  Modeling of the stars in the red clump (RC) is challenging, due to the
uncertainties associated with the physical processes happening in their core
and during the helium flash. By probing the internal stellar structure,
asteroseismology allows us to constrain the core properties of RC stars and
eventually improve our understanding of this evolutionary phase. In this work,
we aim to quantify the impact on the seismic properties of the RC stars of the
two main core modeling uncertainties: core boundary mixing, and helium burning
nuclear reaction rates. Using the MESA stellar evolution code, we compute
models with different core boundary mixing as well as different $3\alpha$ and
carbon alpha (C-alpha) nuclear reaction rates. We investigate the impact of
those parameters on the period spacing $\Delta \Pi$, which is a probe of the
region around the core. We find that different core boundary mixing schemes
yield significantly different period spacings, with differences of 30s between
the maximal $\Delta \Pi$ value computed with semiconvection and maximal
overshoot. We show that increasing the rate of the C-alpha reaction lengthens
the core helium burning phase, which extends the range of $\Delta \Pi$ covered
by the models during their evolution. This results in a difference of 10s
between the models computed with a nominal rate and a rate multiplied by 2,
which is larger than the observational uncertainties. The effect of changing
the 3$\alpha$ reaction rate is comparatively small. In conclusion, the core
boundary mixing is the main source of uncertainty regarding the seismic
modeling of RC stars. Moreover, the effect of the C-alpha reaction rate is
non-negligible, even if difficult to disentangle from the effect of the mixing.
Such degeneracy could be raised in the future, thanks to new seismic data from
the PLATO mission and theoretical constraints from numerical simulations.
