The Modification of the Scalar Field in dense Nuclear Matter

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We show the possible evolution of the nuclear deep inelastic structure function with nuclear density ρ. The nucleon deep inelastic structure function represents distribution of quarks as function of Bjorken variable x which measures the longitudinal fraction of momentum carried by them during the Deep Inelastic Scattering (DIS) of electrons on nuclear targets. Starting with small density and negative pressure in Nuclear Matter (NM) we have relatively large inter-nucleon distances and increasing role of nuclear interaction mediated by virtual mesons.When the density approaches the saturation point, ρ = ρ 0 , we have no longer separate mesons and nucleons but eventually modified nucleon Structure Function (SF) in medium. The ratio of nuclear to nucleon SF measured at saturation point is well known as “EMC effect”. For larger density, ρ > ρ 0 , when the localization of quarks is smaller then 0.3 fm, the nucleons overlap. We argue that nucleon mass should start to decrease in order to satisfy the Momentum Sum Rule (MSR) of DIS. These modifications of the nucleon Structure Function (SF) are calculated in the frame of the nuclear Relativistic Mean Field (RMF) convolution model. The correction to the Fermi energy from term proportional to the pressure is very important and its inclusion modifies the Equation of State (EoS) for nuclear matter.