Center-of-mass corrections in relativistic mean field descriptions of light nuclei

The non-linear sigma-omega model is used to describe light nuclei, such as the alpha particle, in a relativistic mean field calculation. It turns out that, in systems with few particles, the spurious center-of-mass energy is relatively large. In our calculation we remove that energy by means of the Peierls-Yoccoz projection method, assuming a coherent state description for the mesons. We compare this correction to the total energy with the usual harmonic oscillator correction to the COM motion, showing that the former is not appropriate for light nuclei. Finally, we also compare the Hartree and Hartree-Fock approximations, stressing the relevance of the exchange term in few body systems.