  We use random matrix models to investigate the ground state energy of
electrons confined to a nanoparticle. Our expression for the energy includes
the charging effect, the single-particle energies, and the residual screened
interactions treated in Hartree-Fock. This model is applicable to chaotic
quantum dots or nanoparticles--in these systems the single-particle statistics
follows random matrix theory at energy scales less than the Thouless energy. We
find the distribution of Coulomb blockade peak spacings first for a large dot
in which the residual interactions can be taken constant: the spacing
fluctuations are of order the mean level separation Delta. Corrections to this
limit are studied using the small parameter 1/(kf L): both the residual
interactions and the effect of the changing confinement on the single-particle
levels produce fluctuations of order Delta/sqrt(kf L). The distributions we
find are significantly more like the experimental results than the simple
constant interaction model.
