We investigate an idea, how to use analysis of the bremsstrahlung photons to study the internal structure of proton under nuclear reaction with nucleus. A new model is constructed to describe bremsstrahlung emission of photons which accompanies the scattering of protons off nuclei. Our bremsstrahlung formalism uses many-nucleon basis that allows to analyze coherent and incoherent bremsstrahlung emissions. As scattered proton can be under the influence of strong forces and produces the largest bremsstrahlung contribution to full spectrum, we focus on accurate determination of its quantum evolution concerning nucleus basing on quantum mechanics and scattering theory. For such a motivation, we at first time generalize Pauli equation with interacting potential describing evolution of fermion inside strong field, with including the electromagnetic form-factors of nucleon basing on DIS theory. Anomalous magnetic momenta of nucleons reinforce our motivation to develop such a formalism, starting from low energy. The full bremsstrahlung spectrum in our model (after renormalization) is dependent on form-factors of the scattered proton. For calculations, we choose the scattering of $p + ^{197}{rm Au}$ at proton beam energy of 190~MeV, where experimental bremsstrahlung data were obtained with high accuracy. We show that the full bremsstrahlung spectrum is sensitive to the form-factors of the scattered proton. In the limit without such form-factors, we reconstruct our previous result (where internal structure of the scattered proton was not studied).
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