Skip to main content

Thank you for visiting 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.

  • Article
  • Published:

Mapping partial wave dynamics in scattering resonances by rotational de-excitation collisions


One of the most important parameters in a collision is the ‘miss distance’ or impact parameter, which in quantum mechanics is described by quantized partial waves. Usually, the collision outcome is the result of unavoidable averaging over many partial waves. Here we present a study of low-energy NO–He collisions that enables us to probe how individual partial waves evolve during the collision. By tuning the collision energies to scattering resonances between 0.4 and 6 cm−1, the initial conditions are characterized by a limited set of partial waves. By preparing NO in a rotationally excited state before the collision and by studying rotational de-excitation collisions, we were able to add one quantum of angular momentum to the system and trace how it evolves. Distinct fingerprints in the differential cross-sections yield a comprehensive picture of the partial wave dynamics during the scattering process. Exploiting the principle of detailed balance, we show that rotational de-excitation collisions probe time-reversed excitation processes with superior energy and angular resolution.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Collision energy dependence of the ICS and energy level diagram of the involved molecular states.
Fig. 2: Partial-wave contributions to the cross-section at several probed collision energies.
Fig. 3: Experimental and simulated ion images at selected collision energies.
Fig. 4: Experimental and simulated ion images for two inelastic scattering processes subject to the detailed balance principle.

Similar content being viewed by others

Data availability

All data are available online at DANS:


  1. Chadwick, H., Hundt, P. M., van Reijzen, M. E., Yoder, B. L. & Beck, R. D. Quantum state specific reactant preparation in a molecular beam by rapid adiabatic passage. J. Chem. Phys. 140, 034321 (2014).

    Article  Google Scholar 

  2. Perreault, W. E., Mukherjee, N. & Zare, R. N. Quantum control of molecular collisions at 1 Kelvin. Science 358, 356–359 (2017).

    Article  CAS  Google Scholar 

  3. McDonald, M. et al. Photodissociation of ultracold diatomic strontium molecules with quantum state control. Nature 535, 122–126 (2016).

    Article  CAS  Google Scholar 

  4. Hu, M.-G. et al. Direct observation of bimolecular reactions of ultracold KRb molecules. Science 366, 1111–1115 (2019).

    Article  CAS  Google Scholar 

  5. Herschbach, D. R. Molecular dynamics of elementary chemical reactions (Nobel lecture). Angew. Chem. Int. Ed. 26, 1221–1243 (1987).

    Article  Google Scholar 

  6. Herschbach, D. Chemical stereodynamics: retrospect and prospect. Eur. Phys. J. D 38, 3–13 (2006).

    Article  CAS  Google Scholar 

  7. Anggara, K., Leung, L., Timm, M. J., Hu, Z. & Polanyi, J. C. Approaching the forbidden fruit of reaction dynamics: aiming reagent at selected impact parameters. Sci. Adv. 4, eaau2821 (2018).

    Article  CAS  Google Scholar 

  8. Volz, T. et al. Feshbach spectroscopy of a shape resonance. Phys. Rev. A 72, 010704(R) (2005).

    Article  Google Scholar 

  9. Wigner, E. P. On the behavior of cross sections near thresholds. Phys. Rev. 73, 1002–1009 (1948).

    Article  CAS  Google Scholar 

  10. Jankunas, J., Jachymski, K., Hapka, M. & Osterwalder, A. Observation of orbiting resonances in He(3S1) + NH3 Penning ionization. J. Chem. Phys. 142, 164305 (2015).

    Article  Google Scholar 

  11. Klein, A. et al. Directly probing anisotropy in atom–molecule collisions through quantum scattering resonances. Nat. Phys. 13, 35–38 (2017).

    Article  CAS  Google Scholar 

  12. Lavert-Ofir, E. et al. Observation of the isotope effect in sub-kelvin reactions. Nat. Chem. 6, 332–335 (2014).

    Article  CAS  Google Scholar 

  13. Bergeat, A. et al. Understanding the quantum nature of low-energy C(3Pj) + He inelastic collisions. Nat. Chem. 10, 519–522 (2018).

    Article  CAS  Google Scholar 

  14. Bergeat, A., Onvlee, J., Naulin, C., van der Avoird, A. & Costes, M. Quantum dynamical resonances in low-energy CO (j = 0) + He inelastic collisions. Nat. Chem. 7, 349–353 (2015).

    Article  CAS  Google Scholar 

  15. Bergeat, A., Morales, S. B., Naulin, C., Wiesenfeld, L. & Faure, A. Probing low-energy resonances in water-hydrogen inelastic collisions. Phys. Rev. Lett. 125, 143402 (2020).

    Article  CAS  Google Scholar 

  16. de Jongh, T. et al. Imaging the onset of the resonance regime in low-energy NO-He collisions. Science 368, 626–630 (2020).

    Article  Google Scholar 

  17. Onvlee, J., van der Avoird, A., Groenenboom, G. & van de Meerakker, S. Y. T. Probing scattering resonances in (ultra)cold inelastic NO–He collisions. J. Phys. Chem. A 120, 4770–4777 (2016).

    Article  CAS  Google Scholar 

  18. Amarasinghe, C. et al. State-to-state scattering of highly vibrationally excited NO at broadly tunable energies. Nat. Chem. 12, 528–534 (2020).

    Article  CAS  Google Scholar 

  19. van de Meerakker, S. Y. T., Bethlem, H. L., Vanhaecke, N. & Meijer, G. Manipulation and control of molecular beams. Chem. Rev. 112, 4828–4878 (2012).

    Article  Google Scholar 

  20. Eppink, A. T. J. B. & Parker, D. H. Velocity map imaging of ions and electrons using electrostatic lenses: application in photoelectron and photofragment ion imaging of molecular oxygen. Rev. Sci. Instrum. 68, 3477–3484 (1997).

    Article  CAS  Google Scholar 

  21. Aoiz, F. J. et al. Inelastic scattering of He atoms and NO(X2Π) molecules: the role of parity on the differential cross section. J. Phys. Chem. A 113, 14636–14649 (2009).

    Article  CAS  Google Scholar 

  22. NIST Handbook of Mathematical Functions Paperback and CD-ROM (Cambridge Univ. Press, 2010).

  23. Bolzmann, L. Weitere studien über das wärmegleichgewicht unter gasmolekülen. Wien. Ber. 66, 275–370 (1872).

    Google Scholar 

  24. Einstein, A. Strahlungs-emission und -absorption nach der quantentheorie. Verh. Deutsch. Phys. Ges. 18, 318–323 (1916).

    CAS  Google Scholar 

  25. de Jongh, T. et al. Imaging the onset of the resonance regime in low-energy NO-He collisions. Science 368, 626–630 (2020).

    Article  Google Scholar 

  26. Yan, B. et al. A new high intensity and short-pulse molecular beam valve. Rev. Sci. Instrum. 84, 023102 (2013).

    Article  CAS  Google Scholar 

  27. Ball, C. D. & De Lucia, F. C. Direct observation of Λ-doublet and hyperfine branching ratios for rotationally inelastic collisions of NO-He at 4.2 K. Chem. Phys. Lett. 300, 227–235 (1999).

    Article  CAS  Google Scholar 

  28. Even, U. Pulsed supersonic beams from high pressure source: simulation results and experimental measurements. Adv. Chem. 2014, 636042 (2014).

    Article  Google Scholar 

  29. Plomp, V., Gao, Z. & van de Meerakker, S. Y. T. A velocity map imaging apparatus optimised for high-resolution crossed molecular beam experiments. Mol. Phys. 119, e1814437 (2021).

    Article  Google Scholar 

  30. Scharfenberg, L., van de Meerakker, S. Y. T. & Meijer, G. Crossed beam scattering experiments with optimized energy resolution. Phys. Chem. Chem. Phys. 13, 8448–8456 (2011).

    Article  CAS  Google Scholar 

  31. von Zastrow, A. et al. State-resolved diffraction oscillations imaged for inelastic collisions of NO radicals with He, Ne and Ar. Nat. Chem. 6, 216–221 (2014).

    Article  Google Scholar 

Download references


This work is part of the research programme of the Netherlands Organization for Scientific Research. S.Y.T.v.d.M. acknowledges support from the European Research Council under the European Union’s Seventh Framework Program (FP7/2007-2013/ERC grant agreement no. 335646 MOLBIL) and from the European Research Council under the European Union’s Horizon 2020 Research and Innovation Program (grant agreement no. 817947 FICOMOL). We thank N. Janssen and A. van Roij for expert technical support. We thank F. J. M. Harren for stimulating discussions regarding the optical excitation of NO using a quantum cascade laser. We thank T. Karman for fruitful discussions and for critically reading the manuscript.

Author information

Authors and Affiliations



The project was conceived by S.Y.T.v.d.M. The experiments were carried out by T.d.J., Q.S. and S.K. Methods to rovibrationally excite NO using a quantum cascade laser were developed by G.A. and Q.S. Data analysis and simulations were performed by T.d.J. Theoretical calculations were performed by M.B., A.v.d.A. and G.C.G. The manuscript was written by T.d.J. and S.Y.T.v.d.M. with contributions from all authors. All authors were involved in the interpretation of the data and the preparation of the manuscript.

Corresponding authors

Correspondence to Gerrit C. Groenenboom or Sebastiaan Y. T. van de Meerakker.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Chemistry thanks Astrid Bergeat and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Figs. 1–11, Tables 1–3, Methods and Results.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

de Jongh, T., Shuai, Q., Abma, G.L. et al. Mapping partial wave dynamics in scattering resonances by rotational de-excitation collisions. Nat. Chem. 14, 538–544 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing