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arXiv:0712.1730 · The Journal of Chemical Physics

Quantum Monte Carlo study of small pure and mixed spin-polarized tritium clusters

I. Bešlić, Leandra Vranješ Markić, Jordi Boronat

Published Feb 8, 2008• 14 citations
arXivHTMLPDF

Abstract

We have investigated the stability limits of small spin-polarized clusters consisting of up to ten spin-polarized tritium T downward arrow atoms and the mixtures of T downward arrow with spin-polarized deuterium D downward arrow and hydrogen H downward arrow atoms. All of our calculations have been performed using the variational and diffusion Monte Carlo methods. For clusters with D downward arrow atoms, the released node procedure is used in cases where the wave function has nodes. In addition to the energy, we have also calculated the structure of small clusters using unbiased estimators. Results obtained for pure T downward arrow clusters are in good accordance with previous calculations, confirming that the trimer is the smallest spin-polarized tritium cluster. Our results show that mixed T downward arrow-H downward arrow clusters having up to ten atoms are unstable and that it takes at least three tritium atoms to bind one, two, or three D downward arrow atoms. Among all the considered clusters, we have found no other Borromean states except the ground state of the T downward arrow trimer.

DOI
10.1063/1.2827119

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We have investigated the stability limits of small spin-polarized clusters consisting of up to ten spin-polarized tritium T downward arrow atoms and the mixtures of T downward arrow with spin-polarized deuterium D downward arrow and hydrogen H downward arrow atoms. All of our calculations have been performed using the variational and diffusion Monte Carlo methods. For clusters with D downward arrow atoms, the released node procedure is used in cases where the wave function has nodes. In addition to the energy, we have also calculated the structure of small clusters using unbiased estimators. Results obtained for pure T downward arrow clusters are in good accordance with previous calculations, confirming that the trimer is the smallest spin-polarized tritium cluster. Our results show that mixed T downward arrow-H downward arrow clusters having up to ten atoms are unstable and that it takes at least three tritium atoms to bind one, two, or three D downward arrow atoms. Among all the considered clusters, we have found no other Borromean states except the ground state of the T downward arrow trimer.
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 present variational and diffusion Monte Carlo studies of pure and mixed spin-polarised tritium clusters. Our results for pure clusters, consisting of only tritium atoms T↓, are in good agreement with previous calculations. We show that mixed clusters, consisting of up to 60 T↓ atoms and one spin-polarized deuterium D↓ atom are stable. On the other hand, we verified that tritium clusters of up to N = 60 atoms do not bind even one H↓ atom; the ground-state energy of the considered mixed T↓-H↓ clusters is within the errorbars equal to or higher than the energy of the pure tritium cluster. In addition to the energy, we present results of the structure of the clusters, which has been determined using unbiased estimators. For larger N , a D↓ atom forms an Andreev state on the surface of a tritium cluster core. The H↓ atoms stay further away from the center of the cluster than the D↓ atoms and slowly increase their separation as the simulation proceeds, indicating instability.
The ground-state of the helium and spin-polarized hydrogen quantum clusters is investigated in this work using Quantum Monte Carlo methods, as well as the spin-polarized tritium (T↓) liquid. For small mixed helium clusters consisting of up to eight helium atoms the ground-state energy and structure have been obtained. Stability of the 3He4 4He3 cluster, which was previously considered unstable, is predicted. It is confirmed that tritium trimer (T↓)3 is an example of Borromean state. For pure large spin-polarized tritium clusters consisting of up to 320 atoms the ground-state energy is obtained. Stability limits have been investigated for small mixed (T↓)n(D↓)m clusters, for m ≥ 2 i n + m ≤ 10. Especially, it has been shown that all clusters (T↓)ND↓ are stable for N ≥ 3. It is also shown that even 60 T↓ atoms are not enough to form stable cluster (T↓)60H↓. Equation of state, spinodal density, energy per particle at the equilibrium density, unit radius and surface tension of the T↓ liquid have been determined using results obtained in the simulations of liquid phase.
We present an extensive study of the static and dynamic properties of systems of spin-polarized tritium atoms. In particular, we calculate the two-body |F,m(F)>=|0,0> s-wave scattering length and show that it can be manipulated via a Feshbach resonance at a field strength of about 870 G. Such a resonance might be exploited to make and control a Bose-Einstein condensate of tritium in the |0,0> state. It is further shown that the quartet tritium trimer is the only bound hydrogen isotope and that its single vibrational bound state is a Borromean state. The ground state properties of larger spin-polarized tritium clusters are also presented and compared with those of helium clusters.
The ground-state energy of spin-polarized hydrogen, deuterium, and tritium is calculated by means of a modified variational lowest order constrained-variation method, and the calculations are done for five different two-body potentials. Spin-polarized H↓ is not self-bound according to our theoretical results for the ground-state binding energy. For spin-polarized D↓, however, we obtain theoretical results for the ground-state binding energy per particle from −0.42 K at an equilibrium particle density of 0.25 σ−3 or a molar volume of 121 cm3/mol to + 0.32 K at an equilibrium particle density of 0.21 σ−3 or a molar volume of 142 cm3/mol, where σ = 3.69 Å (1 Å = 10−10 m). It is, therefore, not clear whether spin-polarized deuterium should be self-bound or not. For spin-polarized T↓, we obtain theoretical results for the ground-state binding energy per particle from −4.73 K at an equilibrium particle density of 0.41 σ−3 or a molar volume of 74 cm3/mol to −1.21 K at an equilibrium particle density of 0.28 σ−3 or a molar volume of 109 cm3/mol.
Small helium (4He) clusters containing the lighter isotope He3 are studied by means of quantum Monte Carlo methods. Accurate ground state energies and structural properties are obtained using accurate trial wave functions and the Tang–Tonnies–Yiu (TTY) helium–helium pair potential. The dimer He4–3He is not bound; as well as the trimer He4He23. The smallest cluster containing He3 is He24He3 with a nonrigid structure having a marked linear contribution. Interestingly, this weakly bound system, with an energy one order of magnitude less than the He34 trimer, is able to bind another He3 atom, forming the tetramer He24He23, which shows the odd feature of having five out of six unbound pairs. In general, the substitution of a single He4 atom in a pure cluster with a He3 atom leads to an energetic destabilization, as the pair He4–3He is not bound. The isotopic impurity is found to perturb only weakly the distributions of the remaining He4 atoms, which retain the high floppiness already found in the pure clusters. As the number of atoms increases the isotopic impurity has the marked tendency to stay on the surface of the cluster. This behavior is consistent with the formation of the so-called “Andreev states” of a single He3 in liquid He4 helium and droplets, where the impurity tends to form single-particle states on the surface of the pure He4.