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


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.


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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




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.

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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).

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