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Le Journal de Physique Colloques

SMALL CLUSTERS OF PURE AND ADMIXED H↑,3He↑, T↑, AND4He ATOMS

T. K. Lim, S. Nakaichi, Y. Akaishi, Hajime Tanaka

Published Jul 1, 1980• 0 citations
Publisher

Abstract

The results of accurate variational and exact Faddeev-UPE calculations to determine the existence of small clusters of admixed and pure H↑, 3He↑, T↑ and 4He atoms in two and three dimensions are reported. Evidence is found that i) (4He)N-(H↑)n can exist only if N is larger than 20. ii) (T↑)n systems exist with n as small as 3, and iii) bosonic (3He)n clusters exist for n greater than 6.

DOI
10.1051/jphyscol:1980731

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The results of accurate variational and exact Faddeev-UPE calculations to determine the existence of small clusters of admixed and pure H↑, 3He↑, T↑ and 4He atoms in two and three dimensions are reported. Evidence is found that i) (4He)N-(H↑)n can exist only if N is larger than 20. ii) (T↑)n systems exist with n as small as 3, and iii) bosonic (3He)n clusters exist for n greater than 6.
A stability chart of mixed 4He{}^{4}\mathrm{He}4He and 3He{}^{3}\mathrm{He}3He clusters has been obtained by means of the diffusion Monte Carlo method, using both the Aziz HFD-B and the Tang-Toennies-Yiu atom-atom interaction. The investigated clusters contain up to eight 4He{}^{4}\mathrm{He}4He atoms and up to 20 3He{}^{3}\mathrm{He}3He atoms. One single 4He{}^{4}\mathrm{He}4He binds 20 3He{}^{3}\mathrm{He}3He atoms, and two 4He{}^{4}\mathrm{He}4He bind 1, 2, 8, and more than 14 3He{}^{3}\mathrm{He}3He atoms. All clusters with three or more 4He{}^{4}\mathrm{He}4He atoms are bound, although the combinations 4He33He9,10,11{}^{4}{\mathrm{He}}_{3}^{3}{\mathrm{He}}_{9,10,11}4He33​He9,10,11​ and 4He43He9{}^{4}{\mathrm{He}}_{4}^{3}{\mathrm{He}}_{9}4He43​He9​ are metastable. Clusters with 2, 8, and 20 3He{}^{3}\mathrm{He}3He atoms are particularly stable and define magic 3He{}^{3}\mathrm{He}3He numbers.
We have studied the stability of mixed 3He/4He clusters in L 1⁄4 0 \nand L 1⁄4 1 states by the diffusion Monte Carlo method, employing the Tang-Toennies-Yiu (TTY) He-He potential. The clusters 3He4HeM (L 1⁄4 0, S 1⁄4 12) and 3He2 4HeM (L 1⁄4 0, S 1⁄4 0) are stable for M >1, while to bind two 3He in a triplet state the minimum number of 4He is four. Considering clusters with three 3He, 3He3 4He4 is the smallest stable system in the L 1⁄4 1 state, while 3He3 4He8 is the smallest stable system in the L 1⁄4 0 state.
The existence of small helium clusters containing a variable number of 4He^{\mathrm{4}}\mathrm{H}\mathrm{e}4He and 3He^{\mathrm{3}}\mathrm{H}\mathrm{e}3He atoms is studied within a variational Monte Carlo calculation employing the Aziz HFD-B(HE) pair interaction. The clusters 4He2{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{2}4He2​ support one and two 3He^{\mathrm{3}}\mathrm{H}\mathrm{e}3He atoms; however, the system with three 3He^{\mathrm{3}}\mathrm{H}\mathrm{e}3He atoms is metastable, and the next bound system requires at least 18 fermions. All clusters obtained by adding 3He^{\mathrm{3}}\mathrm{H}\mathrm{e}3He atoms to the trimer 4He3{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{3}4He3​ and the tetramer 4He4{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{4}4He4​ are bound, but the clusters 4He3{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{3}4He3​-3He3,4,5{^{\mathrm{3}}\mathrm{H}\mathrm{e}}_{3,4,5}3He3,4,5​ and 4He3,4{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{3,4}4He3,4​-3He9{^{\mathrm{3}}\mathrm{H}\mathrm{e}}_{9}3He9​ are metastable. All remaining clusters with three or more bosons and any number of fermions are stable.
The results of accurate variational calculations for the ground-state binding energies of several NNN-boson systems in two and three dimensions are reported; the systems specifically considered are small (N=2,3,4,and5N=2, 3, 4, \mathrm{and} 5N=2,3,4,and5) clusters of 4He^{4}\mathrm{He}4He atoms interacting through pairwise Lennard-Jones potentials. Evidence is found strongly suggesting each set of systems have a common functional relationship linking the binding energies and the De Boer quantum constant near threshold for self-binding. These calculations also confirm the existence of a unique threshold value of the interaction strength for all NNN-boson systems in 2D2D2D. In addition, the linear relation between the binding energies of helium clusters present in 3D3D3D holds ture in 2D2D2D as well.