2 METHOD clear spin states. [12–14] If only one nuclear spin state is occupied (D ↓$_{1}$ ), the system is in a gas state at zero pressure, while in the case of two (D ↓$_{2}$ ) or three (D ↓$_{3}$ ) equally occupied nuclear spin states, the system remains liquid at zero pressure and zero temperature. Exten- sive investigations of the H ↓ and T ↓ bulk systems have been carried out recently with the diffusion Monte Carlo (DMC) method [2, 6], which provides exact results within errorbars for bosonic systems. Using the DMC method for bulk H ↓ and T ↓ , the energy per particle, structural properties, as well as densities and the pressure of the gas (liquid)-solid transition have been predicted. An ac- curate calculation of the ground-state energy per particle in bulk H ↓ has allowed the confirmation of its gas nature in the limit of zero temperature and up to 170 bar, point at which H ↓ solidifies. A similar investigation of bulk T ↓ has revealed that the system is a liquid up to 9 bars, where it crystallizes. [6] In this work, we expand previously reported studies of pure T ↓ clusters.[1, 4, 5] We report the ground-state en- ergy of clusters having up to 320 atoms, as well as their structural properties, obtained with the DMC method. From the density profiles, we estimate the thickness of the clusters’ surface. Justification for carrying out de- manding calculations for large clusters lies in the fact that the present results for clusters can be used to extrap- olate precise equilibrium T ↓ bulk properties. A goal of our investigation is to examine the validity of the liquid- drop formulas when they are applied to T ↓ clusters, as it was done in the past for $^{3}$He and $^{4}$He clusters. [24, 25] In helium clusters, liquid-drop formulas were successfully applied and the results for the equilibrium energy per particle and the unit liquid radius were in good agree- ment with experimental studies. [24, 25] We have used the energy per particle of the T ↓ clusters to extrapo- late the equilibrium energy per particle in bulk T ↓ . We compare the estimated result with the energy per particle calculated in a recent DMC study of a bulk T ↓ . [6] In ad- dition, the surface tension of liquid T ↓ is estimated and compared with known results for $^{3}$He and $^{4}$He liquids. Furthermore, we extract the unit radius of the liquid us- ing the average distance of the particles to the centre of mass of the cluster. In Sec. II, we report briefly the DMC method and discuss the trial wave functions used for importance sam- pling of the clusters. Sec. III reports the results obtained by the DMC simulations. Finally, Sec. IV comprises a summary of the work and an account of the main con- clusions. In the present simulations Jastrow trial wave functions have been used, DMC solves stochastically the Schr¨ odinger equation (1) by multiplying Ψ( R , t ) with the ψ ( R ), a trial wave function used for importance sampling, and rewriting Eq. (1) in terms of the mixed distribution Φ( R , t ) = Ψ( R , t ) ψ ( R ). Within the Monte Carlo framework, Φ( R , t ) is represented by a set of walkers . In the limit t → ∞ only the lowest energy eigenfunction, not or- thogonal to ψ ( R ), survives and then the sampling of the ground state is effectively achieved. Apart from statisti- cal uncertainties, the energy of a N -body bosonic system is exactly calculated. where V ( r ) is the interaction potential. The inter- atomic interaction between tritium atoms is described with the spin-independent central triplet pair potential b $^{3}$Σ+ $_{u}$, which was determined in an essentially exact way by Kolos and Wolniewicz [15]. As in our recent DMC calculations of bulk H ↓ and T ↓ ,[2, 6] we have used the recent extention of Kolos and Wolniewicz data to larger interparticle distances by Jamieson et al. (JDW). [16] The potential is finally constructed using a cubic spline interpolation of JDW data, which is smoothly connected to the long-range behavior of the T ↓ -T ↓ potential as cal- culated by Yan et al. . [17] The JDW potential used in the present work has a core diameter σ = 3 . 67 ˚ A and a mini- mum of − 6 . 49 K at a distance 4 . 14 ˚ A. We have previously verified that the addition of mass-dependent adiabatic corrections (as calculated by Kolos and Rychlewski [18]) to the JDW potential does not change the energy of bulk spin-polarized tritium. [6] It is worth mentioning that within the Born-Oppenheimer approximation it has been explicitly shown that in the spin-aligned electronic state, tritium nuclei behave as effective bosons. [19] where E$_{r}$ is a constant acting as a reference energy and R ≡ ( r $_{1}$, . . . , r $_{N}$) collectively denotes particle positions. The N -particle Hamiltonian, H , is given as The starting point of the DMC method is the Schr¨ odinger equation written in imaginary time, − ¯ h ∂ Ψ( R , t ) ∂t = ( H − E$_{r}$ )Ψ( R , t ) , (1) H = − ¯ h 2 2 m N ∑ i =1 ∇ 2 i + N ∑ i<j V ( r$_{ij}$ ) , (2) ψ$_{J}$ ( R ) = N ∏ i<j f ( r$_{ij}$ ) , (3) f ( r$_{ij}$ ) = exp [ − ( b r$_{ij}$ ) 5 − sr n ij ] , (4) with a two-body correlation function f ( r ),