Bound states in the three-dimensional electron gas with repulsive or attractive test charges: many-body effects

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Abstract
In the low-density regime bound states between negative (repulsive) test charges are obtained when many-body effects (exchange and correlation) are incorporated in the screening function of the three-dimensional electron gas via the local-field correction. The Schrödinger equation is solved in the momentum space by diagonalizing the corresponding matrix. We also perform variational calculations and find good agreement between the two methods. For high electron density ( is the density parameter) no bound states are found. Below a critical density the number and the energy of bound states increase with decreasing electron density. For large the binding energy for the ground state saturates near . We discuss the wave functions of the ground state and of the lowest excited states. We also present results for the effects of exchange and correlation for a positive (attractive) test charge and we discuss results for the ground state and excited states.