Exploring the nuclear pion dispersion relation through the anomalous coupling of photon to photon and neutral pion

We investigate the possibility of measuring the pion dispersion relation in nuclear matter through the anomalous coupling in the reaction \gamma - \gamma' \pi_0. It is shown that this reaction permits the study of pionic modes for space-like momenta. If the pion is softened in nuclear matter due to mixing with the delta-hole state, significant strength for this reaction is expected to move into the space-like region. Competing background processes are evaluated, and it is concluded that useful insight can be obtained experimentally, but only through a difficult exclusive measurement.