In this paper the propagation of an electrostatic surface wave at the interface between a vacuum and quantum plasma through a Brinkman porous medium is studied by considering exchange–correlation effects. A general analytical expression for dispersion relation is derived using the linearized quantum hydrodynamic model in conjunction with Poisson’s equation in the presence of a static and constant magnetic field. The growth and instability rates of electrostatic surface waves are obtained and separated. Numerical values are used to summarize and analyze the normalized dispersion relations for overcritical dense plasma condition in different cases. The results show that the behavior of surface plasmon waves can be significantly modified by the exchange–correlation effects which have different influences on the system stability. It is shown that the exchange–correlation effects caused the frequency of such waves to down-shift. It is found that the down-shift of the real part of frequency Re(X) by the exchange–correlation effect may increase by either increasing the plasmonic coupling H or increasing the porosity effects. In addition, it is shown that by increasing the magnetic field strength the group velocity is increased. Although the instability of the surface wave is decreased by increasing the plasmonic coupling H, it is increased by increasing the porosity effects (m). The obtained results can help us in the physical understanding of the surface magnetized quantum wave on a semi-bounded quantum plasma through a porous media.
