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Physical Review Letters

Variational Study of 3He Droplets

R. Guardiola, Jesús Navarro

Published Feb 7, 2000• 45 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.84.1144

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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.
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.
We study low-lying excited states of 4He{}^{4}\mathrm{He}4He clusters up to a cluster size of 40 atoms in a variational framework. The ansatz wave function combines two- and three-body correlations, coming from a translationally invariant configuration interaction description, and Jastrow-type short-range correlation. We have previously used this scheme to determine the ground-state energies of 4He{}^{4}\mathrm{He}4He and 3He{}^{3}\mathrm{He}3He clusters. Here we present an extension of this ansatz wave function having a good quantum angular momentum L. The variational procedure is applied independently to the cases with L=0,2,4,L=0,2,4,L=0,2,4, and upper bounds for the corresponding energies are thus obtained. Moreover, centroid energies for L excitations are calculated through the use of sum rules. A comparison with previous calculations is also made.
Abstract This paper describes improved trial wavefunctions for helium clusters and their use in variational QMC calculations of their binding energies, structural properties, and breathing mode vibrational excited states, for clusters of 3 to 270 atoms. The wavefunctions developed were similar to those of earlier work but included convenient analytic functions for two- and three-body correlations. All terms were of the Jastrow exponential form, based on sums of one-, two-, and three-body terms t1(ri), t2(rij), and t3(rij, rjk,rki), expressed as functions of interparticle distances. Excited-state wavefunctions for the breathing vibrational mode were obtained with the aid of procedures adapted from treatment of the quantum mechanics of liquid drop models. The interactions of helium atoms were specified as pairwise-additive with an accurate semi-empirical pair potential. Optimizations of parameters in the trial wavefunctions were carried out for individual cluster sizes with an exhaustive search procedure in a series of trial variational calculations, in which the parameters were varied to minimize the energy. A partial correlation of results was obtained by use of identical initial coordinates and random number seeds in these optimization calculations. Once the wavefunctions were optimized, longer calculations were used to determine properties of the clusters. In addition, diffusion QMC calculations were used to obtain more accurate nonvariational energies for comparisons.
The ground states of drops of spin-polarized liquid 3He^{3}\mathrm{He}3He containing 56, 84, and 120 atoms are calculated with the variational Monte Carlo method using wave functions containing pair, triplet, and backflow correlations. The calculated energies of these drops are higher by \ensuremath{\sim}0.2 K per atom than those of drops of unpolarized liquid 3He^{3}\mathrm{He}3He. The results also indicate that the equilibrium density of liquid $^{3}\mathrm{He}_{\mathrm{\ensuremath{\uparrow}}}$ is larger than that of unpolarized 3He^{3}\mathrm{He}3He by \ensuremath{\sim}5%, and that the thickness of its surface is smaller.
Variational many-body wave functions for the ground state of liquid 3He^{3}\mathrm{He}3He which include triplet and backflow correlations are investigated with use of Monte Carlo integration. Our energy of - 1.9\ifmmode^\circ\else\textdegree\fi{}K removes half of the discrepancy between previous Jastrow-Slater calculations and experimental results. The first exact results for mass-three bosons are also presented. Triplet correlations in the variational wave function are equally effective in lowering the energy of both mass-three bosons and 3He^{3}\mathrm{He}3He.
The (extended) lowest order constrained variational ((E) LOCV) method was used to calculate the ground state energy of liquid helium 3 (3He) droplets at zero temperature. Different types of density distribution profiles, such as the Gaussian, the Quasi-Gaussian and the Woods-Saxon were used. It was shown that at least, on average, near 20 3He atoms are needed to get the bound state for 3He liquid droplet. Depending on the choice of the density profiles and the atomic radius of 3He, the above estimate can increase to 300. Our calculated ground state energy and the number of atoms in liquid 3He droplet were compared with those of Variational Monte Carlo (VMC) method, Diffusion Monte Carlo (DMC) method and Density Functional Theory (DFT), for which a reasonable agreement was found.