  We study the interaction of two localized impurities in a repulsive
one-dimensional Fermi liquid via bosonization. In a previous paper [Phys. Rev.
A 72, 023616 (2005)], it was shown that at distances much larger than the
interparticle spacing the impurities interact through a Casimir-type force
mediated by the zero sound phonons of the underlying quantum liquid. Here we
extend these results and show that the strength and sign of this Casimir
interaction depend sensitively on the impurities separation. These oscillations
in the Casimir interaction have the same period as Friedel oscillations. Their
maxima correspond to tunneling resonances tuned by the impurities separation.
