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Physical Review Letters

Observation of Mixed Fermionic-Bosonic Helium Clusters by Transmission Grating Diffraction

Anton Kalinin, Oleg Kornilov, Wieland Schöllkopf, Jan Peter Toennies

Published Sep 9, 2005• 21 citations
Publisher

Abstract

Small weakly bound boson-fermion $^{4}\mathrm{He}_{m}^{3}\mathrm{He}_{n}$ clusters formed in a free jet expansion are identified using nondestructive transmission grating diffraction. The observations confirm the existence of more than 11 very tenuous complexes including the three-body halo molecule $^{4}\mathrm{He}_{2}^{3}\mathrm{He}$ and the pseudo-Borromean complex $^{4}\mathrm{He}_{2}^{3}\mathrm{He}_{2}$. Effective cluster formation temperatures, extracted from a sudden freeze model for cluster growth using theoretical binding energies, increase smoothly with cluster size, thereby confirming the calculations with the possible exception of $^{4}\mathrm{He}_{2}^{3}\mathrm{He}_{2}$.

DOI
10.1103/physrevlett.95.113402

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Small weakly bound boson-fermion 4Hem3Hen^{4}\mathrm{He}_{m}^{3}\mathrm{He}_{n}4Hem3​Hen​ clusters formed in a free jet expansion are identified using nondestructive transmission grating diffraction. The observations confirm the existence of more than 11 very tenuous complexes including the three-body halo molecule 4He23He^{4}\mathrm{He}_{2}^{3}\mathrm{He}4He23​He and the pseudo-Borromean complex 4He23He2^{4}\mathrm{He}_{2}^{3}\mathrm{He}_{2}4He23​He2​. Effective cluster formation temperatures, extracted from a sudden freeze model for cluster growth using theoretical binding energies, increase smoothly with cluster size, thereby confirming the calculations with the possible exception of 4He23He2^{4}\mathrm{He}_{2}^{3}\mathrm{He}_{2}4He23​He2​.
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We report results for the ground-state energy and structural properties of small (4)He-T↓ clusters consisting of up to four T↓ and eight (4)He atoms. These results have been obtained using very well-known (4)He-(4)He and T↓- T↓ interaction potentials and several models for the (4)He- T↓ interatomic potential. All the calculations have been performed with variational and diffusion Monte Carlo methods. It takes at least three atoms to form a mixed bound state. In particular, for small clusters the binding energies are significantly affected by the precise form of the (4)He- T↓ interatomic potential but the stability limits remain unchanged. The only exception is the (4)He(2)T↓ trimer whose stability in the case of the weakest (4)He- T↓ interaction potential is uncertain while it seems stable for other potentials. The mixed trimer (4)He(T↓)(2), a candidate for the Borromean state, is not bound. All other studied clusters are stable. Some of the weakest bound clusters can be classified as quantum halo as a consequence of having high probability of being in a classically forbidden region.
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.
The existence of small helium clusters containing a variable number of 4He^{\mathrm{4}}\mathrm{H}\mathrm{e}4He and 3He^{\mathrm{3}}\mathrm{H}\mathrm{e}3He atoms is studied within a variational Monte Carlo calculation employing the Aziz HFD-B(HE) pair interaction. The clusters 4He2{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{2}4He2​ support one and two 3He^{\mathrm{3}}\mathrm{H}\mathrm{e}3He atoms; however, the system with three 3He^{\mathrm{3}}\mathrm{H}\mathrm{e}3He atoms is metastable, and the next bound system requires at least 18 fermions. All clusters obtained by adding 3He^{\mathrm{3}}\mathrm{H}\mathrm{e}3He atoms to the trimer 4He3{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{3}4He3​ and the tetramer 4He4{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{4}4He4​ are bound, but the clusters 4He3{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{3}4He3​-3He3,4,5{^{\mathrm{3}}\mathrm{H}\mathrm{e}}_{3,4,5}3He3,4,5​ and 4He3,4{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{3,4}4He3,4​-3He9{^{\mathrm{3}}\mathrm{H}\mathrm{e}}_{9}3He9​ are metastable. All remaining clusters with three or more bosons and any number of fermions are stable.