On the ground state of the two- and three-dimensional excitonic molecules

Abstract

The first calculation of the ground state of the two-dimensional excitonic molecule has been performed. The authors have used the transformation of the coordinates of four bodies with equal masses which excludes the motion of the centre of mass, and allows the isolation of one weakly interacting quasiparticle and a core of two strongly interacting quasiparticles in an effective three-body problem. Since the core problem is exactly solved and the form of the variational wavefunction of the system takes into account the essential part of the exchange interactions, satisfactory values are obtained for the binding energy of the two- and three-dimensional biexcitons even when using rather simple trial functions. The binding energy is E2=0.12 au for a two-dimensional biexciton and E3=0.013 au for a three-dimensional biexciton.