n uc l - th / 9 70 80 04 v 1 5 A ug 1 99 7 UGI - 97 - 09 The Spectral Function of the Rho Meson in Nuclear Matter ∗

We calculate the modification of a rho meson in nuclear matter through its coupling to resonance-hole states. Starting from a recently proposed model, we include all four star resonances up to 1.9 GeV. In contrast to previous works, we include not only resonances that couple to the rho in a relative p-wave, but also those that couple to an s-wave state. In addition, we solve the equation for the rho spectral function self-consistently. We find that s-wave resonances affect the in medium spectral function of the rho strongly. In the transverse channel the rho meson is, especially at non zero momentum, completely washed out and can in the presence of nuclear matter no longer be viewed as a resonant excitation of the vacuum. Instead, our model shows a continuum of possible excitations with the quantum numbers of a transversely polarized rho. In the longitudinal channel, however, the rho retains its resonant character in our calculation. As a consequence of the self-consistent treatment we also find a strong enhancement of the widths of the included nucleon resonances in medium.