  The Casimir effect, a two-body interaction via vacuum fluctuations, is a
fundamental property of quantum systems. In solid state physics it emerges as a
long-range interaction between two impurity atoms via virtual phonons. In the
classical limit for the impurity atoms in $D$ dimensions the interaction is
known to follow the universal power-law $U(r)\sim r^{-D}$. However, for finite
masses of the impurity atoms on a lattice, it was predicted to be $U(r)\sim
r^{-2D-1}$ at large distances. We examine how one power-law can change into
another with increase of the impurity mass and in presence of an external
potential. We provide the exact solution for the system in one-dimension. At
large distances indeed $U(r)\sim r^{-3}$ for finite impurity masses, while for
the infinite impurity masses or in an external potential it crosses over to
$U(r)\sim r^{-1}$ . At short distances the Casimir interaction is not universal
and depends on the impurity mass and the external potential.
