A method to calculate the correlation energy of finite systems will be presented. The method uses the single particle wavefunctions of the confined system to obtain the total energy from a perturbative expansion, summing over all the ladder terms up to infinite order, like in the conventional Brueckner-Hartree-Fock theory for homogeneous systems. This method is particularly useful for finite systems where correlations are important and no functionals for the correlation energy are available, and when the number of particles is too large to make exact calculations like Configuration Interaction or diffusion Monte Carlo. We have chosen as a case of study self assembled quantum dots. The strong confinement of these systems makes the Local Densit Approximation of the Density Functional Theory a too raw approximation. We have found that the energies obtained converge to the exact ones as the confinement increases, so for such systems the BHF method gives almost all of the correlation energy.
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