  If one assumes a translationally invariant motion of the nucleons relative to
the c. m. position in single particle mean fields a correlated single particle
picture of the nuclear wave function emerges. A single particle product ansatz
leads for that Hamiltonian to nonlinear equations for the single particle wave
functions. In contrast to a standard not translationally invariant shell model
picture those single particle s-, p- etc states are coupled. The strength of
the resulting coupling is an open question. The Schroedinger equation for that
Hamiltonian can be solved by few- and many -body techniques, which will allow
to check the validity or non-validity of a single particle product ansatz.
Realistic nuclear wave functions exhibit repulsive 2-body short range
correlations. Therefore a translationally invariant single particle picture --
if useful at all -- can only be expected beyond those ranges. Since exact A = 3
and 4 nucleon ground state wave functions and beyond based on modern nuclear
forces are available, the translationally invariant shell model picture can be
optimized by an adjustment to the exact wave function and its validity or
non-validity decided.
