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With technological advances in the preparation and in the fabrication of microstructures it is now possible to confine electrons and atoms in restricted regions. The principal exem- ples of experimental progress in this area are semiconductor quantum dots (1) and laser trapping of cold atoms (2). Semi- conductor quantum dots constitute a quasi ideal system for the study of the physical properties of a two-dimensional system of strongly interacting electrons, laterally confined by an ex- ternal potential. From the theoretical point of view, computer simulation (3, 4) has achieved the greatest success inusmuch as approximate analytical methods (5) have encountered difi- culties, since both the many body effects and the individual behavior of each electron have a crucial role in these systems. The major difficulty in the theoretical methods is due to the fact that the electrons in the quantum dots are confined in a very small area and hence they cannot be treated as part of a continuous distribution of charges. These systems, consisit- ing of a finite number of electrons confined to a small region in semiconductor structures are known as quantum dots and more recently as artificial atoms. In this paper we report an application of Variational Monte Carlo and Diffusion Monte Carlo method (VMC-DMC) to calculate the ground state energy of a two-dimensional system used as a model for quantum dots. The simulations are per- formed with a confinement frequency~w = 0:28 Hartree (H). We consider a system consisting of a small number of spinless charged particles interacting through a repulsive Coulomb po- tential, moving in two dimensions and an external parabolic potential well. The Hamiltonian is given by e = m ⁄ = 1, the energy and length units are Ry ⁄ = m ⁄ e 2 =2~ 2 (4pee0) 2 and a ⁄ B =~ 2 (4pee0)=m ⁄ e 2 (6). The average density n0 of electrons in the dot may be rep- resented by a parameter rs defined by n0 = N=pr 2 = 1=pr 2 s .

Ground state energy of charged particles clusters by quantum Monte Carlo method