SpringerLink
Log in

Spatio-Temporal Dynamical Systems in Inner-Shell Photoionization in Free Molecules, Clusters, and Solids

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

Dynamic spatial hole localization and symmetry breaking phenomena are examined. Absorption of X-ray synchrotron and free-electron–laser radiation in matter is accompanied by strong dynamic corehole localization and temporary trap of the electron ejected from a deep level within the finite size potential barrier. As a result the symmetry of core excited states is reduced in comparison with ground state as the inversion symmetry is being broken. This is a very general property of coreexcited polyatomic compounds with equivalent atoms as their equivalence implies their equal probability of excitation averaged over large timescale but not simultaneous core excitation. Different approaches to rationalizing the symmetry breaking phenomena are presented and discussed with the emphasis on the quasiatomic dynamic corehole localization model. By examining the experimental ultrafast probe of photoabsorption processes we demonstrate an important role of spatio-temporal (nanometric-femtosecond) dynamically localized coreexcited moieties in molecule, clusters and solids. The photoelectron angular distributions from N and O 1s levels in fixed-in-space N2 and CO2 molecules, the photoelectron induced rotational heating of N2, the Auger decay spectra of N2 and the near S 1s edge X-ray absorption fine structure of free SF6 molecules are discussed in more detail.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Adachi, K. Hosaka, S. Furuya, K. Soejima, M. Takahashi, A. Yagishita, S.K. Semenov, and N.A. Cherepkov, “Shape-resonance-enhanced vibrational effects in the angular distributions of C 1s photoelectrons from fixed-in-space CO molecules,” Phys. Rev. Lett., 91, 163001 (2003).

    Article  Google Scholar 

  2. J. Adachi, K. Hosaka, T. Teramoto, M. Yamazaki, N. Watanabe, M. Takahashi, and A. Yagishita, “Photoelectron–photoion–photoion momentum spectroscopy as a direct probe of the core-hole localization in C 1s photoionization of C 2 H 2,” J. Phys. B, 40, F285 (2007).

    Article  Google Scholar 

  3. M.Ya. Amusia, Atomic photoeffect [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  4. P. S. Bagus and H. F. Schaefer, “Localized and delocalized 1s hole states of the O +2 molecular ion” J. Chem. Phys., 56, No. 1, 224–226 (1972).

    Article  Google Scholar 

  5. U. Becker, O. Gessner, and A. Rüdel, “Photoelectron scattering in molecules and fullerenes,” J. El. Spectroscopy Relat. Phenom., 108, No. 1–3, 189–201 (2000).

    Article  Google Scholar 

  6. H. A. Bethe, Intermediate Quantum Mechanics, W.A. Benjamin, Inc., New York–Amsterdam (1964).

    Google Scholar 

  7. L. S. Cederbaum and W. Domcke, “Localized and delocalized core holes and their interrelation,” J. Chem. Phys., 66, No. 11, 5084–5086 (1977).

    Article  Google Scholar 

  8. C. T. Chen, Y. Ma, and F. Sette, “K-shell photoabsorption of the N 2 molecule,” Phys. Rev. A, 40, 6737–6740 (1989).

    Article  Google Scholar 

  9. W. Domcke and L. S. Cederbaum, “Electronic recoil effects in high-energy photoelectron spectroscopy,” J. El. Spectroscopy Relat. Phenom., 13, No. 3, 161–173 (1978).

    Article  Google Scholar 

  10. E.O. Filatova and A.A. Pavlychev, X-ray Optics and Inner-Shell Electronics of h-BN, Nova Science Publ. Inc, N.Y. (2011).

    Google Scholar 

  11. R. Flesch, E. Serdaroglu, F. Blobner, P. Feulner, X. O. Brykalova, A.A. Pavlychev, N. Kosugi, and E. Rühl, “Gas-to-solid shift of C 1s-excited benzene,” Phys. Chem. Chem. Phys., 14, No. 26, 9397–9402 (2012).

    Article  Google Scholar 

  12. R. Flesch, E. Serdaroglu, E. S. Klyushina, F. Blobner, P. Feulner, X. O. Brykalova, A.A. Pavlychev, and E. Rühl. To appear.

  13. U. Hergenhahn, O. Kugeler, A. Rüdel, E. E. Rennie, and A.M. Bradshaw, “Symmetry-selective observation of the N 1s shape resonance in N 2,” J. Phys. Chem. A, 105, 5704–5708 (2001).

    Article  Google Scholar 

  14. E. Hudson, D.A. Shirley, M. Domke, G. Remmers, A. Puschmann, T. Mandel, C. Xue, and G. Kaindl, “High-resolution measurements of near-edge resonances in the core-level photoionization spectra of SF 6,” Phys. Rev. A, 47, No. 1, 361–373 (1993).

    Article  Google Scholar 

  15. A. Kivimäki, B. Kempgenns, K. Maier, H.M. Köppe, M.N. Piancastelli, M. Neeb, and A. M. Bradshaw, “Vibrationally resolved O 1s photoelectron spectrum of CO 2: vibronic coupling and dynamic core-hole localization,” Phys. Rev. Lett., 79, No. 6, 998–1001 (1997).

    Article  Google Scholar 

  16. N. Kosugi, “Exchange interaction in core excitation of diatomic systems,” Chem. Phys., 289, 117–134 (2003).

    Article  Google Scholar 

  17. E. Kukk, T. D. Thomas, and K. Ueda, “Recoil effects in molecular photoemission,” J. El. Spectroscopy Relat. Phenom., 183, No. 1–3, 53–58 (2011).

    Article  Google Scholar 

  18. E. Kukk, K. Ueda, U. Hergenhahn, X.-J. Liu, G. Prümper, H. Yoshida, Y. Tamenori, C. Makochekanwa, T. Tanaka, M. Kitajima, and H. Tanaka, “Violation of the Franck–Condon Principle due to recoil effects in high energy molecular core-level photoionization,” Phys. Rev. Lett., 95, 133001 (2005).

    Article  Google Scholar 

  19. L.D. Landau and E. M. Lifschitz, Quantum mechanics, Nonrelativistic theory [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  20. A. Mielke and T. Roubíček, “A rate-independent model for inelastic behavior of shape-memory alloys,” Multiscale Model Simul., 1(4), 571–597 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  21. A. A. Pavlychev, X. O. Brykalova, R. Flesch, and E. Rühl, “Shape resonances in molecular clusters: the 2t 2g shape resonances in S 2p-excited sulfur hexafluoride clusters,” J. El. Spectroscopy Relat. Phenom., 8, No. 16, 1914–1921 (2006).

    Google Scholar 

  22. A. A. Pavlychev, X. O. Brykalova, D. A. Mistrov, R. Flesch, and E. Rühl, “Position and line shape of the 2t 2g -shape resonance in S 2p-excited sulfur hexafluoride clusters,” J. El. Spectroscopy Relat. Phenom., 166-167, 45–52 (2008).

    Article  Google Scholar 

  23. A. A. Pavlychev, N. G. Fominych, N. Watanabe, K. Soejima, E. Shigemasa, and A. Yagishita, “Dynamic properties of N and O 1s − 1 σ ∗ u shape resonances in N 2 and CO 2 molecules,” Phys. Rev. Lett., 81, No. 17, 3623–3626 (1998).

    Article  Google Scholar 

  24. A. A. Pavlychev and D. A. Mistrov, “Spectral distributions of vibrational excitations accompanying 1s shell photoionization in small molecules,” J. Phys. B, 42, 055103 (2009).

    Article  Google Scholar 

  25. A. A. Pavlychev and E. Rühl, “Dynamic localization of inner-shell excitations in free atomic and molecular clusters,” J. El. Spectroscopy Relat. Phenom., 106, No. 2-3, 207–220 (2000).

    Article  Google Scholar 

  26. M. N. Piancastelli, D. W. Lindle, T. A. Ferrett, and D.A. Shirley, “The relationship between shape resonances and bond lengths,” J. Chem. Phys., 86, No. 5, 2765–2771 (1987).

    Article  Google Scholar 

  27. E. D. Poliakoff, H.C. Choi, R.M. Rao, A. G. Mihill, S. Kakar, K. Wang, and V. McKoy, “Photoion rotational distributions from near-threshold to deep in the continuum,” J. Chem. Phys., 103, 1773–1787 (1995).

    Article  Google Scholar 

  28. E. Rühl and R. Flesch, “Mechanism of anion formation in C 1s → π ∗-excited carbon dioxide,” J. Chem. Phys., 121, No. 11, 5322–5327 (2004).

    Article  Google Scholar 

  29. M. Schmidbauer, A. L.D. Kilcoyne, H.M. Köppe, J. Feldhaus, and A.M. Bradshaw, “Shape resonances and multielectron effects in the core-level photoionization of CO 2,” Phys, Rev. A, 52, No. 3, 2095–2108 (1995).

    Article  Google Scholar 

  30. M. S. Schöffler, M. S. J. Titze, N. Petridis, T. Jahnke, K. Cole, L. Ph. H. Schmidt, A. Czasch, D. Akoury, O. Jagutsky, J.B. Williams, N.A. Cherepkov, S.K. Semenov, C.W. McCurdy, T. N. Rescigno, C. L. Cocke, T. Osipov, S. Lee, M. H. Prior, A. Belcasem, A. L. Landers, H. Schmidt-Böcking, Th. Weber, and R. Dörner, “Ultrafast probing of core hole localization in N 2,” Science, 320, 920–923 (2008).

    Article  Google Scholar 

  31. S.W. J. Scully, R.A. Mackie, R. Browning, K.F. Dunn, and C. J. Latimer, “Negative photoion spectroscopy of SF 6 in the inner valence and S 2p energy regions,” J. Phys. B, 35, No. 12, 2703–2712 (2002).

    Article  Google Scholar 

  32. Y. Takata, Y. Kayanuma, M. Yabashi, K. Tamasaku, Y. Nishino, D. Miwa, Y. Harada, K. Horiba, S. Shin, S. Tanaka, E. Ikenaga, K. Kobayashi, Y. Senba, H. Ohashi, and T. Ishikawa, “Recoil effects of photoelectrons in a solid,” Phys. Rev. B, 75, 233404 (2007).

    Article  Google Scholar 

  33. A. Thiel, J. Schirmer, and H. Köppel, “An intermediate state representation approach to K-shell ionization in molecules. II. Computational tests,” J. Chem. Phys., 119, 2088–2101 (2003).

    Article  Google Scholar 

  34. T. D. Thomas, E. Kukk, H. Fukuzawa, K. Ueda, R. Püttner, Y. Tamenori, T. Asahina, N. Kuze, H. Kato, M. Hoshino, H. Tanaka, M. Meyer, J. Plenge, A. Wirsing, E. Serdaroglu, R. Flesch, E. Rühl, S. Gavrilyuk, F. Gel’mukhanov, A. Lindblad, and L. J. Saetre, “Photoelectron-recoilinduced rotational excitation of the B 2 Σ + u state in N +2 ,” Phys. Rev. A, 79, 022506 (2009).

    Article  Google Scholar 

  35. K. Ueda, “To be or not to be localized,” Science, 320, 884-885 (2008).

    Article  Google Scholar 

  36. R. V. Vedrinskii, V. L. Kraizman, A.A. Novakovich, and Yu. A. Teterin, “Formation of peculiarities in absorption spectra of poliatomic systems: the case of arbitrary symmetry” [in Russian], Preprint IAE-3368/12, Inst. Atom. Energy, Moscow (1980).

  37. A. S. Vinogradov, S. I. Fedoseenko, S.A. Krasnikov, A.B. Preobrajenski, V.N. Sivkov, D. V. Vyalikh, S. L. Molodtsov, V. K. Adamchuk, C. Laubschat, and G. Kaindl, “Low-lying unoccupied electronic states in 3d transition-metal fluorides probed by NEXAFS at the F 1s threshold” Phys. Rev. B, 71, 045127 (2005).

    Article  Google Scholar 

  38. A. S. Vinogradov and T.M. Zimkina, “Photoabsorption cross section of SF6 in soft and ultrasoft X-rays,” Opt. Spectrosc. (USSR), 32, 17–19 (1972).

    Google Scholar 

  39. M. Vos, M.R. Went, Y. Kayanuma, Y. Takata, and J. Mayers, “Comparison of recoil effects in graphite as observed by photoemission, electron scattering, and neutron scattering,” Phys. Rev. B, 78, 024301 (2008).

    Article  Google Scholar 

  40. N. Watanabe, J. Adachi, K. Soejima, E. Shigemasa, A. Yagishita, N. G. Fominych, and A. A. Pavlychev, “Fixed-molecule 1sσ g,u photoelectron angular distributions as a probe of σ ∗ g and σ ∗ u shape resonances of CO 2,” Phys. Rev. Lett., 78, No. 26, 4910–4913 (1997).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Physics, St. Petersburg State University, 198504, St. Petersburg, Russia

    E. S. Klyushina, Yu. S. Krivosenko & A.A. Pavlychev

Authors
  1. E. S. Klyushina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. S. Krivosenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A.A. Pavlychev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. S. Klyushina.

Additional information

Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 48, Proceedings of the Sixth International Conference on Differential and Functional Differential Equations and International Workshop “Spatio-Temporal Dynamical Systems” (Moscow, Russia, 14–21 August, 2011). Part 4, 2013.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Klyushina, E.S., Krivosenko, Y.S. & Pavlychev, A. Spatio-Temporal Dynamical Systems in Inner-Shell Photoionization in Free Molecules, Clusters, and Solids. J Math Sci 202, 835–848 (2014). https://doi.org/10.1007/s10958-014-2080-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-014-2080-z

Keywords

Search

Navigation