  We present a complete classification of the electron-electron interaction in
chaotic quantum dots based on expansion in inverse powers of $1/M$, the number
of the electron states in the Thouless window, $M \simeq k_F R$. This
classification is quite universal and extends and enlarges the universal non
interacting RMT statistical ensembles. We show that existing Coulomb blockade
peak spacing data for $B=0$ and $B\ne 0$ is described quite accurately by the
interacting GSE and by its extension to $B\ne 0$. The bimodal structure
existing in the interacting GUE case is completely washed out by the combined
effect of the spin orbit, pairing and higher order residual interactions.
