The frequency- and momentum-dependent dielectric function ϵ(q,ω) as well as the energy loss function Im[-ϵ−1(q,ω)\protect{]} are calculated for intermetallic superconductor MgB2
by using two {\it ab initio} methods: the plane-wave pseudopotential method and
the tight-binding version of the LMTO method. We find two plasmon modes
dispersing at energies ∼2-8 eV and ∼18-22 eV. The high energy
plasmon results from a free electron like plasmon mode while the low energy
collective excitation has its origin in a peculiar character of the band
structure. Both plasmon modes demonstrate clearly anisotropic behaviour of both
the peak position and the peak width. In particular, the low energy collective
excitation has practically zero width in the direction perpendicular to boron
layers and broadens in other directions.Comment: 3 pages with 10 postscript figures. Submitted to PRB on May 14 200