\begin{document}$\psi (4040)$\end{document}, \begin{document}$\psi (4160)$\end{document}, and \begin{document}$\psi (4415)$\end{document} mesons. Master rate equations are established for inelastic scattering. The scattering is caused by quark interchange in association with color interactions between all constituent pairs in different mesons. We consider fifty-one reactions between charmed strange and open-charm mesons. Unpolarized cross sections for the reactions are obtained from a temperature-dependent interquark potential. The temperature dependence of the cross sections causes the contributions of the reactions to the production of \begin{document}$\psi (4040)$\end{document}, \begin{document}$\psi (4160)$\end{document}, and \begin{document}$\psi (4415)$\end{document} to change with decreasing temperature during the evolution of hadronic matter. For central Pb-Pb collisions at \begin{document}$\sqrt{s_{_{NN}}}=5.02$\end{document} TeV, the master rate equations reveal that the number density of \begin{document}$\psi(4040)$\end{document} is larger than that of \begin{document}$\psi(4160)$\end{document}, whose number density is larger than that of \begin{document}$\psi(4415)$\end{document}."> Production of <inline-formula><tex-math id="M1">\begin{document}$ {{\boldsymbol\psi} {\bf{ (4040)}}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/b3bd4f6f-fefe-4d09-be72-725a864b89a3/CPC-2024-0228_M1.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/b3bd4f6f-fefe-4d09-be72-725a864b89a3/CPC-2024-0228_M1.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}${ \boldsymbol\psi \bf (4160) }$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/b3bd4f6f-fefe-4d09-be72-725a864b89a3/CPC-2024-0228_M2.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/b3bd4f6f-fefe-4d09-be72-725a864b89a3/CPC-2024-0228_M2.png"/></alternatives></inline-formula>, and <inline-formula><tex-math id="M3">\begin{document}${ \boldsymbol\psi \bf (4415) }$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/b3bd4f6f-fefe-4d09-be72-725a864b89a3/CPC-2024-0228_M3.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/b3bd4f6f-fefe-4d09-be72-725a864b89a3/CPC-2024-0228_M3.png"/></alternatives></inline-formula> mesons in strong interactions -
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