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arXiv:physics/0408127 · Physical Review A

Minimal mass size of a stable He3 cluster

R. Guardiola, Jesús Navarro

Published Mar 18, 2005• 16 citations
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Abstract

The minimal number of $^{3}\mathrm{He}$ atoms required to form a bound cluster has been estimated by means of a diffusion Monte Carlo procedure within the fixed-node approximation. Several importance sampling wave functions have been employed in order to consider different shell-model configurations. The resulting upper bound for the minimal number is 32 atoms.

DOI
10.1103/physreva.71.035201

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The minimal number of 3He^{3}\mathrm{He}3He atoms required to form a bound cluster has been estimated by means of a diffusion Monte Carlo procedure within the fixed-node approximation. Several importance sampling wave functions have been employed in order to consider different shell-model configurations. The resulting upper bound for the minimal number is 32 atoms.
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.
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 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 a single 3He^{3}\mathrm{He}3He atom bound to a cluster with NNN 4He^{4}\mathrm{He}4He atoms, with the aim of establishing the most adequate filling ordering of single-fermion orbits to the mixed clusters with a large number of 3He^{3}\mathrm{He}3He atoms. The resulting ordering looks like the rotational spectrum of a diatomic molecule, being classified only by the angular momentum of the level, although vibrational-like excitations appear at higher energies for sufficiently large NNN.
Small helium (4He) clusters containing the lighter isotope He3 are studied by means of quantum Monte Carlo methods. Accurate ground state energies and structural properties are obtained using accurate trial wave functions and the Tang–Tonnies–Yiu (TTY) helium–helium pair potential. The dimer He4–3He is not bound; as well as the trimer He4He23. The smallest cluster containing He3 is He24He3 with a nonrigid structure having a marked linear contribution. Interestingly, this weakly bound system, with an energy one order of magnitude less than the He34 trimer, is able to bind another He3 atom, forming the tetramer He24He23, which shows the odd feature of having five out of six unbound pairs. In general, the substitution of a single He4 atom in a pure cluster with a He3 atom leads to an energetic destabilization, as the pair He4–3He is not bound. The isotopic impurity is found to perturb only weakly the distributions of the remaining He4 atoms, which retain the high floppiness already found in the pure clusters. As the number of atoms increases the isotopic impurity has the marked tendency to stay on the surface of the cluster. This behavior is consistent with the formation of the so-called “Andreev states” of a single He3 in liquid He4 helium and droplets, where the impurity tends to form single-particle states on the surface of the pure He4.
Optimized variational calculations have been carried out for clusters of He4 between N=20 and N=1000 atoms. For small cluster sizes with less or equal to 112 particles, where comparisons with existing diffusion Monte Carlo results are possible, we find good agreement for the ground state energies and densities. Using a somewhat simpler approximation, we also calculate the bound state energies of He3 atoms attached to these clusters. We then calculate excitations and the dynamic structure function. The complex and nonlocal self-energy introduced for that purpose gives access to the calculation of both elastic and inelastic scattering processes for He4 and He3 atoms impinging on the clusters.