5 CONCLUSIONS case of T ↓ clusters, we observe that the surface thickness is almost a linear function of N , up to N = 320 atoms. We have tried to predict the surface thickness of clusters having more than 320 atoms by fitting our data with the function used in Ref. 27 to predict the width of a free surface. However, with the present results we have not been able to determine the asymptotic value of the surface thickness. Saturation should be probably seen with results for clusters having more than N =320 atoms, but the DMC calculations are already difficult with 320 atoms. density profiles show that the cluster size grows when the number of atoms in the cluster increases, and that the central densities of the largest clusters are very similar to the bulk equilibrium density ρ$_{0}$ = 0 . 007466(7) ˚ A − $^{3}$. The increase of cluster size with increasing number of atoms can also be seen from the pair distribution function P ( r ) shown in Fig. 5 for the same clusters. P ( r ) is normalized such that ∫ P ( r ) r $^{2}$dr = 1. A significant decay of the peak height for the largest clusters, as well as the growing probability for larger interparticle distances in large clusters, is a clear evidence of the size spreading tendency. The surface thickness of clusters s$_{t}$ can be estimated from the density profiles as a difference of radii at which the central density ρ$_{c}$ = ρ ( r = 0) has decreased from 90% to 10% of its value. From the plotted density profiles in Fig. 4 it is obvious that the density error bars are large for small distances. In order to determine the central density as precisely as possible we have tried to fit the density profile with the function used in Ref. 27 General characteristics of large spin-polarized tritium T ↓ clusters have been investigated using the DMC ap- proach. The ground-state energies of clusters consisting of up to 40 T ↓ atoms have been compared with previ- ously published results. For clusters having more than 40 atoms the ground-state energies, as well as the struc- ture description, are determined for the first time. This prediction relies on the use of a very precise potential of interaction between T ↓ -T ↓ atoms. The present results for the ground-state clusters’ energy are also used to extract the energy per particle of liquid T ↓ at equilibrium den- sity using a liquid-drop model. The extrapolation using a liquid-drop formula gives a value E$_{v}$ = − 3 . 66(3) K for the energy per particle in the equilibrium bulk system, which is in very good agreement with the result from a recent DMC calculation of the bulk, e$_{0}$ = − 3 . 656(4) K [6]. The radii of clusters are calculated with pure estima- tors and those results are used to estimate the interval in which the unit radius of the liquid is expected. The result for the unit radius from the bulk calculation lies in the estimated interval. The latter value of the bulk unit radius has been employed to estimate the surface tension t of bulk T ↓ , t =0.08 K ˚ A − $^{2}$. In addition, the sur- face thickness of clusters has been estimated from the clusters’ density profiles. As it is already shown for clusters consisting of up to 40 T ↓ atoms [1], it is concluded that large spin-polarized tritium clusters are less bound and are more diluted than $^{4}$He clusters with the same number of atoms, i.e., inter- particle distances are significantly greater in the corre- sponding T ↓ clusters. J. B. acknowledges support from DGI (Spain) Grant No. FIS2005-04181 and Generalitat de Catalunya Grant No. 2008SGR-04403. I.B and L.V.M. acknowledge support from MSES (Croatia) under Grant No. 177- 1770508-0493. I. B. also acknowledges support from L’Or´ eal ADRIA d.o.o. and Croatian commission for Un- esco, as well as from U.S. National Science Foundation I2CAM International Materials Institute Award, Grant DMR-0645461. We also acknowledge the support of the Central Computing Services at the Johannes Kepler Uni- where ρ$_{0}$ , β , r$_{0}$ and δ are fitting parameters and r is the distance to the centre of mass of the cluster. We find that for T ↓ clusters Eq. (11) can be employed to model den- sity profiles of small clusters, while for greater clusters the same model reproduces poorly the calculated density profiles at small distances. Since the small distances are important for our calculation, we have decided to fit the calculated density profiles to a constant function for dis- tances up to some value r$_{1}$ . We have varied the value of r$_{1}$ from 2 ˚ A to 4 ˚ A, increasing it with the growing size of the cluster. We have considered the constant obtained with the fit as a central density value and used it in fur- ther estimation of the clusters’ surface thickness. The results for the surface thickness are reported in Table I. We can compare our results with the surface thickness of $^{4}$He clusters [24, 28]. Using the VMC method Pandhari- pande et al. [24] showed that in $^{4}$He clusters the surface thickness is ∼ 7 ˚ A for clusters N ≥ 112. In the case of T ↓ clusters, for N ≥ 100, the surface thickness is signif- icantly greater than in $^{4}$He (Table I). This is expected due to the evidently greater interparticle distances in T ↓ clusters, which is a direct consequence of the shallow at- tractive part of T ↓ -T ↓ interaction potential. With the density functional approach, Stringari et al. [28] calcu- lated the surface thickness of several $^{4}$He clusters and we can compare those results with our results for T ↓ clusters having 20, 40 and 240 atoms. The reported surface thick- ness for clusters $^{4}$He$_{20}$ , $^{4}$He$_{40}$ and $^{4}$He$_{240}$ are respectively 8.8 ˚ A, 9.0 ˚ A and 9.3 ˚ A. A comparison with (T ↓ )$_{N}$ reveals larger surface thickness of $^{4}$He$_{N}$ for N =20,40 and smaller surface thickness for N =240. Also, it can be noticed that the surface thickness reported by Stringari et al. is not a linear function of the number of atoms. Contrary, in the ρ ( r ) = ρ$_{0}$ (1 + e β ( r − r 0 $^{)}$) δ , (11)