We present a detailed study of a continuum random-phase approximation approach to quasielastic electron-nucleus and neutrino-nucleus scattering. We compare the $\left(e,e\prime \right)$ cross-section predictions with electron scattering data for the nuclear targets ${}^{12}\mathrm{C}$, ${}^{16}\mathrm{O}$, and ${}^{40}\mathrm{Ca}$, in the kinematic region where quasielastic scattering is expected to dominate. We examine the longitudinal and transverse contributions to ${}^{12}\mathrm{C}\left(e,e\prime \right)$ and compare them with the available data. We find an overall satisfactory description of the $\left(e,e\prime \right)$ data. Further, we study the ${}^{12}\mathrm{C}\left({\nu }_{\mu },{\mu }^{-}\right)$ cross sections relevant for accelerator-based neutrino-oscillation experiments. We pay special attention to low-energy excitations which can account for non-negligible contributions in measurements, and require a beyond-Fermi-gas formalism.

We study the impact of the description of the knockout nucleon wave function on electron- and neutrino-induced quasielastic and single-pion production cross sections. We work in a fully relativistic and quantum mechanical framework, where the relativistic mean-field model is used to describe the target nucleus. The focus is on Pauli blocking and the distortion of the final nucleon; these two nuclear effects are separated and analyzed in detail. We find that a proper quantum mechanical treatment of these effects is crucial to provide the correct magnitude and shape of the inclusive cross section. Also, this seems to be key to predict the right ratio of muon-neutrino to electron-neutrino cross sections at very forward scattering angles.

Background: Nuclear short-range correlations (SRCs) are corrections to mean-field wave functions connected with the short-distance behavior of the nucleon-nucleon interaction. These SRCs provide corrections to lepton-nucleus cross sections as computed in the impulse approximation (IA).

We show that the quasielastic (QE) response calculated with the superscaling approach (SuSAv2) model, that relies on the scaling phenomenon observed in the analysis of $(e,e^{\prime })$ data and on the relativistic mean-field theory, is very similar to that from a relativistic distorted-wave impulse approximation model when only the real part of the optical potentials is employed. The coincidence between the results from these two completely independent approaches, which satisfactorily agree with the inclusive data, reinforces the reliability of the quasielastic predictions stemming from both models and sets constraints for the QE response. We also study the low-energy and momentum-transfer region of the inclusive response by confronting the results of the relativistic mean-field model with those of the Hartree-Fock continuum random-phase approximation model, which accounts for nuclear long-range correlations. Finally, we present a comparison of our results with the recent Jefferson Laboratory (JLab) $(e,e^{\prime })$ data for argon, titanium, and carbon, finding good agreement with the three data sets.

Differences between ${\nu }_e$ and ${\nu }_{\mu }$ quasielastic cross sections are essential in neutrino oscillation analyses and $CP$ violation searches for experiments such as DUNE and T2HK. The ratio of these is however poorly known experimentally and for certain kinematic regions theoretical models give contradictory answers. We use two independent mean-field based models to investigate this ratio using ${}^{40}\mathrm{Ar}$ and ${}^{12}\mathrm{C}$ targets. We demonstrate that a proper treatment of the final nucleon’s wave function confirms the dominance of ${\nu }_{\mu }$ over ${\nu }_e$ induced cross sections at forward lepton scattering.

Background: The neutrino-nucleus ($\nu A$) cross section is a major source of systematic uncertainty in neutrino-oscillation studies. A precise $\nu A$ scattering model, in which multinucleon effects are incorporated, is pivotal for an accurate interpretation of the data.