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Stability of (He2HeM)-He-3-He-4 and (He3HeM)-He-3-He-4 L=0, 1 clusters

Dario Bressanini, Gabriele Morosi

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

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.

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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.
We have studied the stability of mixed 3He/4He^{3}\mathrm{H}\mathrm{e}/^{4}\mathrm{H}\mathrm{e}3He/4He clusters in L=0L=0L=0 states by the diffusion Monte Carlo method, employing the Tang-Toennies-Yiu He-He potential. The clusters 3He4HeN^{3}\mathrm{H}\mathrm{e}^{4}\mathrm{H}\mathrm{e}_{N}3He4HeN​ and 3He24HeN^{3}\mathrm{H}\mathrm{e}_{2}^{4}\mathrm{H}\mathrm{e}_{N}3He24​HeN​ are stable for N>1N>1N>1. The lighter atoms tend to move to the surface of the cluster. The minimum number of 4He^{4}\mathrm{H}\mathrm{e}4He atoms able to bind three 3He^{3}\mathrm{H}\mathrm{e}3He atoms in a L=0L=0L=0 state is nine. Two of three fermionic helium atoms stay on the surface, while the third one penetrates into the cluster.
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We report results for the ground-state energy and structural properties of small (4)He-T↓ clusters consisting of up to four T↓ and eight (4)He atoms. These results have been obtained using very well-known (4)He-(4)He and T↓- T↓ interaction potentials and several models for the (4)He- T↓ interatomic potential. All the calculations have been performed with variational and diffusion Monte Carlo methods. It takes at least three atoms to form a mixed bound state. In particular, for small clusters the binding energies are significantly affected by the precise form of the (4)He- T↓ interatomic potential but the stability limits remain unchanged. The only exception is the (4)He(2)T↓ trimer whose stability in the case of the weakest (4)He- T↓ interaction potential is uncertain while it seems stable for other potentials. The mixed trimer (4)He(T↓)(2), a candidate for the Borromean state, is not bound. All other studied clusters are stable. Some of the weakest bound clusters can be classified as quantum halo as a consequence of having high probability of being in a classically forbidden region.
We report accurate ground state energies and structural properties for small clusters of 4He computed with the diffusion quantum Monte Carlo (DMC) method combined with high quality trial wave functions and using the recent analytical pair potential of Tang, Toennies, and Yiu [Phys. Rev. Lett. 74, 1546 (1995)]. Calculations based on the older HFD-B(He) potential are reported for comparison. The clusters are found to be extremely floppy and to be characterized by very diffuse wave functions. The DMC results for 4He2 and 4He3 are in excellent agreement with other calculations using conventional methods. 4He3 is found to have a noticeable contribution from nearly linear geometries. The internal structure of the clusters is described by a three particle correlation function which reveals a significantly non-spherical internal cluster structure. The energies for all cluster sizes are found to be slightly higher than those obtained with the HFD-B(He) pair potential. Exploratory calculations on the helium trimer indicate that the effects of three body interactions do not exceed the uncertainty margin provided by different state of the art pair potentials.