**16**, 475-487 (2003)

DOI: 10.1140/epja/i2001-10273-1

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

##### Part IV: Simple continuum states

**K.W. Schmid**

Institut für Theoretische Physik der Universität Tübingen, Auf der Morgenstelle 14, D-72076 Tübingen, Germany karl-wilhelm.schmid@uni-tuebingen.de

(Received: 20 February 2001 / Published online: 25 March 2003)

** 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
^{4}He,
^{16}O and
^{40}Ca, 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.

**PACS**

21.60.-n - Nuclear-structure models and methods.

**©**

*Società Italiana di Fisica, Springer-Verlag 2003*