Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

# 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.

## Access options

from\$8.99

All prices are NET prices.

## 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).

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).

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).

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).

6. 6.

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

7. 7.

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

8. 8.

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

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).

10. 10.

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

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).

12. 12.

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

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).

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).

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).

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).

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).

18. 18.

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

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).

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).

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).

23. 23.

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

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).

## 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.

## Author information

Authors

### Contributions

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.

### Corresponding authors

Correspondence to Max Kircher or Reinhard Dörner.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## 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.

## Rights and permissions

Reprints and Permissions

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

• Accepted:

• Published:

• Issue Date:

• ### Compton scattering of keV photons at helium atom near the He$$^+$$(1s) threshold for small momentum transfer

• Henri Bachau
•  & Matabara Dieng

The European Physical Journal D (2021)

• ### Observation of Photoion Backward Emission in Photoionization of He and N2

• Sven Grundmann
• , Max Kircher
• , Isabel Vela-Perez
• , Giammarco Nalin
• , Daniel Trabert
• , Nils Anders
• , Niklas Melzer
• , Jonas Rist
• , Andreas Pier
• , Nico Strenger
• , Juliane Siebert
• , Philipp V. Demekhin
• , Lothar Ph. H. Schmidt
• , Florian Trinter
• , Markus S. Schöffler
• , Till Jahnke
•  & Reinhard Dörner

Physical Review Letters (2020)

• ### Photon-recoil imaging: Expanding the view of nonlinear x-ray physics

• U. Eichmann
• , H. Rottke
• , S. Meise
• , J.-E. Rubensson
• , J. Söderström
• , M. Agåker
• , C. Såthe
• , M. Meyer
• , T. M. Baumann
• , R. Boll
• , A. De Fanis
• , P. Grychtol
• , M. Ilchen
• , T. Mazza
• , J. Montano
• , V. Music
• , Y. Ovcharenko
• , D. E. Rivas
• , S. Serkez
• , R. Wagner
•  & S. Eisebitt

Science (2020)