We estimate the nuclear medium modifications of the quark contribution to the bound nucleon spin sum rule, ${J}^{{q}^{*}}$, as well the separate helicity, $\ensuremath{\Delta}{\ensuremath{\Sigma}}^{*}$, and the angular momentum, ${L}^{{q}^{*}}$, contributions to ${J}^{{q}^{*}}$. For the calculation of the bound nucleon generalized parton distributions (GPDs), we use as input the bound nucleon elastic form factors predicted in the quark-meson coupling model. Our model for the bound nucleon GPDs is relevant for incoherent deeply virtual Compton scattering (DVCS) with nuclear targets. We find that the medium modifications increase ${J}^{{q}^{*}}$ and ${L}^{{q}^{*}}$ and decrease $\ensuremath{\Delta}{\ensuremath{\Sigma}}^{*}$ compared to the free nucleon case. The effect is large and increases with increasing nuclear density \ensuremath{\rho}. For instance, at $\ensuremath{\rho}={\ensuremath{\rho}}_{0}=0.15 {\mathrm{fm}}^{\ensuremath{-}3},{J}^{{q}^{*}}$ increases by 7%, ${L}^{{q}^{*}}$ increases by 20%, and $\ensuremath{\Delta}{\ensuremath{\Sigma}}^{*}$ decreases by 17%. These in-medium modifications of the bound nucleon spin properties are a general feature of relativistic mean-field quark models and may be understood qualitatively in terms of the enhancement of the lower component of the quark Dirac spinor in the nuclear medium.
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