Structure of eta' mesonic nuclei in a relativistic mean field theory

The structure and the energy spectrum of the $\eta^{\prime}$ mesonic nuclei are investigated in a relativistic mean field theory. One expects a substantial attraction for the $\eta^{\prime}$ meson in finite nuclei due to the partial restoration of chiral symmetry in the nuclear medium. Such a hadronic scale interaction for the $\eta^{\prime}$ mesonic nuclei may provide modification of the nuclear structure. The relativistic mean field theory is a self-contained model for finite nuclei which provides the saturation property within the model, and is good to investigate the structure change of the nucleus induced by the $\eta^{\prime}$ meson. Using the local density approximation for the mean fields, we solve the equations of motion for the nucleons and the $\eta^{\prime}$ meson self-consistently, and obtain the nuclear density distribution and the $\eta^{\prime}$ energy spectrum for the $\eta^{\prime}$ mesonic nuclei. We take $^{12}$C, $^{16}$O and $^{40}$Ca for the target nuclei. We find several bound states of the $\eta^{\prime}$ meson for these nuclei thanks to the attraction for $\eta^{\prime}$ in nuclei. We also find a sufficient change of the nuclear structure especially for the $1s$ bound state of $\eta^{\prime}$. This implies that the production of the $1s$ bound state in nuclear reaction may be suppressed.