N N bar,Delta bar N, Delta N bar excitation for the pion propagator in nuclear matter

The particle-hole and Delta -hole excitations are well-known elementary excitation modes for the pion propagator in nuclear matter. But, the excitation also involves antiparticles, namely, nucleon-antinucleon, anti-Delta-nucleon and Delta-antinucleon excitations. These are important for high-energy momentum as well, and have not been studied before, to our knowledge. In this paper, we give both the formulas and the numerical calculations for the real and the imaginary parts of these excitations.