Neutron-antineutron oscillations in nuclei

Abstract

We present calculations of the neutron-antineutron ($n-\overline{n}$) annihilation lifetime $T$ in deuterium, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$ in terms of the free-space oscillation time $T_{n\overline{n}}$. The coupled Schrödinger equations for the $n$ and $\overline{n}$ 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 $\overline{n}$-nucleus optical potential obtained from fits to $\overline{p}$-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 ${\tau }_{n\overline{n}}$: $T>\mathrm{}{10}^{30} or {10}^{31}$ yr leads to ${\tau }_{n\overline{n}}>(1.5-2)\mathrm{}\times {10}^7 or \mathrm{}(5-6)\mathrm{}\times {10}^7$ sec, respectively.