Attraction induced by many-body effects in the quasi-one-dimensional electron gas

We describe screening properties of the quasi-one-dimensional electron gas in quantum wires with cylindrical symmetry. For low density we find an attractive potential for a negative test charge which is strongly enhanced by many-body effects. We describe the dependence of this attraction as a function of the electron density and the wire radius. Bound states (pairing) in the attractive potential are studied with the variational method. For large electron density no bound states are found. Below a critical density and below a critical wire radius the number of bound states increases with decreasing density and decreasing wire radius.