We use the Peierls-Yoccoz projection method to study the motion of a relativistic system of nucleons interacting with sigma and omega mesons, generalizing a method developed for the alpha particle. The nuclear system is described in a mean-field Hartree approach, including explicitly the meson contribution. The formalism is applied to ${}^4\mathrm{He}$, ${}^{16}\mathrm{O},$ and ${}^{40}\mathrm{Ca}$. The center-of-mass correction makes the system too much bounded. It turns out that a new set of model parameters is needed when the center-of-mass motion is consistently treated with respect to the traditional approaches. An appropriate refitting of the model brings the radii and binding energies to reasonable values for the oxygen and calcium.

• Received 20 December 2006

DOI:https://doi.org/10.1103/PhysRevC.75.054324