  A promising astrophysical site to produce the lighter heavy elements of the
first $r$-process peak ($Z = 38-47$) is the moderately neutron rich ($0.4 < Y_e
< 0.5$) neutrino-driven ejecta of explosive environments, such as core-collapse
supernovae and neutron star mergers, where the weak $r$-process operates. This
nucleosynthesis exhibits uncertainties from the absence of experimental data
from $(\alpha,xn)$ reactions on neutron-rich nuclei, which are currently based
on statistical model estimates. In this work, we report on a new study of the
nuclear reaction impact using a Monte Carlo approach and improved $(\alpha,xn)$
rates based on the Atomki-V2 $\alpha$ Optical Model Potential ($\alpha$OMP). We
compare our results with observations from an up-to-date list of metal-poor
stars with [Fe/H] $<$ -1.5 to find conditions of the neutrino-driven wind where
the lighter heavy elements can be synthesized. We identified a list of
$(\alpha,xn)$ reaction rates that affect key elemental ratios in different
astrophysical conditions. Our study aims on motivating more nuclear physics
experiments on $(\alpha, xn)$ reactions using current and the new generation of
radioactive beam facilities and also more observational studies of metal-poor
stars.
