  Using results from the chiral perturbation theory for the s-wave interaction
and the delta-resonance model for the p-wave interaction of pions with
nucleons, we have evaluated the spectral functions of pions in asymmetric
nuclear matter with unequal proton and neutron densities. We find that in hot
dense neutron-rich matter the strength of the spectral function of positively
charged pion at low energies is somewhat larger than that of negatively charged
pion. In a thermal model, this isospin-dependent effect slightly reduces the
ratio of negatively charged to positively charged pions that are produced in
heavy ion collisions induced by radioactive beams. Relevance of our results to
the determination of the nuclear symmetry energy from measured ratio of
negatively to positively charged pions produced in heavy ion collisions is
discussed.
