Stability and universality of small quantum clusters and adsorption effects of graphene and cesium on ground state of small helium clusters

Korištenjem kvantnih Monte Carlo metoda istraženi su energija i strukturna svojstva osnovnog stanja odabranih malih čistih i miješanih helijevih klastera, koje karakterizira mala masa i slabi privlačni dio potencijala interakcije među česticama. U slobodnom je prostoru po prvi put određena stabilnost i struktura klastera 4^He_N(T↓)M (N ≤8, M ≤ 4), te je utvrđeno da je 4^He_2T↓kvantno halo stanje. Proučavanjem realističnih molekulskih sustava koji sadrže He ili T↓te modela kvadratne jame ustanovljene su optimalne skalirane varijable energije i širine te univerzalna linija na kojoj se nalaze kvantni halo dimeri i trimeri. Uočeno je i razdvajanje linija koje opisuju Borromeanova i tango stanja. Nadalje je istražen utjecaj prostornih ograničenja na energije samovezanja i strukturna svojstva klastera 4^He_n (n ≤ 40), u slučaju adsorpcije na slabo privlačnom ceziju te jako privlačnom grafenu. U slučaju grafena konstruirani su različiti modeli interakcije kako bi se procijenili utjecaji korugacija i McLachlanove interakcije koji su se pokazali značajnima. Uključivanje McLachlanove interakcije dovodi do značajnog slabljenja samovezanja. Anizotropnost malo jača samovezanje, ali ipak utječe na procjenu je li energijski preferirana „tekuća” ili „kruta” struktura malih klastera 4Hen adsorbiranih na grafenu. Na ceziju su dodatno istraženi i klasteri 4^He_n 3^He što je omogućilo promatranje pojavljivanja rubnih stanja 3^He, lokaliziranih duž kontaktne linije 4^He i površine cezija, a koja se već naziru za mali n = 3.In this work, the ground state energy and structural properties, of selected small pure and mixed helium clusters, were studied using quantum Monte Carlo methods. They are characterized by the small mass and the weak attractive part of the interaction potential. In free space, for the first time, the binding energy and structural properties of clusters 4^He_N(T↓)M (N ≤ 8,M ≤ 4) were determined. Only 4^HeT↓and 4^He(T↓)_2 seemed to be unstable, while 4^He_2T↓was confirmed as example of quantum halo state. Ground state of other weakly bound dimers and trimers with a radius extending well into the classically forbidden region was explored as well, with the goal to test the predicted universality of quantum halo states. The focus of the study were molecules consisting of T↓, D↓, 3^He, 4^He and alkali atoms, where interaction between particles is much better known than in the case of nuclei, which are traditional examples of quantum halos. The study of realistic systems was supplemented by model calculations in order to analyze how low-energy properties depend on the interaction potential. The use of variational and diffusion Monte Carlo methods enabled very precise calculation of both size and binding energy of the trimers. More convenient scaling variables of binding energy and size were found, so that in the quantum halo regime, all clusters follow almost the same universal line. In addition, it was found that Borromean states separate from tango trimers when the scaled binding energy weakens sufficiently. Furthermore, the effect of reduced dimensionality on self-binding energies and structural properties of clusters 4^He_n (n ≤ 40), in case of adsorption on weakly attractive cesium and strongly attractive graphene, were studied. In the case of graphene, different models of interaction were constructed to test the influence of corrugations and the McLachlan interaction which were shown to be significant. Self-binding energy is significantly lowered, when McLachlan interaction is included. Anisotropy effect slightly strengthen self-binding, but nevertheless affect the assessment whether energy preferred is liquidlike or solidlike structure of small clusters 4^He_n adsorbed on the graphene. Additionally, clusters 4^He_n 3^He adsorbed on cesium were studied to observe the emergence of the edge states of 3^He atom, localized along the contact line of 4^He with a cesium surface, which can be noticed even for such small number of atoms 4^He as n = 3