Estimates of the uncertainties associated with models of the nucleon structure functions in the $\mathrm{\Delta }$ production region

Theoretical studies of the inclusive electron-nucleus cross section at beam energies up to few GeV show that, while the region of the quasi-elastic peak is understood at quantitative level, the data in the $\mathrm{\Delta }$ production region are sizably underestimated. We analize the uncertainty associated with the description of the nucleon structure functions $W_1$ and $W_2$ and its impact on the nuclear cross section. The results of our study suggest that the failure to reproduce the data is to be mostly ascribed to the poor knowledge of the neutron structure functions at low $Q^2$.