Comparison of optical potential for nucleons and $\Delta$ resonances

Precise modeling of neutrino interactions on nuclear targets is essential for neutrino oscillations experiments. The modeling of the energy of final state particles in quasielastic (QE) scattering and resonance production on bound nucleons requires knowledge of both the removal energy of the initial state bound nucleon as well as the Coulomb and nuclear optical potentials for final state leptons and hadrons. We extract the values of the nuclear optical potential for final state nucleons ($U_{opt}^{QE}$) as a function of the nucleon kinetic energy from inclusive electron scattering data on nuclear targets ($\bf_{6}^{12}C$/$\bf_{8}^{16}O$, $\bf_{20}^{40}Ca$/$\bf_{18}^{40}Ar$, $\bf_{3}^{6}Li$, $\bf_{18}^{27}Al$, $\bf_{26}^{56}Fe$, $\bf_{82}^{208}Pb$/$\bf_{79}^{197}Au$) in the QE region and compare to calculations. We also extract values of the nuclear optical potential for a $\Delta(1232)$ resonance in the final state ($U^\Delta_{opt}$) within the impulse approximation. We find that $U^\Delta_{opt}$ is more negative than $U_{opt}^{QE}$.