Nuclear Potential of Final State Nucleons and Nucleons Plus Pions in Lepton Nucleus Scattering

TL;DR

This paper extracts and compares nuclear potentials for nucleons and nucleon-plus-pion states in lepton-nucleus scattering, revealing energy-dependent differences crucial for modeling quasielastic and resonance processes.

Contribution

It provides new energy-dependent values for nuclear potentials of nucleons and nucleon-plus-pion states, derived from electron scattering data, improving modeling accuracy in neutrino interaction simulations.

Findings

Nucleon potential at T=100 MeV is approximately 20 MeV.

Nucleon-plus-pion potential at T=100 MeV is approximately 30 MeV.

Potential differences depend on kinetic energy and resonance contributions.

Abstract

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, nucleons and pions in the Coulomb field of the nucleus $|V_{eff}|$, and the kinetic energy dependent nuclear potential for final state nucleons ($U^{QE}_{opt}$) and "nucleon plus pion" final states in the region of the $\Delta$ resonance which we refer to as $U^{\Delta}_{opt}$. We extract these parameters from electron scattering data. 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 two 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 {\it"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.