  The propagation of surface plasmons on a quantum plasma half-space in the
absence of any external confinement is investigated. By means of Quantum
Hydrodynamic Model in the electrostatic limit it is found that the equilibrium
density profile is a smooth continuous function which, in the linear regime,
supports multiple non-normal surface modes. Defining a spectrum function and
using a cutting condition, the dispersion relations of these modes and their
relevance for realistic dynamics are computed. It is found that the multiple
surface plasmons present a significant red-shift with respect to the case of
fully bounded quantum plasmas.
