Removal energies and final state interaction in lepton nucleus scattering

Abstract

We investigate the binding energy parameters that should be used in modeling electron and neutrino scattering from nucleons bound in a nucleus within the framework of the impulse approximation. We discuss the relation between binding energy, missing energy, removal energy ( ), spectral functions and shell model energy levels and extract updated removal energy parameters from ee p spectral function data. We address the difference in parameters for scattering from bound protons and neutrons. We also use inclusive e-A data to extract an empirical parameter UF SI ((q3 + k) 2 ) to account for the interaction of final state nucleons (FSI) with the optical potential of the nucleus. Similarly we use V ef f to account for the Coulomb potential of the nucleus. With three parameters , UF SI ((q3 + k) 2 ) and V ef f we can describe the energy of final state electrons for all available electron QE scattering data. The use of the updated parameters in neutrino Monte Carlo generators reduces the systematic uncertainty in the combined removal energy (with FSI corrections) from ± 20 MeV to ± 5 MeV.PACS. 13.60.Hb Total and inclusive cross sections (including deep-inelastic processes) -13.15.+g Neutrino interactions -13.60.-r Photon and charged-lepton interactions with hadrons

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

“…We show the slopes and intercepts for U Q E opt and U Δ opt on alternate rows. (*The removal energies [10] are (24.1,27.0) for 16 8 O and (30.9, 32.3) for 40 18 Ar). Note that the fits are only valid in the region for which we have data.…”

“…In Ref. [10] we extract the mean excitation energy E P,N x (or equivalently the removal energy P,N ) using spectral functions measured in exclusive electron scattering experiments on nuclear targets in which both the final state electron and proton are detected (ee P). Some of the neutrino MC generators (e.g.…”

“…In Ref. [10] we estimate that a +20 MeV change in the interaction energy used in the MC corresponds to a change in Δm 2 32 of +0.03 × 10 −3 eV 2 , which is the largest contribution to the total systematic error in Δm 2 32 . This estimate is consistent with the estimate of the t2k collaboration which reports [69] that "for the statistics of the 2018 data set, a shift of 20 MeV in the binding energy parameter introduces a bias of 20% for sin 2 θ 23 and 40% for Δm 2 32 with respect to the size of the systematics errors, assuming maximal sin 2 θ 23 ".…”

“…First we summarize some of the results of our previous publication [10] on removal energies and the average nuclear optical potential for final state nucleons extracted from inclusive quasielastic (QE) electron scattering data on a variety of nuclei. The analysis was done within the framework of the impulse approximation.…”

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

“…Fig. 1 shows examples of fits for two out of 33 measured electron differential cross sections on 12 6 in the region of the QE peak [1]. The solid black curves are the Relativistic Fermi Gas (RFG) fits with the best value of for the final state nucleon.…”