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We review the recent activity in the theoretical description of spin-polarized atomic hydrogen and its isotopes at very low temperatures. Spin-polarized hydrogen is the only system in nature that remains stable in the gas phase even in the zero temperature limit due to its small mass and weak interatomic interaction. Hydrogen and its heavier isotope tritium are bosons, the heavier mass of tritium producing a self-bound (liquid) system at zero temperature. The other isotope, deuterium, is a fermion with nuclear spin one making possible the study of three different quantum systems depending on the population of the three degenerate spin states. From the theoretical point of view, spin-polarized hydrogen is specially appealing because its interatomic potential is very accurately known making possible its precise quantum many-body study. The experimental study of atomic hydrogen has been very difficult due to its high recombination rate, but it finally led to its Bose-Einstein condensate state in 1998. Degeneracy has also been observed in thin films of hydrogen adsorbed on the 4He surface allowing for the possibility of observing the Berezinskii–Kosterlitz–Thouless superfluid transition.

The ground-state properties of helium clusters 4HeN and 4HeN3He, for N≤ 40, adsorbed on the surface of cesium are studied using variational and diffusion Monte Carlo calculations. Binding properties are determined using two different Cs–He interaction potentials. For the smallest clusters, self-binding on a Cs surface is stronger than in two or three dimensions. For N > 10 self-binding in three dimensions is stronger than on Cs for both types of Cs–He interaction potential considered. The obtained binding energies and structure are compared to results of recent density functional calculations. The emergence of edge states of 3He atom, localized along the contact line of 4He cluster with a cesium surface, is studied. First indication that 3He atom prefers to be close to the contact line appears already for the 4He33He cluster.

The ground state properties of helium mixed clusters 3He2,3,4 4He2, 3He2,3,4 4He3, 3He2,3,4 4He4, 3He2,3 4He5, consisting of up to eight helium atoms are studied using variational and diffusion Monte Carlo calculations. For clusters with three and four 3He atoms released-node diffusion Monte Carlo method is used. Our calculations show that, within errorbars, clusters 3He3,4 4He2 have the same binding energy as the cluster 3He2 4He2, and that 3He3 4He3 has the same binding energy as 3He2 4He3. The clusters 3He3,4 4He2 and 3He3 4He3 are in states in which one or two 3He atoms are far away from the rest of the system. Other considered clusters are bound. In particular, we have shown the stability of the cluster 3He4 4He3, which was previously considered unstable. The calculations are performed using several different interatomic potentials and the conclusions concerning stability are insensitive to the particular form of the interaction potential. We compare our results with the recent experiment and other theoretical calculations.

This work expands recent investigations in the field of spin-polarized tritium (T$\downarrow$) clusters . We report the results for the ground state energy and structural properties of large T$\downarrow$ cl usters consisting of up to 320 atoms. All calculations have been performed with variational and diffusi on Monte Carlo methods, using an accurate {\it ab initio} interatomic potential. Our results for $N \le q 40$ are in good agreement with results obtained by other groups. Using a liquid-drop expression for t he energy per particle, we estimate the liquid equilibrium density, which is in good agreement with our recently obtained results for bulk T$\downarrow$. In addition, the calculations of the energy for larg e clusters have allowed for an estimation of the surface tension. From the mean-square radius of the dr op, determined using unbiased estimators, we determine the dependence of the radii on the size of the c luster and extract the unit radius of the T$\downarrow$ liquid., Comment: 8 pages, 5 figures

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.