088/0022-3700/15/13/004[Crossref]
• [36] S. M. Blinder, Foundations of Quantum Dynamics, (Academic Press, London, 1974)
• [37] M. van Veenendaal, P. Carra, B. T. Thole, Phys. Rev. B 54, 16010 (1996). http://dx.doi.org/10.1103/PhysRevB.54.16010[Crossref]
• [38] J. Goulon et al., Phys. Rev. Lett. 85, 4385 (2000) http://dx.doi.org/10.1103/PhysRevLett.85.4385[Crossref]
• [39] J. Goulon et al., Phys. Rev. Lett. 88, 237401 (2002) http://dx.doi.org/10.1103/PhysRevLett.88.237401[Crossref]
• [40] M. van Veenendaal, J. B. Goedkoop, B. T. Thole, Phys. Rev. Lett. 77, 1508 (1996) http://dx.doi.org/10.1103/PhysRevLett.77.1508[Crossref]
• [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
• [42] K. Ishii et al., Phys. Rev. B 83, 241101 (2011) http://dx.doi.org/10.1103/PhysRevB.83.241101[Crossref]
• [43] D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii, Quantum Theory of Angular Momentum, (World Scientific, Singapore, 1988). http://dx.doi.org/10.1142/0270[Crossref]
• [44] H. Weyl, The Classical Groups. Their Invariants and Representations, (Princeton University Press, Princeton, 1946).
• [45] D. R. Lehman, W. C. Parke, J. Math. Phys. 30, 2797 (1989) http://dx.doi.org/10.1063/1.528515[Crossref]

Identyfikatory

DOI

10.2478/s11534-014-0450-2