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Resonant photon scattering in the presence of external fields and its applications for the CERN Gamma Factory project

Jan Richter1,2,*, Mieczyslaw Witold Krasny3,4, Jan Gilles5,6, and Andrey Surzhykov1,7

  • *Contact author: jan.richter@ptb.de
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Phys. Rev. A 111, 062820 – Published 24 June, 2025

DOI: https://doi.org/10.1103/yysz-444v

Abstract

We present a theoretical study of resonant elastic photon scattering by highly charged ions in the presence of external electric and magnetic fields. Special emphasis is placed on head-on collisions of relativistic ion beams and counterpropagating laser photons, as can be observed in ion storage ring experiments. If the collision zone for such a scenario is exposed to a moderate field of a dipole magnet, a fast-moving ion will be subjected to strong electric and magnetic fields in its rest frame due to the Lorentz transformation. To investigate the effect of these fields we performed detailed calculations for the elastic photon scattering by He-like Ca ions moving with the Lorentz factor γL=2395. Such a scenario is of particular interest for the Gamma Factory project which is supported by the CERN Physics Beyond Colliders framework. Based on the results of our calculations, we argue that even moderate magnetic fields significantly modify the rate of detected photons as well as their emission pattern and polarization. This sensitivity to external fields opens interesting avenues for diverse applications for the Gamma Factory project, such as resonance condition tuning, beam cooling, and polarization control.

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References (76)

  1. P. Kane, L. Kissel, R. Pratt, and S. Roy, Elastic scattering of γ-rays and x-rays by atoms, Phys. Rep. 140, 75 (1986).
  2. W. Middents, G. Weber, A. Gumberidze, C. Hahn, T. Krings, N. Kurz, P. Pfäfflein, N. Schell, U. Spillmann, S. Strnat, M. Vockert, A. Volotka, A. Surzhykov, and T. Stöhlker, Angle-differential cross sections for Rayleigh scattering of highly linearly polarized hard x rays on Au atoms, Phys. Rev. A 107, 012805 (2023).
  3. S. Strnat, V. A. Yerokhin, A. V. Volotka, G. Weber, S. Fritzsche, R. A. Müller, and A. Surzhykov, Polarization studies on Rayleigh scattering of hard x rays by closed-shell atoms, Phys. Rev. A 103, 012801 (2021).
  4. S. Strnat, J. Sommerfeldt, V. Yerokhin, W. Middents, T. Stöhlker, and A. Surzhykov, Circular polarimetry of hard X-rays with rayleigh scattering, Atoms 10, 140 (2022).
  5. V. G. Serbo, A. Surzhykov, and A. Volotka, Resonant scattering of plane-wave and twisted photons at the gamma factory, Ann. Phys. 534, 2100199 (2022).
  6. A. Volotka, D. Samoilenko, S. Fritzsche, V. G. Serbo, and A. Surzhykov, Polarization of photons scattered by ultra-relativistic ion beams, Ann. Phys. 534, 2100252 (2022).
  7. D. Samoilenko, A. V. Volotka, and S. Fritzsche, Elastic photon scattering on hydrogenic atoms near resonances, Atoms 8, 12 (2020).
  8. S. Bernitt et al., An unexpectedly low oscillator strength as the origin of the Fe XVII emission problem, Nature (London) 492, 225 (2012).
  9. M. Togawa, J. Richter, C. Shah, M. Botz, J. Nenninger, J. Danisch, J. Goes, S. Kühn, P. Amaro, A. Mohamed, Y. Amano, S. Orlando, R. Totani, M. de Simone, S. Fritzsche, T. Pfeifer, M. Coreno, A. Surzhykov, and J. R. C. López-Urrutia, Hanle effect for lifetime determinations in the soft x-ray regime, Phys. Rev. Lett. 133, 163202 (2024).
  10. J. Richter, M. Togawa, J. R. C. López-Urrutia, and A. Surzhykov, Hanle effect for lifetime analysis: Li-like ions, JINST 20, C03003 (2025).
  11. J. Fink, E. Schierle, E. Weschke, and J. Geck, Resonant elastic soft x-ray scattering, Rep. Prog. Phys. 76, 056502 (2013).
  12. M. W. Krasny, The gamma factory proposal for CERN, arXiv:1511.07794.
  13. R. Alemany, C. Burrage, H. Bartosik, J. Bernhard, J. Boyd, M. Brugger, M. Calviani, C. Carli, N. Charitonidis, D. Curtin et al., Summary report of physics beyond colliders at CERN, arXiv:1902.00260.
  14. H. C. Bryant, B. D. Dieterle, J. Donahue, H. Sharifian, H. Tootoonchi, D. M. Wolfe, P. A. M. Gram, and M. A. Yates-Williams, Observation of resonances near 11 eV in the photodetachment cross section of the H− ion, Phys. Rev. Lett. 38, 228 (1977).
  15. P. A. M. Gram, J. C. Pratt, M. A. Yates-Williams, H. C. Bryant, J. Donahue, H. Sharifian, and H. Tootoonchi, Effect of an electric field upon resonances in the H− ion, Phys. Rev. Lett. 40, 107 (1978).
  16. A. Apyan, M. W. Krasny, and W. Płaczek, Gamma Factory high-intensity muon and positron source: Exploratory studies, Phys. Rev. Accel. Beams 26, 083401 (2023).
  17. D. Budker, J. C. Berengut, V. V. Flambaum, M. Gorchtein, J. Jin, F. Karbstein, M. W. Krasny, Y. A. Litvinov, A. Pálffy, V. Pascalutsa, A. Petrenko, A. Surzhykov, P. G. Thirolf, M. Vanderhaeghen, H. A. Weidenmüller, and V. Zelevinsky, Expanding nuclear physics horizons with the Gamma Factory, Ann. Phys. 534, 2100284 (2022).
  18. R. Balkin, M. W. Krasny, T. Ma, B. R. Safdi, and Y. Soreq, Probing axion-like-particles at the CERN Gamma Factory, Ann. Phys. 534, 2100222 (2022).
  19. D. Nichita, D. L. Balabanski, P. Constantin, M. W. Krasny, and W. Placzek, Radioactive ion beam production at the Gamma Factory, Ann. Phys. 534, 2100207 (2022).
  20. D. Budker, J. R. C. López-Urrutia, A. Derevianko, V. V. Flambaum, M. W. Krasny, A. Petrenko, S. Pustelny, A. Surzhykov, V. A. Yerokhin, and M. Zolotorev, Atomic physics studies at the Gamma Factory at CERN, Ann. Phys. 532, 2000204 (2020).
  21. F. Zimmermann, M. Antonelli, A. Blondel, M. Boscolo, J. Farmer, and A. Latina, Muon collider based on Gamma Factory, FCC-ee and plasma target, JACoW IPAC2022, 1691 (2022).
  22. S. Chakraborti, J. L. Feng, J. K. Koga, and M. Valli, Search prospect for extremely weakly-interacting particles at the Gamma Factory, PoS PANIC2021, 121 (2022).
  23. F. Karbstein, Vacuum birefringence at the Gamma Factory, Ann. Phys. 534, 2100137 (2022).
  24. S. Chakraborti, J. L. Feng, J. K. Koga, and M. Valli, Gamma factory searches for extremely weakly interacting particles, Phys. Rev. D 104, 055023 (2021).
  25. B. Wojtsekhowski and D. Budker, Local Lorentz invariance tests for photons and hadrons at the Gamma Factory, Ann. Phys. 534, 2100141 (2022).
  26. V. V. Flambaum, J. Jin, and D. Budker, Resonance photoproduction of pionic atoms at the proposed Gamma Factory, Phys. Rev. C 103, 054603 (2021).
  27. B. Hu, M. W. Krasny, W. Placzek, Y. Yuan, X. Shi, K. Luo, and W. Luo, Efficient transmutation of long-lived fission products in a Gamma Factory beam driven advanced nuclear energy system, Sci. Rep. 15, 12562 (2025).
  28. P. G. Harris, H. C. Bryant, A. H. Mohagheghi, R. A. Reeder, C. Y. Tang, J. B. Donahue, and C. R. Quick, Observation of doubly excited resonances in the H− ion, Phys. Rev. A 42, 6443 (1990).
  29. M. Halka, P. G. Harris, A. H. Mohagheghi, R. A. Reeder, C. Y. Tang, H. C. Bryant, J. B. Donahue, and C. R. Quick, Electric-field effects on H− photodetachment partial cross sections above 13.4 eV, Phys. Rev. A 48, 419 (1993).
  30. J. Eichler and W. Meyerhof, Relativistic Atomic Collisions (Academic, New York, 1995).
  31. L. Eidam, O. Boine-Frankenheim, and D. Winters, Cooling rates and intensity limitations for laser-cooled ions at relativistic energies, Nucl. Instrum. Methods Phys. Res. Sect. A 887, 102 (2018).
  32. M. W. Krasny, A. Petrenko, and W. Płaczek, High-luminosity Large Hadron Collider with laser-cooled isoscalar ion beams, Prog. Part. Nucl. Phys. 114, 103792 (2020).
  33. P. Kruyt, D. Gamba, and G. Franchetti, Simulation studies of laser cooling for the Gamma Factory proof-of-principle experiment at the CERN SPS, JACoW IPAC2024, MOPS50 (2024).
  34. J. Gilles, S. Fritzsche, L. J. Spieß, P. O. Schmidt, and A. Surzhykov, Quadratic Zeeman and electric quadrupole shifts in highly charged ions, Phys. Rev. A 110, 052812 (2024).
  35. B. Lu, X. Lu, J. Li, and H. Chang, Theoretical calculation of the quadratic Zeeman shift coefficient of the 3P0o clock state for strontium optical lattice clock, Chin. Phys. B 31, 043101 (2022).
  36. J. R. P. Angel, P. G. H. Sandars, and B. Bleaney, The hyperfine structure Stark effect I. Theory, Proc. R. Soc. London A 305, 125 (1968).
  37. V. A. Yerokhin, S. Y. Buhmann, S. Fritzsche, and A. Surzhykov, Electric dipole polarizabilities of Rydberg states of alkali-metal atoms, Phys. Rev. A 94, 032503 (2016).
  38. N. L. Manakov, A. V. Meremianin, A. Maquet, and J. P. J. Carney, Photon-polarization effects and their angular dependence in relativistic two-photon bound-bound transitions, J. Phys. B: At. Mol. Opt. Phys. 33, 4425 (2000).
  39. J. O. Stenflo, Hanle-Zeeman scattering matrix, Astron. Astrophys. 338, 301 (1998).
  40. J. Richter, A. V. Maiorova, A. V. Viatkina, D. Budker, and A. Surzhykov, Parity-violation studies with partially stripped ions, Ann. Phys. 534, 2100561 (2022).
  41. K. Blum, Density Matrix Theory and Applications, 3rd ed., Springer Series on Atomic, Optical, and Plasma Physics (Springer, Berlin, 2012).
  42. M. Puchalski and U. D. Jentschura, Quantum electrodynamic corrections to the g factor of helium p states, Phys. Rev. A 86, 022508 (2012).
  43. E. Kahl and J. Berengut, AMBiT: A programme for high-precision relativistic atomic structure calculations, Comput. Phys. Commun. 238, 232 (2019).
  44. K. Pachucki, V. Patkóš, and V. A. Yerokhin, Testing fundamental interactions on the helium atom, Phys. Rev. A 95, 062510 (2017).
  45. M. Puchalski, K. Piszczatowski, J. Komasa, B. Jeziorski, and K. Szalewicz, Theoretical determination of the polarizability dispersion and the refractive index of helium, Phys. Rev. A 93, 032515 (2016).
  46. Z.-C. Yan, Polarizabilities of the Rydberg states of helium, Phys. Rev. A 62, 052502 (2000).
  47. N. D. Bhaskar and A. Lurio, Tensor polarizability of the 21p1 state of He4 by electric-field level crossing, Phys. Rev. A 10, 1685 (1974).
  48. R. P. M. J. W. Notermans and W. Vassen, High-precision spectroscopy of the forbidden 23S1→21P1 transition in quantum degenerate metastable helium, Phys. Rev. Lett. 112, 253002 (2014).
  49. V. A. Yerokhin and A. Surzhykov, Theoretical energy levels of 1sns and 1snp states of helium-like ions, J. Phys. Chem. Ref. Data 48, 033104 (2019).
  50. R. Si, X. L. Guo, K. Wang, S. Li, J. Yan, C. Y. Chen, T. Brage, and Y. M. Zou, Energy levels and transition rates for helium-like ions with z = 10–36, Astron. Astrophys. 592, A141 (2016).
  51. V. V. Balashov, A. N. Grum-Grzhimailo, and N. M. Kabachnik, Polarization and Correlation Phenomena in Atomic Collisions: A Practical Theory Course (Springer Science & Business Media, Berlin, 2013).
  52. M. Rose, Elementary Theory of Angular Momentum, Structure of Matter Series (Wiley, New York, 1957).
  53. W. Hanle, Über magnetische Beeinflussung der Polarisation der resonanzfluoreszenz, Z. Physik 30, 93 (1924).
  54. P. Avan and C. Cohen-Tannoudji, Hanle effect for monochromatic excitation. Non perturbative calculation for a j=0 to j=1 transition, J. Phys. Lett. 36, 85 (1975).
  55. M. W. Krasny, Gamma Factory, in The Future of the Large Hadron Collider (World Scientific, Singapore, 2024), Chap. 21, pp. 297–303.
  56. A. Gorzawski, A. Abramov, R. Bruce, N. Fuster-Martínez, M. Krasny, J. Molson, S. Redaelli, and M. Schaumann, Collimation of partially stripped ions in the CERN Large Hadron Collider, Phys. Rev. Accel. Beams 23, 101002 (2020).
  57. M. Schaumann et al., First partially stripped ions in the LHC (208Pb81+), in Proceedings of the 10th International Particle Accelerator Conference (IPAC'19), Melbourne, Australia, 19–24 May 2019, No. 10, International Particle Accelerator Conference (JACoW Publishing, Geneva, Switzerland, 2019), pp. 689–692.
  58. S. Hirlaender et al., Lifetime and beam losses studies of partially strip ions in the SPS (129Xe39+), in Proceedings of the 9th International Particle Accelerator Conference (JACoW Publishing, Geneva, Switzerland, 2018), pp. 4070–4072.
  59. G. Mazzola, D. Di Francesca, K. Bilko, L. S. Esposito, R. Garcia Alia, S. Niang, and Y. Dutheil, Radiation to electronics studies for CERN gamma factory-proof of principle experiment in SPS, JACoW IPAC2024, TUPC80 (2024).
  60. X. Y. Lu et al., Stable 500 kW average power of infrared light in a finesse 35 000 enhancement cavity, Appl. Phys. Lett. 124, 251105 (2024).
  61. M. W. Krasny, A. Martens, and Y. Dutheil, Gamma Factory Proof-of-Principle experiment (2020), https://hal.science/hal-02999656.
  62. J. F. Seely and G. A. Doschek, Measurement of wavelengths for inner-shell transitions in CA XVII-XIX, Astrophys. J. 338, 567 (1989).
  63. J. Rice, M. Reinke, J. Ashbourn, C. Gao, M. Victora, M. Chilenski, L. Delgado-Aparicio, N. Howard, A. Hubbard, J. Hughes et al., X-ray observations of Ca19+, Ca18+ and satellites from Alcator C-Mod tokamak plasmas, J. Phys. B 47, 075701 (2014).
  64. J. Wenninger, G. Arduini, C. Arimatea, T. Bohl, P. Collier, and K. Cornelis, Energy calibration of the SPS with proton and lead ion beams, Conf. Proc. C 0505161, 1470 (2005).
  65. E. Todesco and J. Wenninger, Large Hadron Collider momentum calibration and accuracy, Phys. Rev. Accel. Beams 20, 081003 (2017).
  66. P. Indelicato and J. P. Desclaux, Multiconfiguration Dirac-Fock calculations of transition energies with QED corrections in three-electron ions, Phys. Rev. A 42, 5139 (1990).
  67. Y.-K. Kim, D. H. Baik, P. Indelicato, and J. P. Desclaux, Resonance transition energies of Li-, Na-, and Cu-like ions, Phys. Rev. A 44, 148 (1991).
  68. M. H. Chen, K. T. Cheng, W. R. Johnson, and J. Sapirstein, Relativistic configuration-interaction calculations for the n = 2 states of lithiumlike ions, Phys. Rev. A 52, 266 (1995).
  69. W. Johnson, Z. Liu, and J. Sapirstein, Transition rates for lithium-like ions, sodium-like ions, and neutral alkali-metal atoms, At. Data Nucl. Data Tables 64, 279 (1996).
  70. Y. S. Kozhedub, A. V. Volotka, A. N. Artemyev, D. A. Glazov, G. Plunien, V. M. Shabaev, I. I. Tupitsyn, and T. Stöhlker, Relativistic recoil, electron-correlation, and QED effects on the 2pj−2s transition energies in Li-like ions, Phys. Rev. A 81, 042513 (2010).
  71. J. Sapirstein and K. T. Cheng, S-matrix calculations of energy levels of the lithium isoelectronic sequence, Phys. Rev. A 83, 012504 (2011).
  72. V. Yerokhin and A. Surzhykov, Energy levels of core-excited 1s2l2l′ states in lithium-like ions: Argon to uranium, J. Phys. Chem. Ref. Data 47, 023105 (2018).
  73. X. Zhang, N. Nakamura, C. Chen, M. Andersson, Y. Liu, and S. Ohtani, Measurement of the QED energy shift in the 1s22p3/2−−1s22s1/2 x-ray transition in Li-like 208Pb79+, Phys. Rev. A 78, 032504 (2008).
  74. J. Sugar and C. Corliss, Energy levels of calcium, Ca I through Ca XX, J. Phys. Chem. Ref. Data 8, 865 (1979).
  75. L. A. Vainshtein and U. I. Safronova, Energy levels of He- and Li-like ions (States 1snl, 1 s2nl with n = 2-5), Phys. Scr. 31, 519 (1985).
  76. J. Sommerfeldt, S. Strnat, V. A. Yerokhin, W. Middents, T. Stöhlker, and A. Surzhykov, Low-energy tests of Delbrück scattering, Phys. Rev. A 108, 042819 (2023).

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Phys. Rev. A 111, 062820– Published 24 June, 2025
  • Received 11 February 2025
  • Accepted 28 May 2025
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