An analysis of inclusive quasielastic electron scattering is presented using different descriptions of the final state interactions within the framework of the relativistic impulse approximation. The relativistic Green's function approach is compared with calculations based on the use of relativistic purely real mean field potentials in the final state. Both approaches lead to a redistribution of the strength but conserving the total flux. Results for the differential cross section at different energies are presented. Scaling properties are also analyzed and discussed.
Effects of strong final-state interactions in the superscaling properties of neutral-current quasielastic neutrino cross sections are investigated using the Relativistic Impulse Approximation as guidance. First- and second-kind scaling are analyzed for neutrino beam energies ranging from 1 to 2 GeV for the cases of 12C, 16O and 40Ca. Different detection angles of the outgoing nucleon are considered in order to sample various nucleon energy regimes. Scaling of the second kind is shown to be very robust. Validity of first-kind scaling is found to be linked to the kinematics of the process. Super…
We provide a parametrization of a new phenomenological scaling function obtained from a chi-square fit to a selected set of (e,e') cross section data expanding a band centered around the quasielastic peak. We start from a re-analysis of quasielastic electron scattering from nuclear matter within the relativistic mean field model. The cross section depends on the relativistic effective mass of the nucleon, $m_N^*$, and it scales with respect to a new scaling variable, $ψ^*$. This suggests a new superscaling approach with effective mass (SuSAM*) for predicting quasielastic cross sections within …
Superscaling of the quasielastic cross section in charged current neutrino-nucleus reactions at energies of a few GeV is investigated within the framework of the relativistic impulse approximation. Several approaches are used to describe final state interactions and comparisons are made with the plane wave approximation. Superscaling is very successful in all cases. The scaling function obtained using a relativistic mean field for the final states shows an asymmetric shape with a long tail extending towards positive values of the scaling variable, in excellent agreement with the behavior prese…
The analysis of the recent experimental data on charged-current neutrino-nucleus scattering cross sections measured at MiniBooNE requires fully relativistic theoretical descriptions also accounting for the role of final state interactions. In this work we evaluate inclusive quasielastic differential neutrino cross sections within the framework of the relativistic impulse approximation. Results based on the relativistic mean field potential are compared with the ones corresponding to the relativistic Green function approach. An analysis of scaling and superscaling properties provided by both mo…
The superscaling analysis is extended to include quasielastic (QE) scattering via the weak neutral current of neutrinos and antineutrinos from nuclei. The scaling function obtained within the coherent density fluctuation model (used previously in calculations of QE inclusive electron and charge-changing (CC) neutrino scattering) is applied to neutral current neutrino and antineutrino scattering with energies of 1 GeV from $^{12}$C with a proton and neutron knockout (u-channel inclusive processes). The results are compared with those obtained using the scaling function from the relativistic Fer…
The relativistic effective mass $M^*$, and Fermi momentum, $k_F$, are important ingredients in the determination of the nuclear equation of state, but they have rarely been extracted from experimental data below saturation density where translationally invariant nuclear matter becomes unstable against clusterization into the existing atomic nuclei. Using a novel kind of superscaling analysis of the quasielastic cross section electron scattering data involving a suitable selection criterion and $^{12}$C as a reference nucleus, the global scaling properties of the resulting set of data for 21 nu…
The Coulomb sum rule for inclusive quasielastic electron scattering in $^{12}$C, $^{40}$Ca and $^{56}$Fe is analyzed based on scaling and superscaling properties. Results obtained in the relativistic impulse approximation with various descriptions of the final state interactions are shown. A comparison with experimental data measured at Bates and Saclay is provided. The theoretical description based on strong scalar and vector terms present in the relativistic mean field, which has been shown to reproduce the experimental asymmetric superscaling function, leads to results that are in fair agre…
Charged current inclusive neutrino-nucleus cross sections are evaluated using the superscaling model for quasielastic scattering and its extension to the pion production region. The contribution of two-particle-two-hole vector meson-exchange current excitations is also considered within a fully relativistic model tested against electron scattering data. The results are compared with the inclusive neutrino-nucleus data from the T2K and SciBooNE experiments. For experiments where $\langle E_ν\rangle \sim 0.8$ GeV, the three mechanisms considered in this work provide good agreement with the data.…
The semi-relativistic approach to electron and neutrino quasielastic scattering from nuclei is extended to include final-state interactions. Starting with the usual non-relativistic continuum shell model, the problem is relativized by using the semi-relativistic expansion of the current in powers of the initial nucleon momentum and relativistic kinematics. Two different approaches are considered for the final-state interactions: the Smith-Wambach 2p-2h damping model and the Dirac-equation-based potential extracted from a relativistic mean-field plus the Darwin factor. Using the latter the scal…
We evaluate the quasielastic double differential neutrino cross sections obtained in a phenomenological model based on the superscaling behavior of electron scattering data. We compare our results with the recent experimental data for neutrinos of MiniBooNE and estimate the contribution of the vector meson-exchange currents in the 2p-2h sector.
The present study is focused on the superscaling behavior of electron-nucleus cross sections in the region lying above the quasielastic peak, especially the region dominated by electroexcitation of the Delta. Non-quasielastic cross sections are obtained from all available high-quality data for Carbon 12 by subtracting effective quasielastic cross sections based on the superscaling hypothesis. These residuals are then compared with results obtained within a scaling-based extension of the relativistic Fermi gas model, including an investigation of violations of scaling of the first kind in the r…
The superscaling approach is applied to studies of neutral current neutrino reactions in the quasielastic regime. Using input from scaling analyses of electron scattering data, predictions for high-energy neutrino and antineutrino cross sections are given and compared with results obtained using the relativistic Fermi gas model. The influence of strangeness content inside the nucleons in the nucleus is also explored.
We evaluate and discuss the impact of meson-exchange currents (MECs) on charged-current quasielastic neutrino cross sections. We consider the nuclear transverse response arising from two-particle two-hole states excited by the action of electromagnetic, purely isovector meson-exchange currents in a fully relativistic framework based on the work by the Torino Collaboration [A. D. Pace, M. Nardi, W. M. Alberico, T. W. Donnelly, and A. Molinari, Nucl. Phys. A726, 303 (2003)]. An accurate parametrization of this MEC response as a function of the momentum and energy transfers involved is presented.…
We evaluate quasielastic double-differential antineutrino cross sections obtained in a phenomenological model based on the superscaling behavior of electron scattering data and estimate the contribution of the vector meson-exchange currents in the 2p-2h sector. We show that the impact of meson-exchange currents for charge-changing antineutrino reactions is much larger than in the neutrino case.
We reanalyze the scaling properties of inclusive quasielastic electron scattering from $^{12}$C by subtracting from the data the effects of two-particle emission. A model of relativistic meson-exchange currents (MEC) is employed within the mean field theory of nuclear matter, with scalar and vector potentials that induce an effective mass and a vector energy to the nucleons. A new phenomenological quasielastic scaling function is extracted from a selection of the data after the subtraction of the 2p-2h contribution. The resulting superscaling approach with relativistic effective mass (SuSAM*) …
The application of superscaling ideas to predict neutral-current (NC) quasielastic (QE) neutrino cross sections is investigated. Results obtained within the relativistic impulse approximation (RIA) using the same relativistic mean field potential (RMF) for both initial and final nucleons -- a model that reproduces the experimental (e,e') scaling function -- are used to illustrate the ideas involved. While NC reactions are not so well suited for scaling analyses, to a large extent the RIA-RMF predictions do exhibit superscaling. Independence of the scaled response on the nuclear species is very…
The phenomenon of superscaling for quasielastic lepton induced reactions at energies of a few GeV is investigated within the framework of the relativistic impulse approximation. A global analysis of quasielastic inclusive electron and charged-current neutrino scattering reactions on nuclei is presented. Scaling and superscaling properties are shown to emerge from both types of processes. The crucial role played by final state interactions is evaluated by using different approaches. The asymmetric shape presented by the experimental scaling function, with a long tail in the region of positive v…
The so-called semi-relativistic expansion of the weak charged current in powers of the initial nucleon momentum is performed to describe charge-changing, quasielastic neutrino reactions $(ν_μ,μ^-)$ at intermediate energies. The quality of the expansion is tested by comparing with the relativistic Fermi gas model using several choices of kinematics of interest for ongoing neutrino oscillation experiments. The new current is then implemented in a continuum shell model together with relativistic kinematics to investigate the scaling properties of $(e,e')$ and $(ν_μ,μ^-)$ cross sections.
We present a systematic analysis of the quasielastic scaling functions computed within the Relativistic Mean Field (RMF) Theory and we propose an extension of the SuperScaling Approach (SuSA) model based on these results. The main aim of this work is to develop a realistic and accurate phenomenological model (SuSAv2), which incorporates the different RMF effects in the longitudinal and transverse nuclear responses, as well as in the isovector and isoscalar channels. This provides a complete set of reference scaling functions to describe in a consistent way both $(e, e')$ processes and the neut…
We suggest that superscaling analyses of few-GeV inclusive electron scattering from nuclei, both in the quasielastic peak and in the region where the $Δ$-excitation dominates, allow one to make reliable predictions for charge-changing neutrino reactions at energies of a few GeV, relevant for neutrino oscillation experiments.
We investigate the degree to which the scaling functions $F(ψ')$ derived from cross sections for inclusive electron-nucleus quasi-elastic scattering define the same function for different nuclei. In the region where the scaling variable $ψ'< 0$, we find that this superscaling is experimentally realized to a high degree.
We investigate the degree to which the concept of superscaling, initially developed within the framework of the relativistic Fermi gas model, applies to inclusive electron scattering from nuclei. We find that data obtained from the low energy loss side of the quasielastic peak exhibit the superscaling property, i.e., the scaling functions f(ψ') are not only independent of momentum transfer (the usual type of scaling: scaling of the first kind), but coincide for A \geq 4 when plotted versus a dimensionless scaling variable ψ' (scaling of the second kind). We use this behavior to study as yet po…
The superscaling analysis using the scaling function obtained within the coherent density fluctuation model is extended to calculate charge-changing neutrino and antineutrino scattering on $^{12}$C at energies from 1 to 2 GeV not only in the quasielastic but also in the delta excitation region. The results are compared with those obtained using the scaling functions from the relativistic Fermi gas model and from the superscaling analysis of inclusive scattering of electrons from nuclei.
Following recent studies of inclusive electron scattering from nuclei at high energies which focused on two-nucleon emission mediated by meson-exchange currents, in this work the superscaling behavior of such contributions is investigated. Comparisons are made with existing data below the quasielastic peak where at high momentum transfers scaling of the second kind is known to be excellent and scaling of the first kind is good, in the proximity of the peak where both 1p-1h and 2p-2h contributions come into play, and above the peak where inelasticity becomes important and one finds scaling viol…
Superscaling analyses of inclusive electron scattering from nuclei are extended from the quasielastic processes to the delta excitation region. The calculations of $(e,e^\prime)$ cross sections for the target nucleus $^{12}$C at various incident electron energies are performed using scaling functions $f(ψ^{\prime})$ obtained in approaches going beyond the mean-field approximation, such as the coherent density fluctuation model (CDFM) and the one based on the light-front dynamics (LFD) method. The results are compared with those obtained using the relativistic Fermi gas (RFG) model and the exte…
Quasielastic double differential neutrino cross sections can be obtained in a phenomenological model based on the superscaling behavior of electron scattering data. In this talk the superscaling approach (SuSA) is reviewed and its validity is tested in a relativistic shell model. Results including meson exchange currents for the kinematics of the MiniBoone experiment are presented.
We provide integrated cross sections for quasielastic charged-current neutrino-nucleus scattering. Results evaluated using the phenomenological scaling function extracted from the analysis of experimental $(e,e')$ data are compared with those obtained within the framework of the relativistic impulse approximation. We show that very reasonable agreement is reached when a description of final-state interactions based on the relativistic mean field is included. This is consistent with previous studies of differential cross sections which are in accord with the universality property of the supersc…
After a short review of the recent developments in studies of neutrino-nucleus interactions, the predictions for double-differential and integrated charged current-induced quasielastic cross sections are presented within two different relativistic approaches: one is the so-called SuSA method, based on the superscaling behavior exhibited by electron scattering data; the other is a microscopic model based on relativistic mean field theory, and incorporating final-state interactions. The role played by the meson-exchange currents in the two-particle two-hole sector is explored and the results are…
Superscaling analyses of few-GeV inclusive electron scattering from nuclei are extended to include not only quasielastic processes, but now also into the region where $Δ$-excitation dominates. It is shown that, with reasonable assumptions about the basic nuclear scaling function extracted from data and information from other studies of the relative roles played by correlation and MEC effects, the residual strength in the resonance region can be accounted for through an extended scaling analysis. One observes scaling upon assuming that the elementary cross section by which one divides the resid…
We compare the predictions of the SuSAv2 model including two-particle two-hole meson-exchange currents with the recent JLab data for inclusive electron scattering on three different targets (C, Ar and Ti). The agreement is very good over the full energy spectrum, with some discrepancy seen only in the deep inelastic region. The 2p2h response, peaked in the dip region between the quasielastic and $Δ$-resonance peak, is essential to reproduce the data. We also analyze the $k_F$ (Fermi momentum) dependence of the data in terms of scaling of second kind, showing that the 2p2h response scales very …
Using ideas from BCS descriptions of systems of fermions, a covariant extension of the relativistic Fermi gas model is presented as a way to incorporate correlation effects in nuclei. The model is developed for the BCS nuclear ground state and for final states consisting of a single plane-wave nucleon plus a BCS recoiling daughter nucleus. The nuclear spectral function is obtained and from it the superscaling function for use in treating high-energy quasielastic electroweak processes. Interestingly, this model has the capability to yield the asymmetric tail seen in the experimental scaling fun…
A comprehensive treatement of the theoretical approach for describing nuclear effects in inclusive scattering of polarized electrons by polarized $^3$He is presented.
An extended study of scaling of the first and second kinds for inclusive electron scattering from nuclei is presented. Emphasis is placed on the transverse response in the kinematic region lying above the quasielastic peak. In particular, for the region in which electroproduction of resonances is expected to be important, approximate scaling of the second kind is observed and the modest breaking of it is shown probably to be due to the role played by an inelastic version of the usual scaling variable.
We present a covariant extension of the relativistic Fermi gas model which incorporates correlation effects in nuclei. Within this model, inspired by the BCS descriptions of systems of fermions, we obtain the nuclear spectral function and from it the superscaling function for use in treating high-energy quasielastic electroweak processes. Interestingly, this model has the capability to yield the asymmetric tail seen in the experimental scaling function.
Spectral functions that are used in neutrino event generators to model quasielastic (QE) scattering from nuclear targets include Fermi gas, Local Thomas Fermi gas (LTF), Bodek-Ritchie Fermi gas with high momentum tail, and the Benhar-Fantoni two dimensional spectral function. We find that the $ν$ dependence of predictions of these spectral functions for the QE differential cross sections (${d^2σ}/{dQ^2 dν}$) are in disagreement with the prediction of the $ψ'$ superscaling function which is extracted from fits to quasielastic electron scattering data on nuclear targets. It is known that spectra…
We compare the predictions of the SuperScaling model for charged current quasielastic muonic neutrino and antineutrino scattering from $^{12}$C with experimental data spanning an energy range up to 100 GeV. We discuss the sensitivity of the results to different parametrizations of the nucleon vector and axial-vector form factors. Finally, we show the differences between electron and muon (anti-)neutrino cross sections relevant for the $ν$STORM facility.
The inclusive quasielastic response functions that appear in the scattering of polarized electrons from polarized nuclei are computed and analyzed for several closed-shell-minus-one nuclei with special attention paid to 39K. Results are presented using two models for the ejected nucleon --- when described by a distorted wave in the continuum shell model or by a plane wave in PWIA with on- and off-shell nucleons. Relativistic effects in kinematics and in the electromagnetic current have been incorporated throughout. Specifically, the recently obtained expansion of the electromagnetic current in…
We construct a scaling function $f(ψ^{\prime})$ for inclusive electron scattering from nuclei within the Coherent Density Fluctuation Model (CDFM). The latter is a natural extension to finite nuclei of the Relativistic Fermi Gas (RFG) model within which the scaling variable $ψ^{\prime}$ was introduced by Donnelly and collaborators. The calculations show that the high-momentum components of the nucleon momentum distribution in the CDFM and their similarity for different nuclei lead to quantitative description of the superscaling in nuclei. The results are in good agreement with the experimental…
We investigate inclusive electron scattering reactions on two-neutron halo nuclei in the quasielastic region. Expressions for the cross section and structure functions are given assuming that the halo nucleus can be described as a three-body system (${core}+n+n$). The method is applied to $^6$He. We compute cross sections and structure functions, and investigate the kinematic conditions for which the observables are determined either by $α$-knockout or by halo neutron-knockout. The optimal kinematical domain to disantangle the momentum distributions of the various components of the three--body…
We have performed a many body calculation of the inclusive (e,e') cross section which runs over the three traditional regions at intermediate energies: the quasielastic peak, the dip region and the delta region. The longitudinal and transverse response functions in the quasielastic peak have also been evaluated. Traditional effects like polarization, meson exchange currents, final state interaction and delta renormalization in the nuclear medium have been included. Meson exchange currents are generated from a model of pion electroproduction on the nucleon which reproduces accurately the experi…
The superscaling observed in inclusive electron scattering is described within the dilute Fermi gas model with interaction between the particles. The comparison with the relativistic Fermi gas (RFG) model without interaction shows an improvement in the explanation of the scaling function $f(ψ')$ in the region $ψ' < -1$, where the RFG result is $f(ψ') = 0$. It is found that the behavior of $f(ψ')$ for $ψ' < -1$ depends on the particular form of the general power-law asymptotics of the momentum distribution $n(k)\sim 1/ k^{4+m}$ at large $k$. The best agreement with the empirical scaling functio…
We address the problem of including Coulomb distortion effects in inclusive quasielastic (e,e') reactions using an improved version of the effective momentum approximation. Arguments are given that a simple modification of the effective momentum approximation, which is no longer applicable in its original form in the case of highly charged nuclei, leads to very good results. A comparison of the improved effective momentum method with exact calculations is given. A critical remark concerns recent experiments with inclusive quasielastic positron scattering.
Neutral current quasielastic (anti)neutrino scattering cross sections on a $^{12}$C target are analyzed using a realistic spectral function $S(p,E)$ that gives a scaling function in accordance with the ($e,e'$) scattering data. The spectral function accounts for the nucleon-nucleon (NN) correlations by using natural orbitals (NOs) from the Jastrow correlation method and has a realistic energy dependence. The standard value of the axial mass $M_A= 1.032$ GeV is used in all calculations. The role of the final-state interaction (FSI) on the spectral and scaling functions, as well as on the cross …
The superscaling function extracted from inclusive electron scattering data is used to predict high energy charge-changing neutrino cross sections in the quasi-elastic and $Δ$ regions.
Two relativistic approaches are considered to evaluate the quasielastic double-differential and integrated neutrino-nucleus cross sections. One, based on the relativistic impulse approximation, relies on the microscopic description of nuclear dynamics using relativistic mean field theory, and incorporates a description of the final-state interactions. The second is based on the superscaling behavior exhibited by electron scattering data and its applicability, due to the universal character of the scaling function, to the analysis of neutrino scattering reactions. The role played by the vector …
The longitudinal and transverse structure functions are calculated for inclusive electron scattering from ${}^{12}$C and ${}^{40}$Ca in the quasielastic and dip region. The microscopic model presented here incorporates two-body currents derived from one-pion exchange and intermediate $Δ$ excitation. The reaction mechanism involves both one-nucleon and two-nucleon knockout processes. It is demonstrated that, even for quasielastic kinematics, two-body currents give a substantial contribution to the transverse structure function. Furthermore, the observed excess of transverse strength in the dip …
A detailed study of charged current quasielastic neutrino and antineutrino scattering cross sections on a $^{12}$C target with no pions in the final state is presented. The initial nucleus is described by means of a realistic spectral function $S(p,{\cal E})$ in which nucleon-nucleon correlations are implemented by using natural orbitals through the Jastrow method. The roles played by these correlations and by final-state interactions are analyzed and discussed. The model also includes the contribution of weak two-body currents in the two-particle two-hole sector, evaluated within a fully rela…
Relativistic models developed for the exclusive and inclusive quasielastic (QE) electron scattering have been extended to charged-current (CC) and neutral-current (NC) neutrino-nucleus scattering. Different descriptions of final-state interactions (FSI) are compared. For the inclusive electron scattering the relativistic Green's function approach is compared with calculations based on the use of relativistic purely real mean field potentials in the final state. Both approaches lead to a redistribution of the strength but conserving the total flux. Results for the differential cross section at …
The scaling function $f(ψ')$ for medium and heavy nuclei with $Z\neq N$ for which the proton and neutron densities are not similar is constructed within the coherent density fluctuation model (CDFM) as a sum of the proton and neutron scaling functions. The latter are calculated in the cases of $^{62}$Ni, $^{82}$Kr, $^{118}$Sn, and $^{197}$Au nuclei on the basis of the corresponding proton and neutron density distributions which are obtained in deformed self-consistent mean-field Skyrme HF+BCS method. The results are in a reasonable agreement with the empirical data from the inclusive electron …
Models developed for the exclusive and inclusive quasielastic (QE) electron-nucleus scattering have been extended to QE neutrino-nucleus scattering. Different descriptions of final-state interactions (FSI) are compared. For the inclusive electron scattering the relativistic Green's function model (RGF) is compared with a model based on the use of relativistic purely real mean field (RMF) potentials in the final state. Both approaches lead to a redistribution of the strength but conserving the total flux. Results for electron and neutrino scattering are presented and discussed in different cond…
Charge-current quasielastic (CCQE) (anti)neutrino scattering cross sections on a $^{12}$C target are analyzed using a spectral function $S(p,{\cal E})$ that gives a scaling function in accordance with the ($e,e'$) scattering data. The spectral function accounts for the nucleon-nucleon (NN) correlations, it has a realistic energy dependence and natural orbitals (NO's) from the Jastrow correlation method are used in its construction. In all calculations the standard value of the axial mass $M_A= 1.032$ GeV/c$^2$ is used. The results are compared with those when NN correlations are not included, …
Understanding quasielastic electron- and neutrino-scattering from nuclei has taken on new urgency with current and planned neutrino oscillation experiments, and with electron scattering experiments measuring specific final states, such as those involving nucleon pairs in ``back-to-back'' configurations. Accurate many-body methods are available for calculating the response of light ($A \leq 12$) nuclei to electromagnetic and weak probes, but they are computationally intensive and only applicable to the inclusive response. In the present work we introduce a novel approach, based on realistic mod…
