  A recently developed formulation for a direct treatment of the equations for
two- and three-nucleon bound states as set of coupled equations of scalar
functions depending only on vector momenta is extended to three-nucleon
scattering. Starting from the spin-momentum dependence occurring as scalar
products in two- and three-nucleon forces together with other scalar functions,
we present the Faddeev multiple scattering series in which order by order the
spin-degrees can be treated analytically leading to 3D integrations over scalar
functions depending on momentum vectors only. Such formulation is especially
important in view of awaiting extension of 3N Faddeev calculations to
projectile energies above the pion production threshold and applications of
chiral perturbation theory 3N forces, which are to be most efficiently treated
directly in such three-dimensional formulation without having to expand these
forces into a partial wave basis.
