  We study matrix element fluctuations of the two-body screened Coulomb
interaction and of the one-body surface charge potential in ballistic quantum
dots. For chaotic dots, we use a normalized random wave model to obtain
analytic expansions for matrix element variances and covariances in the limit
of large kL (where k is the Fermi wave number and L the linear size of the
dot). These leading-order analytical results are compared with exact numerical
results. Both two-body and one-body matrix elements are shown to follow
strongly non-Gaussian distributions, despite the Gaussian random nature of the
single-electron wave functions.
