  Accurate mass-loss rates and terminal velocities from massive stars winds are
essential to obtain synthetic spectra from radiative transfer calculations and
to determine the evolutionary path of massive stars. From a theoretical point
of view, analytical expressions for the wind parameters and velocity profile
would have many advantages over numerical calculations that solve the complex
non-linear set of hydrodynamic equations. In a previous work, we obtained an
analytical description for the fast wind regime. Now, we propose an approximate
expression for the line-force in terms of new parameters and obtain a velocity
profile closed-form solution (in terms of the Lambert $W$ function) for the
$\delta$-slow regime. Using this analytical velocity profile, we were able to
obtain the mass-loss rates based on the m-CAK theory. Moreover, we established
a relation between this new set of line-force parameters with the known stellar
and m-CAK line-force parameters. To this purpose, we calculated a grid of
numerical hydrodynamical models and performed a multivariate multiple
regression. The numerical and our descriptions lead to good agreement between
their values.
