Volumes and Issues
Home » Optics and Spectroscopy » Year 2026, issue 2 » Article p. 113
<<<>>>
Two-photon ionization of the K-shell of a heavy beryllium-like atomic ion
Russian version
Hopersky A. N. 1, Nadolinsky A. M. 1, Koneev R. V. 1
1Rostov State University for Railway Transportation, Rostov-on-Don, Russia
Email: qedhop@mail.ru, amnrnd@mail.ru, koneev@gmail.com
PDF
Within the framework of the second order of the non-relativistic quantum perturbation theory, the analytical structure and absolute values of the generalized cross-sections of the two-photon resonant single ionization of the K-shell of heavy beryllium-like ions of titanium (Ti18+), chromium (Cr20+), iron (Fe22+) and zinc (Zn26+) atoms were predicted. The complete wave functions of the ground state of the ion and the states of its ionization are obtained in the single-configuration Hartree-Fock approximation. The effects of (a) the occurrence of giant resonances in the subthreshold region of the generalized ionization cross-sections, (b) destructive quantum interference of the probability amplitudes of radiation transitions to intermediate states of p-symmetry, and (c) the leading role of the d-symmetry of the final ionization state in determining the values of the total generalized cross-section in the region of energies of absorbed photons of the hard X-ray range were established. A scheme of the proposed experiment with linearly polarized X-ray photons is presented to verify the theoretical results obtained Keywords: beryllium-like atomic ion, two-photon ionization, probability amplitude, generalized cross-section.
  1. C. Pellegrini, A. Marinelli, S. Reiche. Rev. Mod. Phys., 88, 015006 (2016). DOI: 10.1103/RevModPhys.88.015006
  2. M. Chergui, M. Beye, S. Mukamel, Cr. Svetina, C. Mascioveccio. Nature Rev. Phys., 5, 578 (2023). DOI: 10.1038/s42254-023-00643-7
  3. Y. Kubota, K. Tamasaku. Nonlinear X-Ray Spectroscopy for Materials Science (Springer Series in Optical Science, 2023), 246, Ch. 5, P. 119-145. DOI: 10.1007/978-981-99-6714-8_5
  4. A. Surzhykov, P. Indelicato, S.P. Santos, P. Amaro, S. Fritzsche. Phys. Rev. A, 84, 022511 (2011). DOI: 10.1103/PhysRevA.84.022511
  5. J. Hofbrucker, A.V. Volotka, S. Fritzsche. Phys. Rev. A, 94, 063412 (2016). DOI: 10.1103/PhysRevA.94.063412
  6. J. Hofbrucker, A.V. Volotka, S. Fritzsche. Scientific Reports, 10, 3617 (2020). DOI: 10.1038/s41598-020-60206-z
  7. J. Fan, J. Hofbrucker, A.V. Volotka, S. Fritzsche. Eur. Phys. J. D, 76, 18 (2022). DOI: 10.1140/epjd/s10053-021-00334-x
  8. A.N. Grum-Grzhimailo, E.V. Gryzlova. Phys. Rev. A, 89, 043424 (2014). DOI: 10.1103/PhysRevA.89.043424
  9. J. Hofbrucker, A.V. Volotka, S. Fritzsche. Phys. Rev. A, 96, 013409 (2017). DOI: 10.1103/PhysRevA.96.013409
  10. S.A. Novikov, A.N. Hopersky. J. Phys. B, 33, 2287 (2000). DOI: 10.1088/0953-4075/33/12/310
  11. S.A. Novikov, A.N. Hopersky. J. Phys. B, 34, 4857 (2001). DOI: 10.1088/0953-4075/34/23/327
  12. A.N. Hopersky, A.M. Nadolinsky, S.A. Novikov, R.V. Koneev. arXiv: 2504.05290v1 [physics.optics] (2025). DOI: 10.48550/arXiv.2504.05290
  13. A.N. Hopersky, A.M. Nadolinsky, S.A. Novikov, R.V. Koneev. arXiv: 2506.18117v1 [physics.atom-ph] (2025). DOI: 10.48550/arXiv.2506.18117
  14. J.K. Rudolph, S. Bernitt, S.W. Epp et al. Phys. Rev. Lett., 111, 103002 (2013). DOI: 10.1103/PhysRevLett.111.103002
  15. S.W. Epp, J.R. Crespo Lv opez-Urrutia, G. Brenner et al. Phys. Rev. Lett. 98, 183001 (2007). DOI: 10.1103/PhysRevLett. 98.183001
  16. M.O. Herdrich, D. Hengstler, S. Allgeier et al. J. Phys. B, 57, 085001 (2024). DOI: 10.1088/1361-6455/ad34a2
  17. P. Micke, S. Kuhn, L. Buchauer et al. Rev. Sci. Instrum., 89, 063109 (2018). DOI: 10.1063/1.5026961
  18. P. Beiersdorfer, T. Phillips, V.L. Jacobs et al. Astrophys. J., 409, 846 (1993). DOI: 10.1086/172715
  19. K. Wang, X.L. Guo, H.T. Liu et al. Astrophys. J. Supp. Ser., 218, 16 (2015). DOI: 10.1088/0067-0049/218/2/16
  20. The Hitomi Collaboration. Publ. Astron. Soc. Japan., 70, 12 (P. 1-48) (2018). DOI: 10.1093/pasj/psx127
  21. A.M. Pollock, M.F. Corcoran, I.R. Stevens et al. Astrophys. J., 923, 191 (2021). DOI: 10.3847/1538-4357/ac2430
  22. N.S. Schulz, D.P. Huenemoerder, D.A. Principe et al. arXiv: 2404.19676v1 [astro-ph. SR] (2024). DOI: 10.48550/arXiv.2404.19676
  23. S.P. Regan, B. Yaakobi, T.R. Boehly et al. High Energy Density Physics, 5, 234 (2009). DOI: 10.1016/j.hedp.2009.05.004
  24. R.K. Kirkwood, J.D. Moody, J. Kline et al. Plasma Phys. Control. Fusion, 55, 103001 (2013). DOI: 10.1088/0741-3335/55/10/103001
  25. R. Betti, O.A. Hurricane. Nature Phys., 12, 435 (2016). DOI: 10.1038/nphys3736
  26. A.V. Malyshev, A.V. Volotka, D.A. Glazov et al. Phys. Rev. A, 92, 012514 (2015). DOI: 10.1103/ PhysRevA.92.012514
  27. A.N. Hopersky, A.M. Nadolinsky, S.A. Novikov. Phys. Rev. A, 92, 052709 (2015)
  28. A.N. Khopersky, A.M. Nadolinsky, R.V. Koneev, Yu.N. Tolkunova. Izv. vuzov. Severo-kavkazskiy region. Yestestvennye nauki, (in Russian) 2, 23 (2025); arXiv: 2504.08656v1 [physics. atom-ph] (2025). DOI: 10.18522/1026-2237-2025-2-23-28
  29. L.D. Landau. Dokl. Akad. Nauk SSSR, 60, 207 (1948)
  30. C.N. Yang. Phys. Rev., 77, 242 (1950). DOI: 10.1103/PhysRev.77.242
  31. V.B. Berestetskiy, Ye.M. Lifshits, L.P. Pitayevskiy. Kvantovaya elektrodinamika (Nauka, M., 1980) (in Russian)
  32. A.P. Yutsis, A.Yu. Savukinas. Matematicheskie osnovy teorii atoma (Mintis, Vilnyus, 1973) (in Russian)
  33. A.P. Jucys, E.P. Nav slv enas, P.S. v Zvirblis. Int. J. Quant. Chem., 6, 465 (1972). DOI: 10.1002/qua.560060308
  34. N. Bloembergen. Nonlinear Optics (World Scientific, Singapore, 1996)
  35. P. Lambropoulos, X. Tang. J. Opt. Soc. Am. B, 4, 821 (1987). DOI: 10.1364/JOSAB.4.000821
  36. R.M. Loudon. Kvantovaya teoriya sveta (Mir, M., 1976) (in Russian)
  37. A.N. Khoperskiy, R.V. Koneev. Izv. vuzov. Severo-kavkazskiy region. Yestestvennye nauki, 1, 24 (2023); arXiv: 2504.11567v1 (in Russian) [physics. atom-ph] (2023). DOI: 10.18522/1026-2237-2023-1-24-28
  38. M.H. Chen. Phys. Rev. A, 31, 1449 (1985). DOI: 10.1103/PhysRevA.31.1449
  39. R. Karaziya. Summy atomnykh velichin i srednie kharakteristiki spektrov (Mosklas, Vilnyus, 1991) (in Russian)
  40. M.J. Seaton. Rep. Prog. Phys., 46, 167 (1983). DOI: 10.1088/0034-4885/46/2/002
  41. A.N. Hopersky, A.M. Nadolinsky, S.A. Novikov. J. Phys. B, 57, 215601 (2024). DOI: 10.1088/1361-6455/ad7cab
  42. M. Rid, B. Saymon. Metody sovremennoy matematicheskoy fiziki. T. 1. Funktsionalny analiz (Mir, M.,1977) (in Russian)
  43. A.N. Hopersky, A.M. Nadolinsky, R.V. Koneev. Izv. vuzov. Severo-kavkazskiy region. Yestestvennyye nauki, 1, 39 (2024) (in Russian); arXiv: 2504.13329v1 [physics. atom-ph] (2024). DOI: 10.18522/1026-2237-2024-1-38-42
  44. B. Adams, G. Aeppli, Th. Allison et al. arXiv: 1903.09317v2 [physics. ins-det] (2019). DOI: 10.48550/ arXiv.1903.09317
  45. N. Kujala, W. Freund, J. Liu et al. Rev. Sci. Instrum., 91, 103101 (2020). DOI: 10.1063/5.0019935
  46. Ch. Grech, M.W. Guetg, G.A. Geloni et al. Phys. Rev. Accel. Beam, 27, 050701 (2024). DOI: 10.1103/PhysRevAccelBeams.27.050701
  47. I. Nam, Ch-K. Min, B. Oh et al. Nat. Photonics, 15, 435 (2021). DOI: 10.1038/s41566-021-00777-z
  48. TEP Group, J. Dubau, M. Loulergue. J. Phys. B, 15, 1007 (1982). DOI: 10.1088/0022-3700/15/7/010
  49. V.A. Yerokhin, A. Surzhykov, S. Fritzsche. Phys. Rev. A, 90, 022509 (2014). DOI: 10.1103/ PhysRevA.90.022509
  50. T. Osaka, I. Inoue, J. Yamada et al. Phys. Rev. Res., 4, L012035 (2022). DOI: 10.1103/PhysRevResearch.4.L012035
Publisher:

Ioffe Institute

Institute Officers:

Director: Sergei V. Ivanov

Contact us:

26 Polytekhnicheskaya, Saint Petersburg 194021, Russian Federation
Fax: +7 (812) 297 1017
Phone: +7 (812) 297 2245
E-mail: post@mail.ioffe.ru