In summary, we have traced the source of the troublesome Coulomb finite size errors in quantum many-body calculations for periodic simulation cells to the use of the Ewald interaction, which gives a spurious cell-size-dependent contribution to the electron-electron interaction energy. A new model electron-electron interaction is introduced, which eliminates this problem, based on the idea that the exchange-correlation hole is short ranged. VMC calculations with up to 1000 electrons show that the new interaction gives much smaller finite size effects than the Ewald interaction. Preliminary DMC calculations suggest the new interaction is equally successful in the more sophisticated DMC formalism. This development will allow for significantly more accurate supercell calculations of correlated electron systems.