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The Journal of Chemical Physics

A variational calculation of the binding energy of the fermionic 3He tetramer

S. Nakaichi-Maeda, T. K. Lim, Y. Akaishi

Published Dec 1, 1982• 7 citations
Publisher

Abstract

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.

DOI
10.1063/1.443764

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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.
The three-body Schrdinger equation is approximately solved in the hyperspherical coordinates and the binding energies of the three-body weakly bound systems are calculated with the purpose to find if He-He-Ba trimers could exist. Using the special feature of the B-spline function like the flexible and highly localized properties, hypersphercial potentials are obtained by modifying the knots distribution of the B-spline basis of different weakly bound three-atom systems. Employing the best empirical interaction potentials between each pair of particles, we obtain that in the ground state binding energies of the weakly bound typical three-atom systems, the bindings of the molecules, 4He-4He-138Ba, 4He-3He-138Ba and 3He-3He-138Ba are possible. The binding energies of these systems are shown in the order of 1 Kelvin, each system could support only one bound state. These weakly bound molecules can exist only in a very cold environment. To get insight into the geometry of the molecules, the features of the channel functions associated with the hyperspherical potential curves of each system are investigated.
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.