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Kinematically complete experimental study of Compton scattering at helium atoms near the threshold

Abstract

Compton scattering is one of the fundamental interaction processes of light with matter. When discovered1, it was described as a billiard-type collision of a photon ‘kicking’ a quasi-free electron. With decreasing photon energy, the maximum possible momentum transfer becomes so small that the corresponding energy falls below the binding energy of the electron. In this regime, ionization by Compton scattering becomes an intriguing quantum phenomenon. Here, we report on a kinematically complete experiment studying Compton scattering off helium atoms in that regime. We determine the momentum correlations of the electron, the recoiling ion and the scattered photon in a coincidence experiment based on cold target recoil ion momentum spectroscopy, finding that electrons are not only emitted in the direction of the momentum transfer, but that there is a second peak of ejection to the backward direction. This finding links Compton scattering to processes such as ionization by ultrashort optical pulses2, electron impact ionization3,4, ion impact ionization5,6 and neutron scattering7, where similar momentum patterns occur.

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Fig. 1: Scheme of ionization by Compton scattering at hν = 2.1 keV.
Fig. 2: Electron and ion momentum distributions for different momentum transfer gates.
Fig. 3: Electron energy distribution.
Fig. 4: Fully differential electron angular distributions.

Data availability

The data that support the plots within this Letter are available from the corresponding authors upon reasonable request.

Code availability

The code that supports the theoretical plots within this Letter is available from the corresponding authors upon reasonable request.

References

  1. 1.

    Compton, A. H. in Bulletin of the National Research Council No. 20 Vol. 4, Pt. 2 (National Research Council of the National Academy of Sciences, 1922)

  2. 2.

    Arbó, D. G., Tökèsi, K. & Miraglia, J. E. Atomic ionization by a sudden momentum transfer. Nucl. Instr. Methods Phys. Res. B 267, 382–385 (2009).

    Article  ADS  Google Scholar 

  3. 3.

    Dürr, M. et al. Single ionization of helium by 102 eV electron impact: three dimensional images for electron emission. J. Phys. B 39, 4097–4111 (2006).

    Article  ADS  Google Scholar 

  4. 4.

    Ehrhardt, H., Jung, K., Knoth, G. & Schlemmer, P. Differential cross section of direct single electron impact ionization. Z. Phys. D Atoms Mol. Clusters 1, 3–32 (1986).

    Article  ADS  Google Scholar 

  5. 5.

    Fischer, D., Moshammer, R., Schulz, M., Voitkiv, A. & Ullrich, J. Fully differential cross sections for the single ionization of helium by ion impact. J. Phys. B 36, 3555–3567 (2003).

    Article  ADS  Google Scholar 

  6. 6.

    Schulz, M. et al. Three-dimensional imaging of atomic four-body processes. Nature 422, 48–50 (2003).

    Article  ADS  Google Scholar 

  7. 7.

    Pindzola, M. S. et al. Neutron-impact ionization of He. J. Phys. B 47, 195202 (2014).

    Article  ADS  Google Scholar 

  8. 8.

    Bothe, W. & Geiger, H. Über das Wesen des Comptoneffekts; ein experimenteller Beitrag zur Theorie der Strahlung. Z. Phys. 32, 639–663 (1925).

    Article  ADS  Google Scholar 

  9. 9.

    Bell, F., Tschentscher, T. H., Schneider, J. R. & Rollason, A. J. The triple differential cross section for deep inelastic photon scattering: a (γ,eγ') experiment. J. Phys. B 24, L533–L538 (1991).

    Article  ADS  Google Scholar 

  10. 10.

    Metz, C. et al. Three-dimensional electron momentum density of aluminum by (γ,eγ) spectroscopy. Phys. Rev. B 59, 10512–10520 (1999).

    Article  ADS  Google Scholar 

  11. 11.

    Hopersky, A. N., Nadolinsky, A. M., Novikov, S. A., Yavna, V. A. & Ikoeva, K. K. H. X-ray-photon Compton scattering by a linear molecule. J. Phys. B 48, 175203 (2015).

    Article  ADS  Google Scholar 

  12. 12.

    Ullrich, J. et al. Recoil-ion and electron momentum spectroscopy: reaction-microscopes. Rep. Prog. Phys. 66, 1463–1545 (2003).

    Article  ADS  Google Scholar 

  13. 13.

    Roy, S. C. & Pratt, R. H. Need for further inelastic scattering measurements at X-ray energies. Radiat. Phys. Chem. 69, 193–197 (2004).

    Article  ADS  Google Scholar 

  14. 14.

    Kaliman, Z., Surić, T., Pisk, K. & Pratt, R. H. Triply differential cross section for Compton scattering. Phys. Rev. A 57, 2683–2691 (1998).

    Article  ADS  Google Scholar 

  15. 15.

    Samson, J. A. R., He, Z. X., Bartlett, R. J. & Sagurton, M. Direct measurement of He+ ions produced by Compton scattering between 2.5 and 5.5 keV. Phys. Rev. Lett. 72, 3329–3331 (1994).

    Article  ADS  Google Scholar 

  16. 16.

    Spielberger, L. et al. Separation of photoabsorption and Compton scattering contributions to He single and double ionization. Phys. Rev. Lett. 74, 4615–4618 (1995).

    Article  ADS  Google Scholar 

  17. 17.

    Dunford, R. W., Kanter, E. P., Krässig, B., Southworth, S. H. & Young, L. Higher-order processes in X-ray photoionization and decay. Radiat. Phys. Chem. 70, 149–172 (2004).

    Article  ADS  Google Scholar 

  18. 18.

    Kaliman, Z. & Pisk, K. Compton cross-section calculations in terms of recoil-ion momentum observables. Rad. Phys. Chem. 71, 633–635 (2004).

    Article  ADS  Google Scholar 

  19. 19.

    Henke, B. L., Gullikson, E. M. & Davis, J. C. X-ray interactions: photoabsorbtion, scattering, transmission and reflection at E = 50–30,000 eV, Z = 1–92. At. Data Nucl. Data Tables 54, 181–342 (1993).

    Article  ADS  Google Scholar 

  20. 20.

    Jagutzki, O. et al. Multiple hit readout of a microchannel plate detector with a three-layer delay-line anode. IEEE Trans. Nucl. Sci. 49, 2477–2483 (2002).

    Article  ADS  Google Scholar 

  21. 21.

    Akhiezer, A. I. & Berestetskii, V. B. Quantum Electrodynamics (Wiley, 1965).

  22. 22.

    Bergstrom, P. M. Jr, Surić, T., Pisk, K. & Pratt, R. H. Compton scattering of photons from bound electrons: full relativistic independent-particle-approximation calculations. Phys. Rev. A 48, 1134–1162 (1993).

    Article  ADS  Google Scholar 

  23. 23.

    Chuluunbaatar, O. et al. Role of the cusp conditions in electron–helium double ionization. Phys. Rev. A 74, 014703 (2006).

    Article  ADS  Google Scholar 

  24. 24.

    Tong, X. M. & Lin, C. D. Empirical formula for static field ionization rates of atoms and molecules by lasers in the barrier-suppression regime. J. Phys. B 38, 2593–2600 (2005).

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by DFG and BMBF. O.C. acknowledges support from the Hulubei-Meshcheryakov programme JINR-Romania and the RUDN University Program 5-100. Y.V.P. is grateful to the Russian Foundation of Basic Research (RFBR) for financial support under grant no. 19-02-00014a. S.H. thanks the Direction Generale de la Recherche Scientifique et du Developpement Technologique (DGRSDT-Algeria) for financial support. We are grateful to the staff of PETRA III for excellent support during the beam time. Calculations were performed on the Central Information and Computer Complex and heterogeneous computing platform HybriLIT through supercomputer ‘Govorun’ of JINR.

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M.K., F.T., S.G., I.V.-P., J.R., S.E., K.B., M.N.P., T.J., M.S.S. and R.D. contributed to the experimental work. S.B., N.E., S.H., O.C., Y.V.P., I.P.V. and M.L. contributed to theory and numerical simulations. All authors contributed to the manuscript.

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Correspondence to Max Kircher or Reinhard Dörner.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Steven Manson, Andre Staudte and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Video 1

Electron and ion momentum distributions for different scattering angles. Here, the blue arrow indicates the direction of the incoming photon, the light green arrow the direction of the scattered photon and the dark purple arrow the direction of the momentum transfer.

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Kircher, M., Trinter, F., Grundmann, S. et al. Kinematically complete experimental study of Compton scattering at helium atoms near the threshold. Nat. Phys. 16, 756–760 (2020). https://doi.org/10.1038/s41567-020-0880-2

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