The quadrupole term of the Lorentz-Lorenz effect in pionic atoms

Two-nucleon contributions to the pion-nucleus p-wave optical potential at zero energy, not included in the standard Lorentz-Lorenz treatment, are considered. Such contributions involve coupling the external pion momenta k and k′, which appear in the optical potential, to form a quadrupole term, and their neglect would appear to be justified only in a strict long-wavelength limit for the pion. The contribution of these quadrupole terms to the observed shifts of pionic atom energy levels is evaluated for ²⁷Al and ⁴⁰Ca, under the assumption of short-range repulsive nucleon-nucleon correlations, and found to constitute roughly between 10% and 15% of the standard Lorentz-Lorenz contribution, or 5% to 7% of the observed shifts.