  We present a method for calculating scattering phase shifts which utilizes
continuum-discretized states obtained in a bound-state type calculation. The
wrong asymptotic behavior of the discretized state is remedied by means of the
Green's function formalism. Test examples confirm the accuracy of the method.
The $\alpha+n$ scattering is described using realistic nucleon-nucleon
potentials. The $3/2^-$ and $1/2^-$ phase shifts obtained in a single-channel
calculation are too small in comparison with experiment. The $1/2^+$ phase
shifts are in reasonable agreement with experiment, and gain contributions both
from the tensor and central components of the nucleon-nucleon potential.
