Center-of-Mass Correction in a Relativistic Hartree Approximation

It is a well known fact that mean-field approximation to the nuclear many-body problem introduces center-of-mass (CM) spurious components in the solutions. In particular, Hartree-Fock self-consistent mean-fields obtained using realistic forces in a non-relativistic approach have been considered, and the corresponding CM corrections have been calculated for the energy [1, 2] as well as for other observables [3] in a fully microscopic way. For relativistic theories, as the widely used relativistic mean field theory [4] in the Hartree or Hartree-Fock approximations, the correction for the energy is usually estimated using the harmonic oscillator basis [5]. In this case, the treatment for the CM motion becomes trivial, though generally not consistent with the nuclear wavefunction obtained variationally.