Bound states of a negative test charge due to many-body effects in the two-dimensional electron gas

Bound states of a negative test electron in the low-density regime of the two-dimensional electron gas are obtained when many-body effects (exchange and correlation) are incorporated in the screening function via the local-field correction. Using the Green’s-function method and a variational method we determine the energies and the wave functions of the ground state and the excited states as functions of the electron density. For high electron density no bound state is found. Below a critical density the number and the energy of bound states increase with decreasing electron density. The ground state is described by the wave function ${\mathrm{\psi }}_{2\mathit{s}}$∝r exp(-r/α).