Positron surface states bound by the Newns-Barton potential

The binding energies and eigenfunctions of the surface states of positrons outside materials with negative positron affinity are considered. When the material is represented by a continuum hydrodynamic model with finite dispersion the potential takes the Newns-Barton form. The characteristic material parameter is B = ω_p/β where ω_p is the bulk plasma frequency and $\text{β ? √}\text{3}\text{5}\text{x}$ the Fermi velocity. For aluminium B ? 0.6a^?1 (a is the Bohr radius) and the Newns-Barton potential yields a ground state binding energy E⁽¹⁾ ? 0.46 ev - considerably smaller than the binding energy of the pure image (or non dispersive) potential for which E⁽¹⁾ ? 0.85 ev.