  The gravitational radiation generated by a particle in a close unbounded
orbit around a neutron star is computed as a means to study the importance of
the $w$ modes of the neutron star. For simplicity, attention is restricted to
odd parity (``axial'') modes which do not couple to the neutron star's fluid
modes. We find that for realistic neutron star models, particles in unbounded
orbits only weakly excite the $w$ modes; we conjecture that this is also the
case for astrophysically interesting sources of neutron star perturbations. We
also find that for cases in which there is significant excitation of quadrupole
$w$ modes, there is comparable excitation of higher multipole modes.
