Coherent interactions of a fast proton with a short-range $NN$ correlation in the nucleus

Nuclear structure at short $NN$-distances is still poorly understood. In particular, the full quantum structure of the nucleus with a correlated $NN$-pair is a challenge to theory. So far, model descriptions have been limited to the average mean-field picture of the remaining nuclear system after removing the $NN$-pair. In the recent experiment of the BM@N Collaboration at JINR \cite{Patsyuk:2021fju}, the reactions $^{12}\mbox{C}(p,2pn_s)^{10}\mbox{B}$ and $^{12}\mbox{C}(p,2pp_s)^{10}\mbox{Be}$ induced by the hard elastic $pp$ scattering were studied. Here, $n_s$ or $p_s$ denote the undetected slow nucleon in the rest frame of $^{12}\mbox{C}$. In contrast to the previous experiments, the residual bound nucleus was also detected which requires a new level of theoretical understanding. In the present work, we apply the technique of fractional parentage coefficients of the translationally-invariant shell model (TISM) to calculate the spectroscopic amplitude of the system $NN-B$ where $B$ is the remaining nuclear system. The spectroscopic amplitude enters the full amplitude of a nuclear reaction. The relative $NN-B$ wave function is no longer a free parameter of the model but is uniquely related to the internal state of $B$. The interaction of the target proton with the $NN$-pair is considered in the impulse approximation. We also include the initial- and final state interactions of absorptive type as well as the single charge exchange processes. Our calculations are in a reasonable agreement with the BM@N data.