  We study the gravitational deflection of relativistic massive particles by
Janis-Newman-Winicour (JNW) spacetimes (also known as a rotating source with a
surface-like naked singularity), and a rotating Kerr-like wormholes. Based on
the recent article [K. Jusufi, Phys. Rev. D 98, 064017 (2018)], we extend some
of these results by exploring the effects of naked singularity and Kerr-like
objects on the deflection of particles. We start by introducing coordinate
transformation leading to an isotropic line element which gives the refraction
index of light for the corresponding optical medias. On the other hand, the
refraction index for massive particles is found by considering those particles
as a de Broglie wave packets. To this end, we apply the Gauss-Bonnet theorem to
the isotropic optical metrics to find the deflection angles. Our analysis shows
that, in the case of the JNW spacetime the deflection angle is affected by the
parameter $0<\gamma<1$, similarly, we find that the deformation parameter
$\lambda$ affects the deflection angle in the case of Kerr-like wormholes. In
addition to that, we presented a detailed analysis of the deflection angle by
means of the Hamilton-Jacobi equation that lead to the same results. As a
special case of our results the deflection angle of light is recovered.
Finally, we point out that the deflection of particles by Kerr-like wormholes
is stronger compared to JNW spacetime, in particular this difference can be
used to shed some light from observational point of view in order to
distinguish the two spacetimes.
