A superprocess with a disappearing self-interaction

We start with a system of independent branching Brownian motions which, properly organized and normalized, generate a super Brownian motion in the high density limit. We introduce a weak interaction between the particles, that affects the diffusion but not the branching. The interaction is chosen in such a way that the infinite density limit is absolutely continuous with respect to the noninteracting system. We find that, despite the fact that the interaction mechanism never completely disappears, the limiting superprocesses are identical. We study what actually happens to the interaction mechanism, or ''ghost-process.''