  We study the impact of the neutron star binaries' (NSBs) natal kick
distribution on the Galactic r-process enrichment. We model the growth of a
Milky Way type halo based on N-body simulation results and its star formation
history based on multi epoch abundance matching techniques. We consider the
NSBs that merge well beyond the galaxy's effective radius ($>2\times
R_\mathrm{eff}$) do not contribute to Galactic r-process enrichment. Assuming a
power-law delay-time distribution (DTD) function ($\propto t^{-1}$) with
$t_\mathrm{min}=30$ Myr for binaries' coalescence timescales, and an
exponential profile for their natal kick distribution with an average value of
180 km s$^{-1}$, we show that up to $\sim$ 40% of all formed NSBs do not
contribute to r-process enrichment by $z=0$, either because they merge far from
the galaxy at a given redshift (up to $\sim$ 25%) or have not yet merged by
today ($\sim$15%). Our result is largely insensitive to the details of the DTD
function. Assuming a constant coalescence timescale of 100 Myr well
approximates the adopted DTD with 30% of the NSBs not contributing to r-process
enrichment. Our results, although rather dependent on the adopted natal kick
distribution, represent a first step towards estimating the impact of natal
kicks and DTD functions on r-process enrichment of galaxies that would need to
be incorporated in the hydrodynamical simulations.
