3 (T ↓ )$_{N}$. These differences are mainly due to the fact that there are small differences in the potential of interaction employed in two simulations. Namely, Blume et al. [1] have included in the Hamiltonian the damped three-body Axilrod-Teller potential term [22] which causes a slight raise of the ground-state energy. In Ref. 1, weaker binding and greater spread in the T ↓ clusters were emphasized as the main difference between small (T ↓ )$_{N}$ and ( $^{4}$He)$_{N}$ clusters, for the same N and up to 40. Similar comparison can be done for large clusters. Namely, the energy per particle of the largest investi- gated $^{4}$He cluster with the DMC method, ($^{4}$He)$_{112}$ , is -3.780(3) K [23]. This can be compared with the energy per particle of the largest T ↓ cluster, (T ↓ )$_{320}$, which is - 2.286(8) K (Table I). It is clear from these results that in the ( $^{4}$He)$_{112}$ cluster, which consists of almost three times smaller number of atoms than (T ↓ )$_{320}$ cluster, binding is significantly stronger. From that, we conclude that the binding in large T ↓ clusters is very weak, as it was al- ready concluded for small clusters [1]. The energy per particle of quantum liquid clusters as a function of N is well reproduced by a liquid-drop model, [24, 25] E ( N ) /N = E$_{v}$ + xE$_{s}$ + x $^{2}$E$_{c}$ , (5) where E$_{v}$ , E$_{s}$ and E$_{c}$ are respectively the volume, surface and curvature terms, and the variable x is defined as x = N − 1 / $^{3}$. In Fig. 2, we have plotted results for the energy per particle from Table I, as well as a line on the top of data, which represents the best fit with expression (5). We have included in our fit all the investigated clusters and the best set of parameters obtained with the above mentioned fit is: E$_{v}$ = -3.66(3) K, E$_{s}$ = 10.2(2) K and E$_{c}$ = -6.1(4) K. The parameter E$_{v}$ represents the energy per particle of bulk liquid T ↓ at the equilibrium density. This extrapo- lated result is in a very good agreement with our recent results obtained in calculations of bulk T ↓ [6]. With the DMC method we obtained ρ$_{0}$ = 0 . 007466(7) ˚ A − 3 as the equilibrium density of liquid T ↓ and e$_{0}$ = − 3 . 656(4) K as the energy per particle at that density. It is also important to emphasize that the parameters E$_{v}$ , E$_{s}$ and E$_{c}$ have been obtained without including in the fit the bulk energy per particle at equilibrium. Fur- thermore, the parameters in Eq. (5) remain practically the same when the energy per particle at the equilib- rium density is included in the fit. Thus, the demanding DMC calculations have been worthwhile because the re- sult of our liquid-drop model (5) does not depend on the knowledge of the equilibrium energy per particle of the bulk. Also, we have determined that (T ↓ )$_{280}$ is the ’smallest’ cluster needed to be included in the fit in or- der to extrapolate the parameter E$_{v}$ properly. Namely, using just DMC results for clusters having N = 20 − 280 atoms in the fit we get E$_{v}$ = -3.69(3) K, which is within Our DMC results for the ground-state energy per par- ticle and radii of the investigated clusters are given in Table I. For clusters consisting of up to 10 T ↓ atoms we have already shown [4] good agreement with results obtained by Blume et al. [1]. Here, we extend this com- parison for clusters consisting of up to 40 T ↓ atoms. In Fig. 1, comparison of our results and the ones by Blume et al. is shown. As in the case of small clusters, we report slightly lower ground-state energy for all clusters RESULTS In order to eliminate bias coming from the time-step value used in simulations, all calculations have been per- formed with several Δ t time-steps which assume values within the interval 5 × 10 − $^{4}$− 1 . 3 × 10 − $^{3}$K − $^{1}$. From the ob- tained results, we have extrapolated the result to Δ t → 0. In accordance with the DMC method used in this work, which is accurate to second order in the time step [21], the extrapolation is made with a quadratic function. Second order DMC enables the use of greater time-steps than the linear DMC method. For several clusters we have verified that 1000 walkers are enough for excluding the bias coming from the size of the population ensemble used in a simulation. Thus, we have decided to employ this number of walkers in all the remaining DMC calculations. The same conclusion emerged also from previous experience in pure and mixed T ↓ clusters. The optimization of the trial wave functions has been done for all clusters by means of the variational Monte Carlo method. For clusters with N ≤ 60 the best varia- tional parameters vary from b =3.574 ˚ A to b =3.605 ˚ A and from s =0.0328 ˚ A − 1 to s =0.0073 ˚ A − 1 for increasing N . In case of clusters having N ≥ 80 atoms, the parame- ter b assumes values from 3.574 ˚ A to 3.605 ˚ A, while at the same time s varies from 000162 ˚ A − 2 to 0.0000145 ˚ A − $^{2}$. It is worth noticing that in both types of two-body correlation functions ( n = 1 , 2) the parameter b remains practically constant, while s always decreases with N . where n = 1 or n = 2, depending on the size of the cluster, and b and s are variational parameters. Previ- ous experience in work with small pure and mixed spin- polarized tritium clusters [4] has shown that the best choice for the two-body correlation function is obtained with n = 1. We have used this type of function for clus- ters having N ≤ 60 atoms, but for larger clusters the variational energies obtained with this type of function worsen significantly. Then, for larger clusters, it is better to consider the model with n = 2, which is similar to f ( r ) which has been used in recent investigations of vortices in large $^{4}$He clusters. [20] Eq. (4) with n = 2 defines much better the confinement of space in which large number of T ↓ atoms is settled and definitely provides better VMC energies for clusters having N ≥ 80 atoms.