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Plasmons in strong superconductors

We present a study of the possible plasmon excitations that can occur in systems where strong superconductivity is present. In these systems the plasmon energy is comparable to, or smaller than the pairing gap. As a prototype of these systems we consider the proton component of neutron star matter just below the crust when electron screening is not taken into account. For the realistic case we consider in detail the different aspects of the elementary excitations when the proton, electron components are considered within the Random Phase Approximation generalized to the superfluid case, while the influence of the neutron component is considered only at qualitative level. Electron screening plays a major role in modifying the proton spectrum and spectral function. At the same time the electron plasmon is strongly modified and damped by the indirect coupling with the superfluid proton component, even at moderately low values of the gap. The excitation spectrum shows the interplay of the different components and their relevance for each excitation mode. The results are relevant for neutrino physics and thermodynamical processes in neutron stars. If electron screening is neglected, the spectral properties of the proton component show some resemblance with the physical situation in high T$_c$ superconductors, and we briefly discuss similarities and differences in this connection. In a general prospect, the results of the study emphasize the role of Coulomb interaction in strong superconductors.