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

Abstract:

The effects of the restoration of Galilei invariance on many-nucleon states with one nucleon in the continuum are investigated within a simple knock-out model for quasi-elastic electron scattering using a Woods-Saxon partial-wave expansion for the continuum nucleon and simple Slater determinants for the bound states. For the total longitudinal response functions of the three nuclei ⁴He, ¹⁶O and ⁴⁰Ca, as seen in inclusive experiments, a rather good agreement of the Galilei-invariant prescription and the usual spectral-function approximation is obtained, provided that in the latter the momentum transfer is quenched by a factor (A - 1)/A, and furthermore relative motion wave functions are used for the various hole states. The agreement is worse if exclusive scattering is considered. Then the above modifications of the spectral-function approximation still yield the right positions and shapes for the partial longitudinal response functions of the various residual hole states. However, as expected from the different spectroscopic factors obtained for the Galilei invariant with respect to the normal approximation in the first of the present series of papers, for holes out of the last occupied shell the corrected spectral-function approach underestimates the Galilei-invariant strengths, while for holes from the lower shells a considerable overestimation of the strengths is observed.