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 Lepton Nucleus Scattering
A. Bodek,* T. Cai
*corresponding author
Full text: Not available
Abstract
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.
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