- Physical Review Journals
All JournalsPhysics Magazine

Physical Review A

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Laser-assisted electron–molecular-ion radiative recombination

D. Habibović1,*, A. Čerkić1, M. Busuladžić1,2, and D. B. Milošević1,3

  • *Contact author: dhfizika1@gmail.com
PDF

Phys. Rev. A 114, 033118 – Published 29 September, 2026

DOI: https://doi.org/10.1103/2271-df63

Abstract

We formulate a theory of laser-assisted radiative recombination of electron with diatomic homonuclear ion in a linearly polarized laser field using the S-matrix formalism. We investigate how the multicenter molecular structure modifies the differential power spectra and polarization properties of the emitted x-rays. The emitted spectra exhibit characteristic two-center interference minima whose positions depend on the molecular orientation, internuclear distance, symmetry of the molecular orbital, and the incident electron momentum. We show that the visibility of the interference minima is strongly influenced by the molecular orientation and by the component of the incident electron momentum perpendicular to the laser-field polarization vector. The minima remain comparatively robust against imperfect molecular alignment. In addition, the emitted x-rays remain linearly polarized, while their polarization direction depends on the emitted-photon energy and on the geometry of the recombination process. The obtained results demonstrate that laser-assisted radiative recombination provides direct access to structural and symmetry properties of molecular targets.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (80)

  1. L. F. DiMauro and P. Agostini, Ionization dynamics in strong laser fields, Adv. At. Mol. Opt. Phys. 35, 79 (1995).
  2. M. Protopapas, C. H. Keitel, and P. L. Knight, Atomic physics with super-high intensity lasers, Rep. Prog. Phys. 60, 389 (1997).
  3. C. J. Joachain, M. Dörr, and N. Kylstra, High-intensity laser-atom physics, Adv. At. Mol. Opt. Phys. 42, 225 (2000).
  4. W. Becker, F. Grasbon, R. Kopold, D. B. Milošević, G. G. Paulus, and H. Walther, Above-threshold ionization: From classical features to quantum effects, Adv. At. Mol. Opt. Phys. 48, 35 (2002).
  5. D. B. Milošević and F. Ehlotzky, Scattering and reaction processes in powerful laser fields, Adv. At. Mol. Opt. Phys. 49, 373 (2003).
  6. D. B. Milošević, G. G. Paulus, D. Bauer, and W. Becker, Above-threshold ionization by few-cycle pulses, J. Phys. B: At. Mol. Opt. Phys. 39, R203 (2006).
  7. M. C. Kohler, T. Pfeifer, K. Z. Hatsagortsyan, and C. H. Keitel, Frontiers of atomic high-harmonic generation, Adv. At. Mol. Opt. Phys. 61, 159 (2012).
  8. P. Agostini and L. F. DiMauro, Atomic and molecular ionization dynamics in strong laser fields: From optical to x-rays, Adv. At. Mol. Opt. Phys. 61, 117 (2012).
  9. S. V. Popruzhenko, Keldysh theory of strong field ionization: History, applications, difficulties and perspectives, J. Phys. B: At. Mol. Opt. Phys. 47, 204001 (2014).
  10. F. Calegari, G. Sansone, S. Stagira, C. Vozzi, and M. Nisoli, Advances in attosecond science, J. Phys. B: At. Mol. Opt. Phys. 49, 062001 (2016).
  11. W. Becker, S. P. Goreslavski, D. B. Milošević, and G. G. Paulus, The plateau in above-threshold ionization: The keystone of rescattering physics, J. Phys. B: At. Mol. Opt. Phys. 51, 162002 (2018).
  12. K. Amini, J. Biegert, F. Calegari, A. Chacón, M. F. Ciappina, A. Dauphin, D. K. Efimov, C. Figueira de Morisson Faria, K. Giergiel, P. Gniewek, A. S. Landsman, M. Lesiuk, M. Mandrysz, A. S. Maxwell, R. Moszyński, L. Ortmann, J. A. Pérez-Hernández, A. Picón, E. Pisanty, J. Prauzner-Bechcicki, et al., Symphony on strong field approximation, Rep. Prog. Phys. 82, 116001 (2019).
  13. P. B. Corkum, Plasma perspective on strong field multiphoton ionization, Phys. Rev. Lett. 71, 1994 (1993).
  14. K. C. Kulander, K. J. Schafer, and J. L. Krause, Dynamics of short-pulse excitation, ionization and harmonic conversion, in Super-Intense Laser-Atom Physics, edited by B. Piraux, A. L'Huillier, and K. Rzążewski, NATO Advanced Science Institutes Series, Series B: Physics (Plenum, New York, 1993), Vol. 316, p. 95.
  15. P. Salières, A. L' Huillier, P. Antoine, and M. Lewenstein, Study of the spatial and temporal coherence of high-order harmonics, Adv. At. Mol. Opt. Phys. 41, 83 (1999).
  16. T. Brabec and F. Krausz, Intense few-cycle laser fields: Frontiers of nonlinear optics, Rev. Mod. Phys. 72, 545 (2000).
  17. R. V. Karapetyan and M. V. Fedorov, Spontaneous bremsstrahlung of an electron in the field of an intense electromagnetic wave, Zh. Eksp. Teor. Fiz. 75, 816 (1978) [Sov. Phys. JETP 48, 412 (1978)].
  18. F. Zhou and L. Rosenberg, Bremsstrahlung in laser-assisted scattering, Phys. Rev. A 48, 505 (1993).
  19. F. Ehlotzky, A. Jaroń, and J. Z. Kamiński, Electron-atom collisions in a laser field, Phys. Rep. 297, 63 (1998).
  20. M. Dondera and V. Florescu, Bremsstrahlung in the presence of a laser field, Radiat. Phys. Chem. 75, 1380 (2006).
  21. A. N. Zheltukhin, A. V. Flegel, M. V. Frolov, N. L. Manakov, and A. F. Starace, Resonant electron-atom bremsstrahlung in an intense laser field, Phys. Rev. A 89, 023407 (2014).
  22. A. N. Zheltukhin, A. V. Flegel, M. V. Frolov, N. L. Manakov, and A. F. Starace, Rescattering effects in laser-assisted electron-atom bremsstrahlung, J. Phys. B: At. Mol. Opt. Phys. 48, 075202 (2015).
  23. D. B. Milošević and F. Ehlotzky, X-ray-atom scattering in the presence of a laser field, Phys. Rev. A 58, 2319 (1998).
  24. D. B. Milošević and A. F. Starace, Static-electric-field-induced, high-energy plateau for scattered x-ray photons in laser-assisted, x-ray–atom scattering, Phys. Rev. Lett. 81, 5097 (1998).
  25. D. B. Milošević and A. F. Starace, Phase control of x-ray-atom scattering in the presence of a bichromatic laser field, J. Phys. B: At. Mol. Opt. Phys. 32, 1831 (1999).
  26. A. Jaroń, J. Z. Kamiński, and F. Ehlotzky, Stimulated radiative recombination and x-ray generation, Phys. Rev. A 61, 023404 (2000).
  27. M. Y. Kuchiev and V. N. Ostrovsky, Multiphoton radiative recombination of electron assisted by a laser field, Phys. Rev. A 61, 033414 (2000).
  28. M. Y. Kuchiev and V. N. Ostrovsky, Effective ATI channels in high harmonic generation, J. Phys. B: At. Mol. Opt. Phys. 34, 405 (2001).
  29. C. Leone, S. Bivona, R. Burlon, and G. Ferrante, Strong-field and plasma aspects of multiphoton radiative recombination, Phys. Rev. A 66, 051403 (2002).
  30. S. X. Hu and L. A. Collins, Intense laser-induced recombination: The inverse above-threshold ionization process, Phys. Rev. A 70, 013407 (2004).
  31. S. Bivona, R. Burlon, G. Ferrante, and C. Leone, Radiative recombination in a strong laser field: Low-frequency approximation, J. Opt. Soc. Am. B 22, 2076 (2005).
  32. G. Shchedrin and A. Volberg, Analytical model for laser-assisted recombination of hydrogenic atoms, J. Phys. A: Math. Theor. 44, 245301 (2011).
  33. I. I. Fabrikant and H. B. Ambalampitiya, Semiclassical theory of laser-assisted radiative recombination, Phys. Rev. A 101, 053401 (2020).
  34. A. V. Flegel, N. L. Manakov, I. V. Breev, and M. V. Frolov, Adiabatic expressions for the wave function of an electron in a finite-range potential and an intense low-frequency laser pulse, Phys. Rev. A 104, 033109 (2021).
  35. D. Kanti, M. M. Majczak, J. Z. Kamiński, L.-Y. Peng, and K. Krajewska, Laser-assisted radiative recombination beyond the dipole approximation, Phys. Rev. A 110, 043112 (2024).
  36. A. Jaroń, J. Z. Kamiński, and F. Ehlotzky, Coherent phase control in laser-assisted radiative recombination and x-ray generation, J. Phys. B: At. Mol. Opt. Phys. 34, 1221 (2001).
  37. S. Odžak and D. B. Milošević, Bicircular-laser-field-assisted electron-ion radiative recombination, Phys. Rev. A 92, 053416 (2015).
  38. A. Čerkić, M. Busuladžić, and D. B. Milošević, Electron-ion radiative recombination assisted by a bichromatic elliptically polarized laser field, Phys. Rev. A 95, 063401 (2017).
  39. A. Tutmić, A. Čerkić, M. Busuladžić, and D. B. Milošević, Role of the relative phase and intensity ratio in electron-ion recombination assisted by a bicircular laser field, Eur. Phys. J. D 73, 231 (2019).
  40. D. Kanti, J. Z. Kamiński, L.-Y. Peng, and K. Krajewska, Electron-ion radiative recombination assisted by bicircular laser pulses, Photonics 12, 320 (2025).
  41. J. Z. Kamiński and F. Ehlotzky, Time-frequency analysis of x-ray generation by recombination in short laser pulses, Phys. Rev. A 71, 043402 (2005).
  42. J. Z. Kamiński and F. Ehlotzky, Generation of attosecond pulses in electron-ion recombination processes, J. Mod. Opt. 53, 7 (2006).
  43. S. Bivona, R. Burlon, G. Ferrante, and C. Leone, Radiative recombination in the presence of a few cycle laser pulse, Opt. Express 14, 3715 (2006).
  44. S. Bivona, R. Burlon, and C. Leone, Controlling laser assisted radiative recombination with few-cycle laser pulses, Laser Phys. Lett. 4, 44 (2007).
  45. D. Kanti, J. Z. Kamiński, L.-Y. Peng, and K. Krajewska, Laser-assisted electron-atom radiative recombination in short laser pulses, Phys. Rev. A 104, 033112 (2021).
  46. I. I. Fabrikant and H. B. Ambalampitiya, Laser-assisted radiative recombination in a cold hydrogen plasma, J. Phys. B: At. Mol. Opt. Phys. 57, 195201 (2024).
  47. J.-H. Mun, S.-H. Jang, and S. K. Nam, Quantum-optical radiative recombination between electrons and ions analyzed with a semiclassical picture, Phys. Rev. A 110, 043115 (2024).
  48. K. R. Overstreet, R. R. Jones, and T. F. Gallagher, Phase-dependent electron-ion recombination in a microwave field, Phys. Rev. Lett. 106, 033002 (2011).
  49. T. Mohamed, G. Andler, M. Fogle, E. Justiniano, S. Madzunkov, and R. Schuch, Effects of polarization on laser-induced electron-ion recombination, Phys. Rev. A 83, 032702 (2011).
  50. M. L. Rogelstad, F. B. Yousif, T. J. Morgan, and J. B. A. Mitchell, Stimulated radiative recombination of H+ and He+, J. Phys. B: At. Mol. Opt. Phys. 30, 3913 (1997).
  51. C. Wesdorp, F. Robicheaux, and L. D. Noordam, Field-induced electron-ion recombination: A novel route towards neutral (anti-)matter, Phys. Rev. Lett. 84, 3799 (2000).
  52. G. Gabrielse, Atoms made entirely of antimatter: Two methods produce slow antihydrogen, Adv. At. Mol. Opt. Phys. 50, 155 (2005).
  53. R. A. Müller, D. Seipt, S. Fritzsche, and A. Surzhykov, Effect of bound-state dressing in laser-assisted radiative recombination, Phys. Rev. A 92, 053426 (2015).
  54. V. A. Zaytsev, V. G. Serbo, and V. M. Shabaev, Radiative recombination of twisted electrons with bare nuclei: Going beyond the Born approximation, Phys. Rev. A 95, 012702 (2017).
  55. M. Busuladžić, A. Gazibegović-Busuladžić, D. B. Milošević, and W. Becker, Angle-resolved high-order above-threshold ionization of a molecule: Sensitive tool for molecular characterization, Phys. Rev. Lett. 100, 203003 (2008).
  56. M. Busuladžić, A. Gazibegović-Busuladžić, D. B. Milošević, and W. Becker, Strong-field approximation for ionization of a diatomic molecule by a strong laser field. II. The role of electron rescattering off the molecular centers, Phys. Rev. A 78, 033412 (2008).
  57. S. Odžak and D. B. Milošević, Interference effects in high-order harmonic generation by homonuclear diatomic molecules, Phys. Rev. A 79, 023414 (2009).
  58. D. Habibović and D. B. Milošević, Ellipticity of high-order harmonics generated by aligned homonuclear diatomic molecules exposed to an orthogonal two-color laser field, Photonics 7, 110 (2020).
  59. D. Habibović, A. Gazibegović-Busuladžić, M. Busuladžić, A. Čerkić, and D. B. Milošević, Strong-field ionization of homonuclear diatomic molecules using orthogonally polarized two-color laser fields, Phys. Rev. A 102, 023111 (2020).
  60. D. Habibović, A. Gazibegović-Busuladžić, M. Busuladžić, and D. B. Milošević, Strong-field ionization of heteronuclear diatomic molecules using an orthogonally polarized two-color laser field, Phys. Rev. A 103, 053101 (2021).
  61. C. F. de Morisson Faria and B. B. Augstein, Molecular high-order harmonic generation with more than one active orbital: Quantum interference effects, Phys. Rev. A 81, 043409 (2010).
  62. B. B. Augstein and C. F. de Morisson Faria, Multielectron corrections in molecular high-order harmonic generation for different formulations of the strong-field approximation, J. Mod. Opt. 58, 1173 (2011).
  63. D. B. Milošević, Strong-field approximation for ionization of a diatomic molecule by a strong laser field, Phys. Rev. A 74, 063404 (2006).
  64. A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1965), Sec. IX, p. 13.
  65. P. W. Atkins and R. S. Friedman, Molecular Quantum Mechanics, 3rd ed. (Oxford University Press, Oxford, 2001).
  66. A. Jaroń, J. Z. Kamiński, and F. Ehlotzky, Bohr's correspondence principle and x-ray generation by laser-stimulated electron-ion recombination, Phys. Rev. A 63, 055401 (2001).
  67. D. B. Milošević and F. Ehlotzky, Rescattering effects in soft-x-ray generation by laser-assisted electron-ion recombination, Phys. Rev. A 65, 042504 (2002).
  68. I. N. Levine, Quantum Chemistry, 5th ed. (Prentice-Hall, Upper Saddle River, NJ, 2000).
  69. A. C. Wahl, Self consistent field wavefunctions and computed properties for homonuclear diatomic molecules, J. Chem. Phys. 41, 2600 (1964).
  70. D. B. Milošević, A. S. Jašarević, D. Habibović, E. Hasović, A. Čerkić, and W. Becker, Asymptotic methods applied to integrals occurring in strong-laser-field processes, J. Phys. A: Math. Theor. 57, 393001 (2024).
  71. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, 1999).
  72. E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, New York, 1993).
  73. D. B. Milošević, M. Busuladžić, A. Gazibegović-Busuladžić, and W. Becker, Strong-field approximation for high-order above-threshold ionization of randomly oriented diatomic molecules, Chem. Phys. 366, 85 (2009).
  74. H. R. Reiss, The tunnelling model of laser-induced ionization and its failure at low frequencies, J. Phys. B: At. Mol. Opt. Phys. 47, 204006 (2014).
  75. J. Maurer and U. Keller, Ionization in intense laser fields beyond the electric dipole approximation: Concepts, methods, achievements and future directions, J. Phys. B: At. Mol. Opt. Phys. 54, 094001 (2021).
  76. X. Zhou, R. Lock, N. Wagner, W. Li, H. C. Kapteyn, and M. M. Murnane, Elliptically polarized high-order harmonic emission from molecules in linearly polarized laser fields, Phys. Rev. Lett. 102, 073902 (2009).
  77. A.-T. Le, R. R. Lucchese, and C. D. Lin, Polarization and ellipticity of high-order harmonics from aligned molecules generated by linearly polarized intense laser pulses, Phys. Rev. A 82, 023814 (2010).
  78. D. Habibović, T. Rook, and D. B. Milošević, Application of catastrophe theory to multicolor-laser-field-assisted scattering, Commun. Phys. 9, 138 (2026).
  79. M. Busuladžić, A. Gazibegović-Busuladžić, and D. B. Milošević, Strong-field ionization of homonuclear diatomic molecules by a bicircular laser field: Rotational and reflection symmetries, Phys. Rev. A 95, 033411 (2017).
  80. R. G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (Springer-Verlag, New York, 1982).

Outline

Information

Phys. Rev. A 114, 033118– Published 29 September, 2026
  • Received 12 June 2026
  • Accepted 11 September 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation