  We consider a helical system of fermions with a generic spin (or pseudospin)
orbit coupling. Using the equation of motion approach for the single-particle
distribution functions, and a mean-field decoupling of the higher order
distribution functions, we find a closed form for the charge and spin density
fluctuations in terms of the charge and spin density linear response functions.
Approximating the nonlocal exchange term with a Hubbard-like local-field
factor, we obtain coupled spin and charge density response matrix beyond the
random phase approximation, whose poles give the dispersion of four collective
spin-charge modes. We apply our generic technique to the well-explored
two-dimensional system with Rashba spin-orbit coupling and illustrate how it
gives results for the collective modes, Drude weight, and spin-Hall
conductivity which are in very good agreement with the results obtained from
other more sophisticated approaches.
