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Glory scattering in deeply inelastic molecular collisions


For molecular collisions, the deflection of a molecule’s trajectory provides one of the most sensitive probes of the interaction potential and there are general rules of thumb that relate the direction of deflection to precollision conditions. Following intuition, forward scattering results from glancing collisions, whereas near head-on collisions result in back scattering. Here we present the observation of forward scattering in inelastic processes that defies this common wisdom. For deeply inelastic collisions between NO radicals and CO or HD molecules, we observed forward scattering in fully resolved pair-correlated differential cross-sections, despite the low impact parameters that are needed to induce a sufficient energy transfer. We rationalized these findings by extending the textbook model of hard-sphere scattering—taking inelastic energy transfer into account—and attribute the forward scattering to glory-type trajectories caused by attractive forces. This phenomenon, which we refer to as hard-collision glory scattering, is predicted to be ubiquitous. We derive under which conditions hard-collision glory scattering occurs and retrospectively identify such behaviour in previously studied systems.

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Fig. 1: Trajectories and deflection functions predicted from hard-sphere models with hard-sphere radius a for the scattering of NO with HD at a collision energy of 133 cm−1.
Fig. 2: Experimental and simulated scattering images for inelastic scattering.
Fig. 3: Inelastic scattering modelled by CC calculations (solid lines) and semiclassical (dot-dashed lines) calculations for selected inelastic channels in NO−CO and NO−HD collisions at a collision energy of 220 and 133 cm−1, respectively.
Fig. 4: HCGS intensity dependence |db/dχ| at a deflection angle of χ(bHCGS) = 0, normalized to the intensity for backscattering, for various combinations of Vmin/E and ΔE/E.

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The computer codes used in this study are available from the corresponding authors upon reasonable request.


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This work is part of the research programme of the Netherlands Organization for Scientific Research (NWO). S.Y.T.v.d.M. acknowledges support from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7/2007-2013/ERC grant agreement no. 335646 MOLBIL) and from the ERC under the European Union’s Horizon 2020 Research and Innovation Program (grant agreement no. 817947 FICOMOL). G.T. acknowledges support from the China Scholarship Council. We thank N. Janssen and A. van Roij for expert technical support. We thank S. Vogels for assistance during the NO−HD experiments. We thank M. van Hemert for the quasiclassical calculations of RET in bimolecular systems. We thank M. van Hemert and D. Parker for fruitful discussions and for carefully reading the manuscript.

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Authors and Affiliations



The experiments were carried out by G.T. and Z.G. and supervised by S.Y.T.v.d.M. Theoretical calculations were performed by M.B., A.v.d.A., G.C.G. and T.K. Data analysis and simulations were performed by G.T. and Z.G. The manuscript was written by M.B., S.Y.T.v.d.M. and T.K. with contributions from all the authors. All the authors were involved in the interpretation of the data and the preparation of the manuscript.

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Correspondence to Sebastiaan Y. T. van de Meerakker or Tijs Karman.

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Supplemental material including detailed descriptions of numerical calculations, theoretical models, application to several molecules, and Supplementary Figs. 1–32.

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Besemer, M., Tang, G., Gao, Z. et al. Glory scattering in deeply inelastic molecular collisions. Nat. Chem. 14, 664–669 (2022).

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