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

Abstract

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.

Comments: 24 pages, 11 figures, references corrected