  We present a rigorous study of the classical scattering for anytwo-body
inter-particle potential of the form $v(r)=g/r^\gamma$,
with$\gamma\textgreater{}0$, for repulsive ($g\textgreater{}0$) and attractive
($g\textless{}0$)interactions. We give a derivation of the complete power
series of thedeflection angle in terms of the impact factor for the weak
scatteringregime (large impact factors) as well as the asymptotic
expressionsfor the hard scattering regime (small impact factors). We see a
verydifferent qualitative and quantitative behavior depending whether
theinteraction is repulsive or attractive. In the latter case, thefamilies of
trajectories depend also strongly on the value of$\gamma$. We also study
carefully the modifications of the resultswhen a regularization is introduced
in the potential at small scales.We check and illustrate all the results with
the exact integration ofthe equations of motion.
