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The Journal of Chemical Physics

The structure of mixed 3He-4He droplets doped with OCS: A density functional approach

Antonio Leal, David Mateo, Martí Pi, M. Barranco, Jesús Navarro

Published Nov 5, 2013• 2 citations
Publisher

Abstract

We have investigated the structure and energetics of mixed (3)He-(4)He droplets doped with a carbonyl sulfide molecule within a density functional approach considering a small but finite temperature of 0.1 K. The molecule is treated as an external field to which the helium droplet is attached. The energetics and appearance of these droplets are discussed for selected numbers of helium atoms, identifying the first magic numbers of the fermionic component.

DOI
10.1063/1.4827499

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We have investigated the structure and energetics of mixed (3)He-(4)He droplets doped with a carbonyl sulfide molecule within a density functional approach considering a small but finite temperature of 0.1 K. The molecule is treated as an external field to which the helium droplet is attached. The energetics and appearance of these droplets are discussed for selected numbers of helium atoms, identifying the first magic numbers of the fermionic component.
Due to the immiscibility of 3He{}^{3}\mathrm{He}3He into 4He{}^{4}\mathrm{He}4He at very low temperatures, mixed helium droplets consist of a core of 4He{}^{4}\mathrm{He}4He atoms coated by a 3He{}^{3}\mathrm{He}3He layer whose thickness depends on the number of atoms of each isotope. When these numbers are such that the centrifugal kinetic energy of the 3He{}^{3}\mathrm{He}3He atoms is small and can be considered as a perturbation to the mean-field energy, a novel shell structure arises, with magic numbers different from these of pure 3He{}^{3}\mathrm{He}3He droplets. If the outermost shell is not completely filled, the valence atoms align their spins up to the maximum value allowed by the Pauli principle.
Helium systems at zero temperature are strongly correlated neutral systems which can only be described by means of quantum mechanics. The existence of the two isotopes 4He and 3He allows the comparison between the quantum effects due to different statistics, bosonic and fermionic. In this Thesis, an analysis of Helium droplets has been done. Throughout this work, both energetic and structural properties of systems with different number of particles N are obtained by means of the Quantum Monte Carlo techniques (Variational and Diffusion Monte Carlo - VMC and DMC-). Several studies on Helium droplets have been published in the last years, most of them using the mean field theory (as the Density Functional) and variational approaches (as VMC). In the case of 4He, also exact DMC results have already been reported, actually, a great number of works have described with high accuracy the ground state of this bosonic system. The appearance of magic numbers from experimental point of view has motivated the study of 4He droplets, and one chapter of this Thesis is focused on this bosonic system. We have carried out a one-by-one energetic study in the range from 20 to 30 particles using the DMC technique to discuss the existence of magic numbers. On the other hand, a brief study about vortices is also done; using out code, one can calculate the energy of a droplet with one vortex inside (EV) and, therefore, the energy of a vortex (EV -E0). About 3He droplets, the sign problem makes their study quite more difficult, for this reason, the number of works is considerably smaller than in the bosonic case. One aim of this thesis was to write a DMC code using both Fixed and Released Node approximations (FN and RN) able to perform high accurate calculations of energetic and structural properties of these finite fermionic systems.
Diffuse clusters of arbitrary numbers of helium atoms are treated in a mean-field theory of the many-body system. The nonlinear Hartree self-consistent-field equations are solved numerically to give their energy eigenvalues and eigenfunctions. Both isotopes 4He and 3He are treated according to their bosonic and fermionic statistics and symmetry requirements. Clusters of all sizes of 4He atoms are stable, but there is a minimum threshold of ∼70 atoms for the formation of 3He clusters. All the excited states in addition to the ground state were found. The wave functions are seen to have interesting differences from electronic wave functions in atoms.
Experimental and theoretical results for mixed helium droplets doped with one calcium atom are reported. The absorption spectrum around the $4s4p\ensuremath{\leftarrow}4{s}^{2}$ transition is calculated as a function of the composition of the droplet and compared to the experiment. Our study reveals the distinct feature that for specific 3He^{3}\text{H}\text{e}3He concentrations, Ca atoms sit at the 3He-4He^{3}\text{H}\text{e-}^{4}\text{H}\text{e}3He-4He interface. This particular property of Ca, likely not shared with any other atomic or molecular species but the heavier alkaline-earth atoms, might offer the possibility of using it to probe the 3He-4He^{3}\text{H}\text{e-}^{4}\text{H}\text{e}3He-4He interface of the droplet.
In this paper, quantum fluctuations of a carbonyl sulfide molecule in helium-4 clusters are studied as a function of cluster size N in a small-to-large size regime (2<or=N<or=64). The molecular rotation of the dopant shows nonmonotonic size dependence in the range of 10<or=N<or=20, reflecting the density distribution of the helium atoms around the molecule. The size dependence on the rotational constant shows a plateau for N>or=20, which is larger than the experimental nanodroplet value. Superfluid response of the doped cluster is found to show remarkable anisotropy especially for N<or=20. The superfluid fraction regarding the axis perpendicular to the molecular axis shows a steep increase at N=10, giving the significant enhancement of the rotational fluctuation of the molecule. On the other hand, the superfluid fraction regarding the axis parallel to the molecular axis reaches 0.9 at N=5, arising from the bosonic exchange cycles of the helium atoms around the molecular axis. The anisotropy in the superfluid response is found to be the direct consequence of the configurations of the bosonic exchange cycles.
The infrared spectrum of single oxygen carbon sulfide (OCS) molecules was measured inside large superfluid pure helium-4 droplets and nonsuperfluid pure helium-3 droplets, both consisting of about 10(4) atoms. In the helium-4 droplets, sharp rotational lines were observed, whereas in helium-3 only a broad peak was found. This difference is interpreted as evidence that the narrow rotational lines, which imply free rotations, are a microscopic manifestation of superfluidity. Upon addition of 60 helium-4 atoms to the pure helium-3 droplets, the same sharp rotational lines were found; it appears that 60 is the minimum number needed for superfluidity.