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arXiv:quant-ph/0211076 · Journal of Physics B Atomic Molecular and Optical Physics

Inelastic diffraction and spectroscopy of very weakly bound clusters

Martin Stoll, Thorsten K hler

Published Nov 27, 2002• 2 citations
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Abstract

We study the coherent inelastic diffraction of very weakly bound two-body clusters from a material transmission grating. We show that internal transitions of the clusters can lead to new separate peaks in the diffraction pattern, whose angular positions determine the excitation energies. Using a quantum mechanical approach to few-body scattering theory, we determine the relative peak intensities for the diffraction of the van der Waals dimers (D 2 ) 2 and H 2 D 2 . Based on the results for these realistic examples, we discuss the possible applications and experimental challenges of this coherent inelastic diffraction technique.

DOI
10.1088/0953-4075/35/24/305

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We study the coherent inelastic diffraction of very weakly bound two-body clusters from a material transmission grating. We show that internal transitions of the clusters can lead to new separate peaks in the diffraction pattern, whose angular positions determine the excitation energies. Using a quantum mechanical approach to few-body scattering theory, we determine the relative peak intensities for the diffraction of the van der Waals dimers (D 2 ) 2 and H 2 D 2 . Based on the results for these realistic examples, we discuss the possible applications and experimental challenges of this coherent inelastic diffraction technique.
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Exciting experiments in the field of atom and molecule optics have lately drawn much attention to the effects involved in the coherent diffraction of particle beams. We review the influence of the finite size of the particles and of their energy level spectrum on the diffraction pattern. In turn, we demonstrate how experimental diffraction measurements allow to determine these quantities of weakly bound molecules by considering the diffraction of the dimer and trimer of helium, and the deuterium molecule dimer.
A molecular beam consisting of small helium clusters is diffracted from a 100 nm period transmission grating. The relative dimer intensities have been measured out to the 7th order and are used to determine the reduction of the effective slit width resulting from the finite size of the dimer. From a theoretical analysis of the data which also takes into account the van der Waals interaction with the grating bars, the bond length (mean internuclear distance) and the binding energy are found to be $〈r〉\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}52\ifmmode\pm\else\textpm\fi{}4\AA{}$ and $|{E}_{b}|\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.1+0.3/\ensuremath{-}0.2$ mK.
A few years ago, diffraction of atoms by double slits and gratings was achieved for the first time, and standard optical wave-theory provided an excellent description of the experiments. More recently, diffraction of weakly bound molecules and even clusters has been observed. Due to their size and to possible breakup processes optical wave-theory is no longer adequate and a more sophisticated approach is needed. Moreover, surface effects, which can modify the diffraction pattern of atoms and molecules, give rise to further complications. In this article a fully quantum mechanical approach to these questions is discussed.
Atomic diffraction through double slits and transmission gratings is well described in terms of the associated de Broglie waves and classical wave optics. However, for weakly bound and relatively large systems, such as the He2{}_{2}2​ dimer, this might no longer hold true due to the possibility of breakup processes and finite-size effects. We therefore study the diffraction of weakly bound two-particle systems. If the bar and slit widths of the grating are much larger than the diameter of the two-particle system, we recover the usual optics results. For smaller widths, however, deviations therefrom occur. We find that the location of possible diffraction peaks is indeed still governed by the usual grating function from optics, but the peaks may have a lower intensity. This is not unexpected when breakup processes are allowed. More unusually though, diffraction peaks that would be absent for de Broglie waves may reappear. The results are illustrated for diffraction of He2{}_{2}2​.