Short range correlations in the pion s-wave self-energy of pionic atoms

We evaluate the contribution of second order terms to the pion-nucleus s-wave optical potential of pionic atoms generated by short range nuclear correlation. The corrections are sizeable because they involve the isoscalar s-wave $\pi N$ amplitude for half off-shell situations where the amplitude is considerably larger than the on-shell one. In addition, the s-wave optical potential is reanalyzed by looking at all the different conventional contributions together lowest order, Pauli corrected rescattering term, second order absorptive effects, terms from the interaction of pions with the virtual pion cloud (chiral corrections) and correlation effects. Different off-shell extrapolations for the $\pi N$ amplitude are used and it is found that, although some individual terms are sensitive to the extrapolation, the sum of them is rather insensitive. The results are compared with empirical values from best fits to the data and are found to be compatible, within theoretical and empirical uncertainties. The results do not rule out further contributions but they put stringent constraints on their strength.