arXiv:1001.1224v1 [cond-mat.other] 8 Jan 2010 Quantum Monte Carlo study of large spin-polarized tritium clusters I. Beˇsli´ c L. Vranjeˇs Marki´ c Faculty of Science, University of Split, HR-21000 Split, Croatia and ICAM/I2CAM, 4415 Chem Annex, UC Davis, One Shield Avenue, Davis, CA 95616 Faculty of Science, University of Split, HR-21000 Split, Croatia and Institut f¨ ur Theoretische Physik, Johannes Kepler Universit¨ at, A-4040 Linz, Austria J. Boronat Departament de F´ısica i Enginyeria Nuclear, Campus Nord B4-B5, Universitat Polit` ecnica de Catalunya, E-08034 Barcelona, Spain (Dated: November 15, 2018) This work expands recent investigations in the field of spin-polarized tritium (T ↓ ) clusters. We report the results for the ground state energy and structural properties of large T ↓ clusters consisting of up to 320 atoms. All calculations have been performed with variational and diffusion Monte Carlo methods, using an accurate ab initio interatomic potential. Our results for N ≤ 40 are in good agreement with results obtained by other groups. Using a liquid-drop expression for the energy per particle, we estimate the liquid equilibrium density, which is in good agreement with our recently obtained results for bulk T ↓ . In addition, the calculations of the energy for large clusters have allowed for an estimation of the surface tension. From the mean-square radius of the drop, determined using unbiased estimators, we determine the dependence of the radii on the size of the cluster and extract the unit radius of the T ↓ liquid. PACS numbers: 67.65.+z,02.70.Ss ment method, was reported by Salci et al [11]. Because of evident resemblance of bosonic T ↓ and $^{4}$He atoms Blume et al. [1] also compared general properties of both types of clusters. They showed that common attributes of T ↓ clusters are weaker binding and greater interparticle dis- tances between atoms, in comparison with $^{4}$He clusters having the same number of atoms. In the same work, results of coupled-channel scattering calculations for two T ↓ atoms are reported, indicating the possibility for for- mation of a tritium condensate using its broad Feshbach resonance. Mixed clusters consisting of spin-polarized hydrogen- tritium and deuterium-tritium atoms have also been in- vestigated. [4, 5] It has been shown that three T ↓ atoms are needed to bind one D ↓ atom in a stable system, mak- ing thus clusters (T ↓ )$_{N}$D ↓ stable for all N ≥ 3. On the contrary, it has been shown that even 60 T ↓ are not enough to bind one H ↓ in a stable system. Namely, the ground-state energy of the cluster (T ↓ )$_{60}$H ↓ is within the error bar equal to the ground state energy of (T ↓ )$_{60}$, lead- ing to the conclusion that clusters (T ↓ )$_{N}$H ↓ for N ≤ 60 are effectively unstable or are at the threshold of binding. Due to the more complicated calculations in the case of several fermionic D ↓ atoms, so far only the stability limits of small mixed spin-polarized deuterium-tritium clusters having up to 5 D ↓ atoms have been examined. [4] Despite the lack of experimental verification, bulk properties of all spin-polarized hydrogen isotopes have been theoretically predicted. Bulk properties of the D ↓ system are conditioned by the number of occupied nu- Further investigation related to possible candidates for BEC state in hydrogen systems was done by Blume et al. . In their work [1], spin-polarized tritium clusters as well as optically pumped tritium condensate were theoretically investigated for the first time. Blume et al. reported their DMC results for the ground state energy and structural properties of T ↓ clusters consisting of up to 40 atoms. In addition, it was also shown that the smallest T ↓ cluster is a trimer, i.e. (T ↓ )$_{3}$; negative ground-state energy was not obtained for the dimer (T ↓ )$_{2}$, which means that T ↓ trimer is an example of Borromean or halo state. The same conclusion for (T ↓ )$_{3}$, obtained with the finite ele- The extreme quantum nature of electron spin- polarized hydrogen (H ↓ ) and its isotopes, spin-polarized deuterium (D ↓ ) and spin-polarized tritium (T ↓ ), pro- moted renewed theoretical interest [1–6] in their con- densed phases. They are characterized by the small mass of their atoms and their weakly attractive interatomic po- tential, which is very accurately determined in ab initio calculations. Already in the seventies, several theoret- ical predictions of the spin-polarized hydrogen systems appeared [7, 8]. In 1976, Stwally and Nosanow [9] under- lined H ↓ as a first candidate for achieving a Bose-Einstein condensate (BEC) state. Their theoretical prediction was experimentally confirmed in 1998 by Fried et al. [10], who succeeded to overcome demanding experimental obsta- cles and reported the formation of a BEC state with H ↓ atoms. INTRODUCTION