We study a problem of $pi$ production in heavy ion collisions in the context of the Isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model. We generated nucleon densities using two different models, the Skyrme-Hartree-Fock (SHF) model and configuration interaction shell model (SM). Indeed, inter-nucleon correlations are explicitly taken into account in SM, while they are averaged in the SHF model. As an application of our theoretical frameworks, we calculated the $pi^{-}$ and $pi^{+}$ yields in collisions of nuclei with $A = 30-40$ nucleons. We used different harmonic oscillator lengths $b_{HO}$ to generate the harmonic oscillator basis for SM in order to study both theoretical and experimental cases. It is found that SM framework with $b_{HO}$ = 2.5 fm and SHF can be distinguished by the yield of $pi$ mesons, in this case the density distribution calculated by the shell model produces more $pi$ in the collision. In comparison, SM with $b_{HO}$ = 2.0 fm is characterized from SHF by the double $pi^{-}/pi^{+}$ ratios with different large impact parameters, from which one can find the double $pi^{-}/pi^{+}$ ratios of SM change smoother and are less than those of SHF.
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