  Context. The stars in the Milky Way thin and thick disks can be distinguished
by several properties such as metallicity and kinematics. It is not clear
whether the two populations also differ in the properties of planets orbiting
the stars. In order to study this, a careful analysis of both the chemical
composition and mass detection limits is required for a sufficiently large
sample. Currently, this information is still limited only to large
radial-velocity (RV) programs. Based on the recently published archival
database of the High Accuracy Radial velocity Planet Searcher (HARPS)
spectrograph, we present a first analysis of low-mass (small) planet occurrence
rates in a sample of thin- and thick-disk stars. Aims. We aim to assess the
effects of stellar properties on planet occurrence rates and to obtain first
estimates of planet occurrence rates in the thin and thick disks of the Galaxy.
As a baseline for comparison, we also aim to provide an updated value for the
small close-in planet occurrence rate and compare it to results of previous RV
and transit ($\textit{Kepler}$) works. Methods. We used archival HARPS RV
datasets to calculate detection limits of a sample of stars that were
previously analysed for their elemental abundances. For stars with known
planets we first subtracted the Keplerian orbit. We then used this information
to calculate planet occurrence rates according to a simplified Bayesian model
in different regimes of stellar and planet properties. Results. Our results
suggest that metal-poor stars and more massive stars host fewer low-mass
close-in planets. We find the occurrence rates of these planets in the thin and
thick disks to be comparable. In the iron-poor regimes, we find these
occurrence rates to be significantly larger at the high-$\alpha$ region
(thick-disk stars) as compared with the low-$\alpha$ region (thin-disk stars).
In general, we find the...
