Incoherent processes in dileptons production in proton-nucleus scattering at high energies

$\mathbf{Purpose}$: Incoherent processes in production of lepton pairs in the scattering of protons off nuclei are investigated. $\mathbf{Methods}$: New quantum mechanical model is constructed which uses generalization of the nuclear model of emission of photons in the proton-nucleus reactions in region from low up to high energies with inclusion of formalism of production of lepton pairs. $\mathbf{Results}$: (1) Model with the coherent matrix elements is tested for the scattering of protons on the Be nuclei at energy of proton beam $E_{\rm p}$ of 2.1 GeV. The calculated cross section of production of lepton pairs is in good agreement with experimental data obtained by DLS Collaboration. (2) We analyzed dilepton production for nuclei-targets $\isotope[9]{Be}$, $\isotope[12]{C}$, $\isotope[16]{O}$, $\isotope[24]{Mg}$, $\isotope[44]{Ca}$, $\isotope[197]{Au}$ at $E_{\rm p}=2.1$ GeV. Coherent cross sections of dilepton production are monotonously decreased with increasing of nucleus-target mass. (3) Production of lepton pairs is more intensive at larger $E_{\rm p}$. (4) For $p + \isotope{9}Be$ at $E_{\rm p}=2.1$ GeV we analyzed role of incoherent processes in production of pairs of leptons. Inclusion of incoherent proton-nucleon processes to the model improves agreement with experimental data a little. (5) Adding of the longitudinal amplitude of virtual photon suppresses the cross section of dilepton production a little. (6) The incoherent contribution has a leading role in dilepton production (ratio between incoherent and coherent contributions is 10-100). Model provides the full spectrum for $p + \isotope[93]{Nb}$ at $E_{\rm p}=3.5$ GeV in good agreement with experimental data of HADES collaboration, shows large role of incoherent processes. Conclusion: Results above confirms importance of incoherent processes in study of dilepton production in this reaction.