  Analytical r-mode solutions are investigated within the linearized theory in
the case of a slowly rotating, Newtonian, barotropic, non-magnetized,
perfect-fluid star in which the gravitational radiation (GR) reaction force is
present. For the GR reaction term we use the 3.5 post-Newtonian order expansion
of the GR force, in order to include the contribution of the current quadrupole
moment. We find the explicit expression for the r-mode velocity perturbations
and we conclude that they are sinusoidal with the same frequency as the
well-known GR force-free linear r-mode solution, and that the GR force drives
the r-modes unstable with a growth timescale that agrees with the expression
first found by Lindblom, Owen and Morsink. We also show that the amplitude of
these velocity perturbations is corrected, relatively to the GR force-free
case, by a term of order W^6, where W is the angular velocity of the star.
