Screening properties of a charged Bose condensate: Bound states between equally charged particles

We study the screening properties of three- and two-dimensional charged Bose condensates including many-body effects via a local-field correction. The screened test-charge-test-charge interaction, the test-charge-boson interaction and the boson-boson interaction for equally charged particles are calculated and found to be attractive at intermediate distances due to overscreening effects. Using the variational method and the matrix diagonalization method we determine the energies and wave functions of the ground state and excited states as functions of the Bose condensate density. For densities larger than a critical density no bound states are found. Below the critical density the number and the energy of bound states relative to the continuum increase and then saturate with decreasing Bose condensate density.