Dissociation cross sections of $\psi (3770)$, $\psi (4040)$, $\psi (4160)$, and $\psi (4415)$ mesons with nucleons

We study the dissociation of $\psi (3770)$, $\psi (4040)$, $\psi (4160)$, and $\psi (4415)$ mesons in collisions with nucleons, which takes place in high-energy proton-nucleus collisions. Quark interchange between a nucleon and a $c\bar c$ meson leads to the dissociation of the $c\bar c$ meson. We consider the reactions: $pR \to \Lambda_c^+ \bar{D}^0$, $pR \to \Lambda_c^+ \bar{D}^{*0}$, $pR \to \Sigma_c^{++} D^-$, $pR \to \Sigma_c^{++} D^{*-}$, $pR \to \Sigma_c^{+} \bar{D}^0$, $pR \to \Sigma_c^{+} \bar{D}^{*0}$, $pR \to \Sigma_c^{*++} D^-$, $pR \to \Sigma_c^{*++} D^{*-}$, $pR \to \Sigma_c^{*+} \bar{D}^0$, and $pR \to \Sigma_c^{*+} \bar{D}^{*0}$, where $R$ stands for $\psi (3770)$, $\psi (4040)$, $\psi (4160)$, or $\psi (4415)$. A reaction of a neutron and a $c\bar c$ meson corresponds to a reaction of a proton and the $c\bar c$ meson by replacing the up quark with the down quark and vice versa. Transition-amplitude formulas are derived from the $S$-matrix element. Unpolarized cross sections are calculated with the transition amplitudes for scattering in the prior form and in the post form. The cross sections relate to nodes in the radial wave functions of $\psi (3770)$, $\psi (4040)$, $\psi (4160)$, and $\psi (4415)$ mesons.