  In a previous paper virtual Compton scattering off the nucleon has been
investigated in the one-loop approximation of the linear sigma model in order
to determine the 3 scalar generalized polarizabilities. We have now extended
this work and calculated the 7 vector polarizabilities showing up in the
spin-dependent amplitude of virtual Compton scattering. The results fulfill 3
model-independent constraints recently derived. Compared to the constituent
quark model there exist enormous differences for some of the vector
polarizabilities. At vanishing three-momentum of the virtual photon, the
analytical results of the sigma model and of chiral perturbation theory can be
related. The influence of the $\pi^{0}$ exchange in the $t$ channel has been
discussed in some detail. Besides, the vector polarizabilities determine 2
linear combinations of the third order spin-polarizabilities appearing in real
Compton scattering.
