  There is a Casimir force between two metal plates. It is generally believed
that the Casimir force is mediated by virtual photons in a vacuum, which
correspond to the massless intermediate particles used in our theoretical
calculations. Studies have shown that not only virtual photons in a vacuum, but
also other virtual particles that have masses. The lightest chargeless virtual
particles with mass are positronium (1 MeV) and $\pi^{0}$ mesons (135 MeV).
This paper primarily focuses on studying the corrections to the Casimir force
caused by positronium and $\pi^{0}$ mesons. Especially when the distance
between the two plates is on the order of $1/m_{positronium}$ , the
contribution of positronium becomes significant, and on the order of
$1/m_{\pi^0}$ , the contribution of the $\pi^{0}$ meson becomes significant. We
hope that the calculation results can reduce the error in the theoretical
calculation of the Casimir force when the distance between the plates is large
and provide significant corrections when the distance is small.
