Some considerations on the restoration of Galilei invariance in the nuclear many-body problem

The effects of the restoration of Galilei invariance in the nuclear many-body problem on the electromagnetic properties of simple bound states are investigated. For this purpose the form factors for elastic electron scattering from the oscillator ground states of ⁴He, ¹⁶O and ⁴⁰Ca as well as those for elastic and inelastic electron scattering between various one-hole states with respect to these reference configurations are computed with and without projection into the center-of-momentum rest frame. It is demonstrated that, in some cases, the full restoration of Galilei invariance produces results which are considerably different from those obtained with the usual approximate way to treat the center-of-mass motion. The same holds for the mathematical Coulomb sum rules and their first and second moments obtained for the above-mentioned nuclei. Received: 21 February 2001 / Accepted: 20 December 2001