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arXiv:quant-ph/0301069

Diffraction of Weakly Bound Clusters: Spectroscopy and Size Effects

Stoll, Martin, Thorsten Köhler, Gerhard C. Hegerfeldt

Published Jan 15, 2003• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.quant-ph/0301069

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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.
In atom optics, optical wave theory has been very successful in describing the diffraction of atoms by microfabricated structures. For a molecule, however, with a binding energy smaller than the kinetic energy and with a non-negligible diameter, wave optics may no longer be adequate due to the effects of finite size and breakups. To study the role of the two effects we consider the diffraction of weakly bound diatomic systems such as the helium dimer. We find striking deviations from classical optics, in particular from Babinet's principle, and use the results to clarify the role of finite size and breakups, respectively, in the diffraction from strips, slits, and transmission gratings. As an application the determination of the He2{\mathrm{He}}_{2}He2​ size by transmission through holes and by diffraction experiments is investigated.
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​.
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.
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.
Many microscopic properties of the only natural superfluid element helium have become available within the last 18 years through a number of novel experiments. The diffraction of matter-waves of small helium clusters has established the unusually large bond distance (5.2 nm) and extremely weak binding energy (10−7 eV) of the dimer and other exotic properties of small helium clusters. The high-resolution spectroscopy of closed-shell chromophore molecules attached to small clusters or embedded inside large superfluid droplets have revealed that as a result of superfluidity, molecules rotate virtually without friction and that only a handful of He atoms are required for microscopic superfluidity. The frictionless translational motion of atoms and molecules inside the droplets has also been observed. These and a number of other experiments demonstrate that helium droplets are the most gentle and coldest of all cryomatrices with enormous potential for a wide range of future applications.
The total cross sections of the helium dimer, trimer, and tetramer for scattering from Kr atoms have been measured for cluster beam velocities between 250 and 820 m/s. The dimer cross section is twice that of the atom within 5% indicating that the Kr atoms scatter from the He atoms independently, which is consistent with the large dimer bond distance of about 50 A. The trimer and tetramer cross sections are somewhat larger and can be described by an impulse approximation with a multiple "eclipse" correction, extending ideas of Glauber for high energy collisions with the deuteron.