Neutron-antineutron oscillations in nuclei

We present calculations of the neutron-antineutron (n-n̄) annihilation lifetime T in deuterium, ¹⁶O, and ⁵⁶Fe in terms of the free-space oscillation time Tnn̄. The coupled Schr\"odinger equations for the n and n̄ wave functions in a nucleus are solved numerically, using a realistic shell-model potential which fits the empirical binding energies of the neutron orbits, and a complex n̄-nucleus optical potential obtained from fits to p̄-atom level shifts. Most previous estimates of T in nuclei, which exhibit large variations, are found to be quite inaccurate. When the nuclear-physics aspects of the problem are handled properly (in particular, the finite neutron binding, the nuclear radius, and the surface diffuseness), the results are found to be rather stable with respect to allowable changes in the parameters of the nuclear model. We conclude that experimental limits on T in nuclei can be used to give reasonably precise constraints on τnn̄: T>10³⁰ or 10³¹ yr leads to τnn̄>(1.5-2)×10⁷ or (5-6)×10⁷ sec, respectively.