  We calculated the populations of core-helium-burning (CHeB) stars and found
that the secondary red clump (SRC) stars can form an SRC peak in the
distributions of the frequency of maximum seismic amplitude ($\nu_{max}$) and
mean large-frequency separation ($\Delta\nu$) of CHeB stars when metallicity $Z
\geq$ 0.02. The $\nu_{max}$ and $\Delta\nu$ of CHeB stars are dependent not
only on He core mass but on H-shell burning. The SRC peak is composed of the
CHeB stars with mass roughly between the critical mass M_{Hef} and M_{Hef}+0.2
while He core mass is between about 0.33 and 0.36 M_{sun}. The location of the
SRC peak can be affected by the mixing-length parameter $\alpha$, metallicity
$Z$, and overshooting parameter $\delta_{ov}$. A decrease in $\alpha$ or
increase in $Z$ or $\delta_{ov}$ leads to a movement of the SRC peak towards a
lower frequency. However, the change in $Z$ and $\alpha$ only slightly affects
the value of M_{Hef} but the variation in $\delta_{ov}$ can significantly
affects the value of M_{Hef}. Thus the SRC peak might aid in determining the
value of M_{Hef} and calibrating $\delta_{ov}$. In addition, the effects of
convective acceleration of SRC stars and the $\nu_{max}$ of `semi-degenerate'
stars decreasing with mass result in the appearance of a shoulder between about
40 and 50 $\mu$hz in the \dnu{} distribution. However, the convective
acceleration of stars with M < M_{Hef} leads to the deficit in the $\nu_{max}$
distribution between about 9 and 20 $\mu$hz{}. Moreover, the value of the
parameter $b$ of the relation between $\nu_{max}$ and $\Delta\nu$ for the
populations with M > M_{Hef} is obviously larger than that for the populations
with $M <$ \dmhef{}.

Solar and Stellar Astrophysics