  We study on the spectrum and short-distance two-body force of holographic
baryons by the matrix model, which is derived from Sakai-Sugimoto model in
D0-D4 background (D0-D4/D8 system). The matrix model is derived by using the
standard technique in string theory and it can describe multi-baryon system. We
re-derive the action of the matrix model from open string theory on the wrapped
baryon vertex, which is embedded in the D0- D4/D8 system. The matrix model
offers a more systematic approach to the dynamics of the baryons at short
distances. In our system, we find that the matrix model describe stable
baryonic states only if $\zeta=U_{Q_{0}}^{3}/U_{KK}^{3}<2$, where
$U_{Q_{0}}^{3}$ is related to the number density of smeared D0-branes. This
result in our paper is exactly the same as some previous presented results
studied on this system as \cite{key-24 Baryons in D0-D4}. We also compute the
baryon spectrum ($k=1$ case) and short-distance two-body force of baryons
($k=2$ case). The baryon spectrum is modified and could be able to fit the
experimental data if we choose suitable value for $\zeta$. And the
short-distance two-body force of baryons is also modified by the appearance of
smeared D0-branes from the original Sakai-Sugimoto model. If $\zeta>2$, we find
that the baryon spectrum would be totally complex and an attractive force will
appear in the short-distance interaction of baryons, which may consistently
correspond to the existence of unstable baryonic states.
