PoS - Proceedings of Science
Volume 390 - 40th International Conference on High Energy physics (ICHEP2020) - Parallel: Neutrino Physics
Nuclear Potential of Final State Nucleons and Nucleons Plus Single Pions in Lepton Nucleus Scattering
A. Bodek,* T. Cai
*corresponding author
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Pre-published on: January 13, 2021
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We summarize some of the results presented in two of our recent papers: "Removal Energies and Final State Interaction in Lepton Nucleus Scattering" Eur. Phys. J. C79 (2019) 293 (arXiv:1801.07875[nucl-th],) and
"Comparison of optical potential for nucleons and $\Delta$ resonances", Eur. Phys. J. C80, (2020) 655 (arXiv:2004.00087 [hep-ph]). In addition we address comments made in a paper by U. Mosel, "Comment on "Comparison of optical potential for nucleons and $\Delta$ resonances", e-Print: arXiv:2007.10260 [nucl-th]

Within the impulse approximation, the modeling of the energy of final state leptons in electron and neutrino quasielastic and pion production processes on nuclear targets in the region of the $\Delta$ resonance depends on several parameters. These parameters include the removal energy of the initial state nucleon from the nucleus $\epsilon^{P,N}$, the potentials of electrons, single protons and protons plus pion states in the Coulomb field of the nucleus $|V_{eff}|$, and the kinetic energy dependent nuclear potential for final state nucleons ($U^{QE}_{opt}$) and final state nucleons plus pions in the region of the $\Delta$ resonance which we refer to as $U^{\Delta}_{opt}$. We extract these parameters from electron scattering data. The average removal energies $\epsilon^{P,N}$ are extracted from spectral functions measured in $ee^\prime P$ experiments. $|V_{eff}|$ is extracted from comparisons of electron and positron scattering, and $U^{QE}_{opt}$ and $U^{\Delta}_{opt}$ are extracted from the peak positions in the energy of final state electrons in QE scattering and pion production in the region of the $\Delta$(1232) resonance .

Previous studies have shown that real part of the optical potential for a nucleon bound in $_{6}^{12}C$ at zero kinetic energy $U^{P,N}_{opt}(T=0)\approx$~44~MeV is larger than that for the $\Delta$(1232) resonance $U^{\Delta}_{opt}(T=0)\approx$~30~MeV. We find the reverse at higher kinetic energies. For example at T=100 MeV we find a nucleon potential $U^{P,N}_{opt}(T=100~MeV)$=20$\pm$5 MeV and $U^{\Delta}_{opt}(T=100~MeV)$= 30$\pm$5 MeV. The paper by arXiv:2007.10260 [nucl-th] claims that the our results are inconsistent with the T=0 values. However, our results are consistent for two reasons. First, theoretically the kinetic energy dependence of the $\Delta$ potential is flatter than that of the nucleon. Secondly, in our analysis the extracted $U^{\Delta}_{opt}$ values are the nuclear potential for nucleon plus pion final states in the region of the $\Delta$ resonances and therefore includes contributions from both resonance and non resonance pion production processes. For Monte Carlo generators that only include the effects of Fermi motion and nuclear potentials, the relevant parameter is the effective nuclear potential for the"nucleon plus pion"final state.
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