Stability of Matter-Antimatter Molecules

We examine the stability of matter-antimatter molecules by reducing the four-body problem into a simpler two-body problem with residual interactions. We find that matter-antimatter molecules with constituents (m1+, m2-, m2bar+, m1bar-) possess bound states if their constituent mass ratio m1/m2 is greater than about 4. This stability condition suggests that the binding of matter-antimatter molecules is a rather common phenomenon. We evaluate the binding energies and eigenstates of matter-antimatter molecules (mu+ e-)-(e+ mu-), (pi+ e-)-(e+ pi-), (K+ e-)-(e+ K-), (p e-)-(e+ pbar), (p mu-)-(mu+ pbar), and (K+ mu-)-(mu+ K-), which satisfy the stability condition. We estimate the molecular annihilation lifetimes in their s states.