  We present a microscopic model for Na clusters embedded in raregas matrices.
The valence electrons of the Na cluster are described by time-dependent
density-functional theory at the level of the local-density approximation
(LDA). Particular attention is paid to the semi-classical picture in terms of
Vlasov-LDA. The Na ions and Argon atoms are handled as classical particles
whereby the Ar atoms carry two degrees of freedom, position and dipole
polarization. The interaction between Na ions and electrons is mediated through
local pseudo-potentials. The coupling to the Ar atoms is described by
(long-range) polarization potentials and (short-range) repulsive cores. The
ingredients are taken from elsewhere developed standards. A final fine-tuning
is performed using the NaAr molecule as benchmark. The model is then applied to
embedded systems Na8ArN. By close comparison with quantum-mechanical results,
we explore the capability of the Vlasov-LDA to describe such embedded clusters.
We show that one can obtain a reasonable description by appropriate adjustments
in the fine-tuning phase of the model.
