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Physical Review Letters

Structure and Stability of 3He Droplets

M. Barranco, Jesús Navarro, A. Poves

Published Jun 23, 1997• 50 citations
Publisher

Abstract

We have studied the structure of ${}^{3}\mathrm{He}$ droplets at zero temperature using a density functional approach plus a configuration interaction calculation in an harmonic oscillator major shell. The most salient feature of open shell drops is that the valence atoms couple their spins to the maximum value compatible with Pauli's principle, building a large magnetic moment. We have determined that 29 atoms constitute the smallest self-bound droplet.

DOI
10.1103/physrevlett.78.4729

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We have studied the structure of 3He{}^{3}\mathrm{He}3He droplets at zero temperature using a density functional approach plus a configuration interaction calculation in an harmonic oscillator major shell. The most salient feature of open shell drops is that the valence atoms couple their spins to the maximum value compatible with Pauli's principle, building a large magnetic moment. We have determined that 29 atoms constitute the smallest self-bound droplet.
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.
We report variational calculations of energies of (3)He(N) droplets ( 20</=N</=40), using Aziz atom-atom interactions. The trial wave function has a simple structure, combining two- and three-body correlation functions coming from a translationally invariant configuration-interaction description, superimposed to a Jastrow-type correlated wave function with backflow. We find that the smallest bound drop has N = 35 atoms, and that for each N the minimum energy states have the highest spin values.
Small and stable drops of 3He^{3}\mathrm{He}3He atoms can only exist above a minimum number of particles, due to the combination of the 3He^{3}\mathrm{He}3He atom Fermi statistics and its light mass. An accurate estimation of this minimum number using microscopic theory has been difficult due to the inhomogeneous and fermionic nature of these systems. We present a diffusion Monte Carlo calculation of 3He^{3}\mathrm{He}3He drops with sizes near the minimum in order to determine the stability threshold. The results show that the minimum self-bound drop is formed by N=30N=30N=30 atoms with preferred orbitals for open shells corresponding to maximum value of the spin.
We present recent results from a diffusion Monte Carlo study of small 3 He drops in the limit of zero temperature. Using the same methodology than in previous calculations carried out for bulk 3 He , we have obtained accurate results for their energy and structure properties. A relevant concern of this analysis has been the determination of the stability threshold for self binding. Our results show that the smallest self-bound drop is formed by N = 30 atoms, with preferred orbitals for open shells corresponding to maximum value of the spin. The quality of the upper bound energies provided by the fixed node approximation is analyzed by performing released-node estimations for short released times. Possible improvements of the nodal surface by including BCS-like correlation functions are also discussed.
The diffusion Monte Carlo technique is used to calculate and analyze the excitation spectrum of 3He atoms bound to a cluster of 4He atoms by using a previously determined optimum filling of single-fermion orbits with well-defined orbital angular momentum L, spin S, and parity quantum numbers. The study concentrates on the energies and shapes of the three kinds of states for which the fermionic part of the wave function is a single Slater determinant: maximum L or maximum S states within a given orbit, and fully polarized clusters. The picture that emerges is that of systems with strong shell effects, whose binding and excitation energies are essentially determined by averages over configuration at fixed number of particles and spin, i.e., by the monopole properties of an effective Hamiltonian.
We analyze a configuration consisting of a 3He{}^{3}\mathrm{He}3He droplet inmersed in a Bose-Einstein condensate at $T\ensuremath{\approx}0.$ We investigate the stationary density and oscillations of the condensate, as well as the dynamics of the droplet in the frame of a simple model. Our paper takes into account the actual interaction potential between the 3He{}^{3}\mathrm{He}3He and condensate atoms and reveals the stability of the dynamics of a small 3He{}^{3}\mathrm{He}3He droplet inside the condensate.