  We consider the spin 1/2 model coupled to a slowly varying magnetic field in
the presence of a weak damping represented by a Lindblad-form operators. We
show that Berry's geometrical phase remains unaltered by the two dissipation
mechanism considered. Dissipation effects are twofold: a shrinking in the
modulus of the Bloch's vector, which characterizes coherence loss and a time
dependent (dissipation related) precession angle. We show that the line
broadening of the Fourier transformation of the components of magnetization is
only due to the presence of dissipation.
