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Short-range correlated (SRC) NN pairs play an important role in structure of atomic nuclei and are studied using mainly electron beams [1]. A new step was done at BM@N in JINR [2] where the reaction 12C+p→10A+pp+N is studied using the $^{12}$C beam at energy of 4 GeV/nucleon in inverse kinematics providing interaction with the hydrogen target to probe the SRC pairs in the $^{12}$C. In theoretical analysis [3] of the SRC effects in this reaction is used a properly modified approach developed earlier (see Ref. [4] and references therein) to describe the quasi-elastic knock-out of fast deuterons from the light nuclei $^{12}$C and $^{7,6}$Li by protons in the reactions (p,pd) and (p,nd) [5]. Elementary sub-processes in the (p,Nd) were the backward quasi-elastic scattering of the proton on the two-nucleon clusters p{pn}→pd and p{nn}→nd at the proton beam energy 670 MeV. As in Ref. [4], the spectroscopic amplitudes for NN-pairs in the ground state of the 12C nucleus are calculated here within the translation-invariant shell model (TISM) with mixing configurations. Factorization of the two-nucleon momentum distribution over the internal $n_{rel}$ ($q_{rel}$) and the c.m.s. ncm ($k_{c.m.}$) momenta is assumed and for nrel ($q_{rel}$) the squared deuteron (or singlet deuteron) wave function the CD Bonn NN-interaction potential is used. Relativistic effects in the sub-process p+{NN}➛p+N+N of quasi-elastic knockout of nucleon from the SRC pair are taken into account in the light-front dynamics. We found that the c.m. distribution of the deuteron clusters obtained within the TISM and used in [4], [5] to describe the (p,Nd) data [4] has to be modified considerably [6] to describe the kc.m. distribution of the SCR NN pairs measured in the electron data [6]. The ratio of the spin-singlet to spin-triplet pairs $\{pp\}_s/\{pn\}_t$ is calculated [7] and found to be in agreement with existing data. Here the initial and final state interaction effects are estimated within the eikonal approximation using the Glauber model for the N$^{10}$A scattering [8]. The one-loop approximation with elastic N$^{10}$A rescatterings is applied and the effect is found to be moderate.

This work was supported in part by the RFBR grant № 18-02-40046.

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