4 and g$_{2}$ ( x ) = cx + d x . (10) The parameters extracted from the fits are: a = 1 . 85(12) ˚ A, b = 2 . 34(3) ˚ A, c = 2 . 55(1) ˚ A and d = 3 . 73(12) ˚ A. Using these interpolation parameters and the definition of unit radii given in (8), in the limit N → ∞ , we extract an equilibrium radius r$_{0}$ = 3 . 02(4) ˚ A using the function (9) and r$_{0}$ = 3 . 29(1) ˚ A using the function (10). Since in both cases the quality of the fit is very good, we cannot state which of the two extracted results for equilibrium unit radius should be considered as the better estimation. We can thus only conclude that the equilibrium unit radius assumes a value within the inter- val from 3.02(4) ˚ A to 3.29(1) ˚ A. Therefore, the estimation of the equilibrium unit ra- dius from the results obtained in clusters calculations is very sensitive to the choice of interpolating function. Because of that, we decided to include the unit radius 3.18(1) ˚ A , derived from the bulk T ↓ , in the estimation of the surface tension. From r$_{0}$ , it is possible to calculate the liquid surface tension t using expression (6); we have obtained t = 0 . 08 K ˚ A − $^{2}$. There is no experimental result for the surface tension of liquid T ↓ , and this prediction is, to the best of our knowledge, the first estimation of t for liquid T ↓ . Contrary to liquid T ↓ , the surface tensions of $^{4}$He and $^{3}$He liquids have been experimentally investigated and the measured values are respectively 0.27 K ˚ A − 2 and 0.11 K ˚ A − $^{2}$. [24] In the case of liquid T ↓ our estimated value of the surface tension is even smaller than the surface tension of the $^{3}$He liquid, although bulk T ↓ is a bosonic system. Explanation for such a small value of the surface tension lies in the fact that the interaction between T ↓ atoms is described with a very shallow potential. In addition to the ground-state energy, we have also studied the structure of T ↓ clusters. Exact estimators of DMC method have been employed to calculate values such as the pair distribution function P ( r ), as well as the distribution of particles with respect to the centre of mass of the cluster ρ ( r ). Possible bias in our results coming from the type of trial wave function used in the simulations is resolved with the use of pure estimators which ensure unbiased results. [26] In Fig. 4, the density distributions of T ↓ clusters hav- ing 40, 80, 120, 180, 240 and 320 atoms are plotted. The g$_{1}$ ( x ) = a + bx, (9) The second method for obtaining the unit radius, Eq. (8), was previously used in the study of $^{4}$He clus- ters. [24, 25] In Ref. 24, it is emphasized that only those $^{4}$He clusters with more than ten atoms have a radius which increases approximately as N 1 / $^{3}$. Since in our cal- culations we obtain unbiased mean-square radii of clus- ters with pure estimators, we tried to interpolate our data for clusters radii, R$_{cm}$ ( N ) = √ 〈 r $^{2}$( N ) 〉 , with sev- eral polynomial functions of the variable x = N 1 / $^{3}$. As in the case of the interpolation of the energy per particle, we have included all clusters having N = 20 − 320 atoms. In Fig. 3, clusters’ radii obtained from the calculations are plotted, as well as two lines on top of data which represent two interpolations, using functions Using the result for the equilibrium density of the T ↓ liquid ρ$_{0}$ = 0 . 007466(7) ˚ A − 3 [6] and Eq. (7), we obtain r$_{0}$ =3.18(1) ˚ A . where 〈 r $^{2}$( N ) 〉 is the mean-square radius of a cluster with N atoms. r$_{0}$ ( N ) = [ 5 3 〈 r $^{2}$( N ) 〉 ] 1 / 2 N − 1 / 3 , (8) 4 π 3 r 3 $_{0}$ρ$_{0}$ = 1 , (7) or from the expression where r$_{0}$ is the unit radius of the liquid. The unit radius of the liquid can be determined in two ways, using the result of the equilibrium density of the bulk liquid t = E$_{s}$ 4 πr 2 0 , (6) The second parameter E$_{s}$ extracted from Eq. (5) is related to the surface tension of liquid T ↓ through It is useful to compare the value r$_{0}$ with σ = 3 . 67 ˚ A. If we consider r$_{0}$ as the radius of the sphere that one T ↓ atom occupies at equilibrium density in a liquid, σ has to be smaller than 2 r$_{0}$ , as it is in our case. On the other hand, the value of r$_{0}$ of liquid T ↓ is also greater than the unit radius of liquid $^{4}$He ( r$_{0}$ =2.1799 ˚ A ) [25]. This also explains the greater spread in T ↓ clusters because it is clear that T ↓ atoms occupy more space than $^{4}$He atoms at equilibrium density. We have also tried to fit all the obtained data for E/N with a linear function in N − 1 / $^{3}$, as in Ref. 25, but that kind of fit has not been so precise as the one performed including a quadratic dependence on N − 1 / $^{3}$. With the linear fit E$_{v}$ = -3.26(3) K, which is around 11% higher than the e$_{0}$ obtained for bulk, showing the necessity of including the second-order term. the error bars the same as the result obtained including the largest cluster ( N =320, E$_{v}$ =-3.66(3) K). However, the extrapolation of the equilibrium energy per particle with fits including just results for clusters smaller than (T ↓ )$_{280}$ always produces lower energy than the one cal- culated for the bulk. For example, the extrapolated bulk energy with results for clusters having up to 120 atoms is -3.85(2) K, which is around 5% lower than e$_{0}$ . Sim- ilar conclusions about this fit emerged for $^{4}$He clusters [25], where it was emphasized that an accurate extrapo- lation of the bulk equilibrium energy from finite cluster calculations should include relatively large clusters.