  A practical method to solve cut-off Coulomb problems of two-cluster systems
in the momentum space is given. When a sharply cut-off Coulomb force with a
cut-off radius $\rho$ is introduced at the level of constituent particles,
two-cluster direct potential of the Coulomb force becomes in general a local
screened Coulomb potential. The asymptotic Hamiltonian yields two types of
asymptotic waves; one is an approximate Coulomb wave with $\rho$ in the
middle-range region, and the other a free (no-Coulomb) wave in the
longest-range region. The constant Wronskians of this Hamiltonian can be
calculated in either region. We can evaluate the Coulomb-modified nuclear phase
shifts for the screened Coulomb problem, using the matching condition proposed
by Vincent and Phatak for the sharply cut-off Coulomb problem. We apply this
method first to an exactly solvable model of the $\alpha \alpha$ scattering
with the Ali-Bodmer potential and confirm that a complete solution is obtained
with a finite $\rho$. The stability of nuclear phase shifts with respect to the
change of $\rho$ in some appropriate range is demonstrated in the $\alpha
\alpha$ resonating-group method (RGM) using the Minnesota three-range force. An
application to the pd elastic scattering is also discussed.
