The stability of four-body systems ${(m}_a^{+}{m}_b^{+}{m}_1^{-}{m}_2^{-})$ in three (3D) and two dimensions (2D) is discussed using accurate numerical results obtained by means of diffusion Monte Carlo calculations. In 3D, we extend our proof of the stability for the class of systems ${(m}_a^{+}{m}_b^{+}{m}_1^{-}{m}_1^{-})$, showing that they are stable against the dissociation in ${(m}_a^{+}{m}_1^{-})$ and ${(m}_b^{+}{m}_1^{-})$ for any value of the mass ratio $m_a^{+}{/m}_b^{+}$. In 2D, using the ground-state energy of the dipositronium, it is possible to prove that the stability of four-body systems follows the same scenario. We also give upper and lower bounds to the binding energies for the class ${(M}^{+}{M}^{+}{m}^{-}{m}^{-})$ in 2D, useful to discuss the relative stability of biexciton molecules in semiconductors.

• Received 30 January 1998

DOI:https://doi.org/10.1103/PhysRevA.57.4956