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We use random matrix models to investigate the ground state energy ofelectrons confined to a nanoparticle. Our expression for the energy includesthe charging effect, the single-particle energies, and the residual screenedinteractions treated in Hartree-Fock. This model is applicable to chaoticquantum dots or nanoparticles--in these systems the single-particle statisticsfollows random matrix theory at energy scales less than the Thouless energy. Wefind the distribution of Coulomb blockade peak spacings first for a large dotin which the residual interactions can be taken constant: the spacingfluctuations are of order the mean level separation Delta. Corrections to thislimit are studied using the small parameter 1/(kf L): both the residualinteractions and the effect of the changing confinement on the single-particlelevels produce fluctuations of order Delta/sqrt(kf L). The distributions wefind are significantly more like the experimental results than the simpleconstant interaction model.Comment: 17 pages, 4 figures, submitted to Phys. Rev.

Interactions in chaotic nanoparticles: Fluctuations in Coulomb blockade peak spacings