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Molecular Physics

Variational calculation on the possible existence of a bound state of He3

Slobodan Danko Bosanac, John Norman Murrell

Published Aug 1, 1973• 12 citations
Publisher

Abstract

A variational calculation has confirmed earlier suggestions that 4He3 has a bound state. The partial wave expansion of Simonov was found to be slowly convergent and by this method no bound state was obtained although there was clear evidence that He3 would be closer to a stable bound state than He2. A variational wave function based directly on interparticle separations and the use of Morse-potential eigenfunctions was rapidly convergent and gave a lower limit to the binding energy of 0·63 K.

DOI
10.1080/00268977300101701

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Physical Review A•May 1, 1973•4 citations
A variational calculation has confirmed earlier suggestions that 4He3 has a bound state. The partial wave expansion of Simonov was found to be slowly convergent and by this method no bound state was obtained although there was clear evidence that He3 would be closer to a stable bound state than He2. A variational wave function based directly on interparticle separations and the use of Morse-potential eigenfunctions was rapidly convergent and gave a lower limit to the binding energy of 0·63 K.
The bound state of a He3{\mathrm{He}}^{3}He3 atom trapped in the free surface of He4{\mathrm{He}}^{4}He4 is studied, using a trial function suggested by Lekner. The effective potential which determines the bound-state wave function is calculated from first principles, and results in a binding energy 20% larger than the observed value.
A variational calculation is performed for the (3He)4 system interacting pairwise through the Lennard-Jones He–He potential. Use of an integrodifferential Euler equation is made to determine an optimum wave function, leading to results showing that the existence of this molecule is unlikely. It is confirmed that states of the system with nonzero orbital angular momentum yield lower energies. Also, it appears that the number of 3He atoms needed to form self-bound molecules must be larger than 5.
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.
Abstract The helium dimer 4He2 has recently been detected, confirming earlier ab initio predictions of stability for a single bound state with binding energy of 1.310 mK. The predicted potential minimum is at 2.96 Å, with a radial distribution function peaking at 6.96 Å. We model this system using a Dirac bubble potential, which also admits just one bound j = 0 state. With the bubble located at 6.96 Å, an overlap of 0.9994 with the ab initio wave function is obtained. An average internuclear distance of 52.6 Å is calculated, in good agreement with the ab initio result. The root mean square deviation from the mean, 48.0 Å, indicates an enormous spread of the radial wave function. Also consistent with our model is the absence of bound states for the isotopic variants 3He4He and 3He2. Cross sections for helium‐helium scattering are also computed, using both a partial‐wave expansion and the Born approximation. General trends in the energy dependence of the total cross section are accounted for, in qualitative agreement with experimental results. © 1995 John Wiley & Sons, Inc.
Through a variational calculation, the ground-state binding energy of the 4He^{4}\mathrm{He}4He trimer is computed using the ab initio potential of Bertoncini and Wahl. These results indicate a stable trimer bound by 0.3 \ifmmode^\circ\else\textdegree\fi{}K.