Quasielastic Region Research Articles

Inclusive quasielastic neutrino-nucleus scattering with energy density functional nuclear models* *Supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (2018R1A5A1025563, 2023R1A2C1003177, IBS-R031-D1)

In this study, we calculated the inclusive charged-current neutrino-nucleus scattering from 40Ar in the quasielastic region. To explore the effect of uncertainties stemming from the nuclear structure, we used the KIDS (Korea-IBS-Daegu-SKKU) nuclear energy density functional and Skyrme force models, namely SLy4, SkI3, and MSk7. These models were selected to have distinct behavior in terms of the density dependence of the symmetry energy and the effective mass of the nucleon. In the charged-current neutrino scattering, the single- and double-differential cross sections were calculated for various kinematics. Total cross sections are reported as a function of the incident neutrino energy. The theoretical cross sections were compared with experimental data, and the roles of the effective mass and symmetry energy were investigated in terms of charged-current neutrino-nucleus scattering.

Low-velocity impact experiments of porous ice balls simulating Saturn's ring particles: Porosity dependence of restitution coefficients and the mechanism of inelastic collision

We investigated the porosity dependence of the restitution coefficient (ε) of porous ice balls with porosities of 49.6%, 53.8%, and 60.8% colliding with granite, ice and porous ice plates at a low impact velocity (vi = 0.93–96.9 cm s−1) and temperature of −13.8 °C. The relationship between the impact velocity and the restitution coefficient was divided into two regions by the critical velocity vc: In the quasi-elastic region (vi≤vc), the restitution coefficient had a constant value of εqe regardless of the impact velocity and could be explained by using Dilley's viscous dissipation model. In the inelastic region (vi≥vc), the restitution coefficient decreased with the impact velocity and could be explained by using the improved Andrews' plastic deformation model. We then determined the porosity dependence of the εqe and vc empirically for collisions between the porous ice ball and the porous ice plate from our results. Then we extrapolated the porosity dependence of the restitution coefficient by substituting the calculated εqe and vc for the porosity of 10 to 70%. The restitution coefficient was found to decrease with increasing porosity of the porous ice, and to be strongly dependent on the porosity of the porous ice. Considering the energy budget in the steady-state dense ring system which is controlled by the restitution coefficient of the ring particles, the velocity dispersion of the ring particles was estimated to be ∼10−2 mm s−1 to cm s−1 for the ring particles with the porosity from 45% to 70% and < 10–90 cm s−1 for those with the porosity <45%.

Bethe-Heitler lepton pair production in the deuteron breakup reaction* *Supported by the National Natural Science Foundation of China (12075003, 12175117, 12335006)

We study the lepton pair production via the Bethe-Heitler mechanism in the deuteron breakup reaction. The complete seven-fold differential cross section is calculated with final state interactions taken into account. The deuteron bound state is described by a relativistic covariant deuteron-nucleon vertex. The numerical results indicate that the differential cross section is highly dependent on the lepton's azimuthal angle in regions of small polar angles and exhibits sharp peaks in the distribution over the invariant mass of the generated lepton pair or the two nucleons in the final state. We demonstrate that such a nearly singular feature originates from the collinearity between the produced lepton or antilepton and the incident photon, and it is physically regularized by the lepton mass in our calculation. The final state interaction between the knocked-out nucleon and recoil nucleon redistributes the differential cross section over the missing momentum, with a significant enhancement at a large missing momentum and a suppression in the intermediate region. With a further decomposition of the final state interaction contribution, It is found that the on-shell term dominates the near quasi-elastic region, while the off-shell term dominates the other end. Additionally, we examine the contribution from the interference between the proton amplitude and neutron amplitude, which, as expected, is found negligible even if the proton-neutron rescattering is included. The results of this study can serve as inputs for the analysis and background estimation of multiple exclusive measurements at Jefferson Lab and future electron-ion colliders.

Lepton–Nucleus Interactions within Microscopic Approaches

This review paper emphasizes the significance of microscopic calculations with quantified theoretical error estimates in studying lepton–nucleus interactions and their implications for electron scattering and accelerator neutrino oscillation measurements. We investigate two approaches: Green’s Function Monte Carlo and the extended factorization scheme, utilizing realistic nuclear target spectral functions. In our study, we include relativistic effects in Green’s Function Monte Carlo and validate the inclusive electron scattering cross section on carbon using available data. We compare the flux-folded cross sections for neutrino-carbon scattering with T2K and MINERνA experiments, noting the substantial impact of relativistic effects in reducing the theoretical curve strength when compared to MINERνA data. Additionally, we demonstrate that quantum Monte Carlo-based spectral functions accurately reproduce the quasi-elastic region in electron scattering data and T2K flux-folded cross sections. By comparing results from Green’s Function Monte Carlo and the spectral function approach, which share a similar initial target state description, we quantify errors associated with approximations in the factorization scheme and the relativistic treatment of kinematics in Green’s Function Monte Carlo.

Quasielastic charged-current neutrino-nucleus scattering with relativistic nuclear models

Charged-current neutrino-nucleus scattering is studied in the quasielastic region with various relativistic nuclear models that include the relativistic Hartree, the nonlinear $\ensuremath{\sigma}$, the quark-meson coupling, and the chiral quark-meson coupling models. Theoretical results at several kinematics are compared with experimental data measured from MiniBooNE, T2K, MicroBooNE, and SciBooNE. While the theoretical double-differential cross sections in terms of the kinetic energy and polar angle of outgoing muon describe the T2K data well, the single-differential cross sections in terms of energy loss and the total cross sections of incident neutrino energy do not properly describe MiniBooNE, MicroBooNE, and SciBooNE data. Additionally, differences from the relativistic nuclear models are examined in detail by comparing with the experimental data. In particular, the MiniBooNE data are not consistent with MicroBooNE and SciBooNE data, where the incident neutrino energies are below 1 GeV.

Quasielastic charged-current neutrino-nucleus scattering with nonrelativistic nuclear energy density functionals

Charged-current neutrino-nucleus scattering is studied in the quasielastic region with the KIDS (Korea-IBS-Daegu-SKKU) nuclear energy density functional. We focus on the uncertainties stemming from the axial mass and the in-medium effective mass of the nucleon. Comparing the result of theory to the state-of-the-art data from MiniBooNE, T2K, and MINERνA, we constrain the axial mass and the effective mass that are compatible with the data. We find that the total cross section is insensitive to the effective mass, so the axial mass could be determined independently of the uncertainty in the effective mass. Differential cross sections at different kinematics are, on the other hand, sensitive to the effective mass as well as the axial mass. Within the uncertainty of the axial mass constrained from the total cross section, dependence on the effective mass is examined. As a result we obtain the axial mass and the effective mass that are consistent with the experimental data.

SuSAv2 model for inelastic neutrino-nucleus scattering

The susperscaling model SuSAv2, already available for charged-current neutrino-nucleus cross sections in the quasielastic region, is extended to the full inelastic regime. In the model the resonance production and deep inelastic reactions are described through the extension to the neutrino sector of the SuSAv2 inelastic model developed for ($e$, ${e}^{\ensuremath{'}}$) reactions, which combines phenomenological structure functions with a nuclear scaling function. This work also compares two different descriptions of the $\mathrm{\ensuremath{\Delta}}$ resonance region, one based on a global scaling function for the full inelastic spectrum and the other on a semiphenomenological $\mathrm{\ensuremath{\Delta}}$ scaling function extracted from ($e$, ${e}^{\ensuremath{'}}$) data for this specific region and updated with respect to previous work. The results of the model are tested against ($e$, ${e}^{\ensuremath{'}}$) data on $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{40}\mathrm{Ca}$, and $^{40}\mathrm{Ar}$ and applied to the study of the charged current inclusive neutrino cross-section on $^{12}\mathrm{C}$ and $^{40}\mathrm{Ar}$ measured by the T2K, MicroBooNE, ArgoNEUT, and MINERvA experiments, thus covering several kinematical regions.

Novel event generator for the automated simulation of neutrino scattering

An event generation framework is presented that enables the automatic simulation of events for next-generation neutrino experiments in the Standard Model or extensions thereof. The new generator combines the calculation of the leptonic current based on an automated matrix element generator and the computation of the hadronic current based on a state-of-the-art nuclear physics model. The approach is validated in Standard Model simulations for electron scattering and neutrino scattering. Furthermore, the first fully differential neutrino trident production results are shown in the quasielastic region.

Inclusive electron scattering in the quasielastic region with the Korea-IBS-Daegu-SKKU density functional

With the framework of KIDS (Korea-IBS-Daegu-SKKU) density functional model, the isoscalar and isovector effective masses of nucleon and the effect of symmetry energy in nuclear medium are investigated in inclusive $(e,e')$ reaction in quasielastic region. The effective masses are varied in the range $(0.7 \sim 1.0)M$ with free nucleon mass $M$, and the symmetry energy is varied within the uncertainty allowed by nuclear data and neutron star observation. The wave functions of nucleons inside target nucleus are generated by solving Hartree-Fock equation with adjusting equation of state, binding energy and radius of various stable nuclei, and effective mass of nucleon in the KIDS model. With the obtained wave functions, we calculate the differential cross section for the inclusive $(e,e')$ reaction and compare the theoretical results with Bates, Saclay, and SLAC experimental data. Our model describes experimental data better at SLAC-type high incident electron energy than those measured from Bates and Saclay. The influence of the effective mass and symmetry energy appears to be precise on the longitudinal cross section.

Coulomb sum rule in the quasielastic region using various nuclear models

We calculate the Coulomb sum rule of inclusive $(e,{e}^{\ensuremath{'}})$ reactions from $^{12}\mathrm{C}, ^{40}\mathrm{Ca}, ^{56}\mathrm{Fe}$, and $^{208}\mathrm{Pb}$ in the quasielastic region using various relativistic single-particle models, which include the relativistic Hartree, the nonlinear sigma, the quark-meson-coupling, and the chiral quark-meson-coupling models. We investigate the cross sections calculated in these nuclear models by comparing them with Bates, Saclay, and SLAC data for three-momentum transfer $q$ ranging from 300 to 500 $\mathrm{MeV}/c$. We find that the extracted longitudinal structure functions are not so sensitive to the nuclear model but the transverse structure functions strongly depend on the model. We report that, for three-momentum transfer $q&gt;400 \mathrm{MeV}/c$, the values of the Coulomb sum rule from various nuclear models except the Hartree model are greater than 1.

Machine-learning-based inversion of nuclear responses

A microscopic description of the interaction of atomic nuclei with external electroweak probes is required for elucidating aspects of short-range nuclear dynamics and for the correct interpretation of neutrino oscillation experiments. Nuclear quantum Monte Carlo methods infer the nuclear electroweak response functions from their Laplace transforms. Inverting the Laplace transform is a notoriously ill-posed problem; and Bayesian techniques, such as maximum entropy, are typically used to reconstruct the original response functions in the quasielastic region. In this work, we present a physics-informed artificial neural network architecture suitable for approximating the inverse of the Laplace transform. Utilizing simulated, albeit realistic, electromagnetic response functions, we show that this physics-informed artificial neural network outperforms maximum entropy in both the low-energy transfer and the quasielastic regions, thereby allowing for robust calculations of electron scattering and neutrino scattering on nuclei and inclusive muon capture rates.

An event excess observed in the deeply bound region of the 12C (K−, p) missing-mass spectrum

Abstract We have measured, for the first time, the inclusive missing-mass spectrum of the $^{12}$C$(K^-, p)$ reaction at an incident kaon momentum of 1.8 GeV/$c$ at the J-PARC K1.8 beamline. We observed a prominent quasi-elastic peak ($K^-p \rightarrow K^-p$) in this spectrum. In the quasi-elastic peak region, the effect of secondary interaction is apparently observed as a peak shift, and the peak exhibits a tail in the bound region. We compared the spectrum with a theoretical calculation based on the Green’s function method by assuming different values of the parameters for the $\bar{K}$–nucleus optical potential. We found that the spectrum shape in the binding-energy region $-300 \, \text{MeV} &amp;lt; B_{K} &amp;lt; 40$ MeV is best reproduced with the potential depths $V_0 = -80$ MeV (real part) and $W_0 = -40$ MeV (imaginary part). On the other hand, we observed a significant event excess in the deeply bound region around $B_{K} \sim 100$ MeV, where the major decay channel of $K^- NN \to \pi\Sigma N$ is energetically closed, and the non-mesonic decay modes ($K^- NN \to \Lambda N$ and $\Sigma N$) should mainly contribute. The enhancement is fitted well by a Breit–Wigner function with a kaon-binding energy of 90 MeV and width 100 MeV. A possible interpretation is a deeply bound state of a $Y^{*}$-nucleus system.

Lepton scattering fromAr40andTi48in the quasielastic peak region

Neutron and proton spectral functions of $^{40}$Ar, $^{40}$Ca, and $^{48}$Ti isotopes are computed using the ab initio self-consistent Green's function approach. The resulting radii and charge distributions are in good agreement with available experimental data. The spectral functions of Ar and Ti are then utilized to calculate inclusive ($e$,$e$') cross sections within a factorization scheme and are found to correctly reproduce the recent Jefferson Lab measurements. Based on these successful agreements, the weak charged and neutral current double-differential cross sections for neutrino-$^{40}$Ar scattering are predicted in the quasielastic region. Results obtained by replacing the (experimentally inaccessible) neutron spectral distribution of $^{40}$Ar with the (experimentally accessible) proton distribution of $^{48}$Ti are compared and the accuracy of this approximation is assessed.

Asymmetric relativistic Fermi gas model for quasielastic lepton-nucleus scattering

We develop an asymmetric relativistic Fermi gas model for the study of the electroweak nuclear response in the quasielastic region. The model takes into account the differences between neutron and proton densities in asymmetric (N > Z) nuclei, as well as differences in the neutron and proton separation energies. We present numerical results for both neutral and charged current processes, focusing on nuclei of interest for ongoing and future neutrino oscillation experiments. We point out some important differences with respect to the commonly employed symmetric Fermi gas model.

Relativistic effects in ab initio electron-nucleus scattering

The electromagnetic responses obtained from Green's function Monte Carlo (GFMC) calculations are based on realistic treatments of nuclear interactions and currents. The main limitations of this method comes from its nonrelativistic nature and its computational cost, the latter hampering the direct evaluation of the inclusive cross sections as measured by experiments. We extend the applicability of GFMC in the quasielastic region to intermediate momentum transfers by performing the calculations in a reference frame that minimizes nucleon momenta. Additional relativistic effects in the kinematics are accounted for employing the two-fragment model. In addition, we developed a novel algorithm, based on the concept of first-kind scaling, to compute the inclusive electromagnetic cross section of $^4$He through an accurate and reliable interpolation of the response functions. A very good agreement is obtained between theoretical and experimental cross sections for a variety of kinematical setups. This offers a promising prospect for the data analysis of neutrino-oscillation experiments that requires an accurate description of nuclear dynamics in which relativistic effects are fully accounted for.

Intercomparison of lepton-nucleus scattering models in the quasielastic region

We present a discussion of models of nuclear effects used to describe an inclusive electron-nucleus scattering in the quasielastic (QE) peak region, aiming to compare them and draw conclusion of their reliability when applied in neutrino-nucleus interactions. A basic motivation is to reduce systematic errors in neutrino oscillation experiments. We concentrate on the neutrino energy profile of the T2K experiment, which provides us a region of the greatest importance in terms of the highest contribution to the charge-current quasielastic (CCQE) cross section. We choose only electron-nucleus data that overlaps with this region. In order to clearify the analysis, we split the data sets into three groups and draw conclusion separately from each one of them. We selected six models for this comparison: Benhar's spectral function with and without final state interaction (Benhar's SF+FSI), Valencia spectral function (Valencia SF), for higher energy transfer only with the hole spectral function; GiBUU and also the local and global Fermi gas models. The latter two are included as a benchmark to quantify the effect of various nuclear effects. All the six models are often used in neutrino scattering studies. A short theoretical description of each model is given. Although in the selected data sets the QE mechanism dominates, we also briefly discuss a possible impact of $2p2h$ and $\Delta$ contributions.

Extraction of structure functions for lepton-nucleus scattering in the quasi-elastic region

Extraction of structure functions for lepton-nucleus scattering in the quasi-elastic region

Broadband light scattering spectroscopy utilizing an ultra-narrowband holographic notch filter

The broadband spectroscopic analysis over Brillouin, quasi-elastic, and Raman regions arising from the same position of the sample has been achieved by employing an ultra-narrowband holographic notch filter (HNF) and an optical isolator. Recently, HNFs are often employed to reject strong elastic scattering in low-frequency Raman experiments. Meanwhile, the rejected spectral component agrees with the frequency range that can be observed by a triple-pass tandem Fabry–Pérot interferometer. Thus the broadband spectroscopy can be accomplished by introducing the rejected light to the interferometer. This system, in combination with the local symmetry analysis by polarization-direction-resolved Raman spectroscopy, is particularly advantageous for the investigation of spatially inhomogeneous systems.

Relativity versus exchange currents inO16(e,e′p)

The 16O(e,e'p) reaction in the quasi-elastic region has been studied in several experiments to determine spectroscopic factors, hence, the degree to which $^{16}$O looks like a closed shell. By varying the kinematics, experimentalists are able to extract response functions which comprise the cross section. However, analysis of the response functions separately produces very different spectroscopic factors. Two calculations led to different conclusions as to whether exchange currents can eliminate the discrepancies. Neither calculation considered relativistic corrections. The purpose of the article is to investigate the disagreement as to whether exchange currents are the solution to obtaining consistent spectroscopic factors, and to show that relativistic corrections have a much greater influence on providing this consistency. This calculation employs the recoil corrected continuum shell model, a model that uses a realistic interaction, and produces non-spurious scatterings states that are solutions to the coupled channels problems. Pionic and pair contributions to the exchange currents were calculated as developed by Dubach, Koch, and Donnelly. Relativistic effects are included by use of the direct Pauli reduction. Contributions of the exchange currents are shown to be insufficient to provide consistent spectroscopic factors. However, the inclusion of relativistic corrections, that can be large, lead to more consistent spectroscopic factors and cross sections. The influence of channel coupling is also shown to be significant. Tests of current conservation show that inclusion of the direct Pauli reduction produces small increases in its violation. Response functions which depend on the transverse current are sensitive to the lower component of relativistic wave functions, and hence, would provide a measure of the appropriateness of any relativistic model.

The effects of density-dependent form factors for (e, e’p) reaction in quasi-elastic region

Within the framework of a relativistic single particle model, the effects of density-dependent electromagnetic form factors on the exclusive $ (e,e'p)$ reaction are investigated in the quasi-elastic region. The density-dependent electromagnetic form factors are generated from a quark-meson coupling model and used to calculate the cross sections in two different densities, either at the normal density of $ \rho_0 \sim 0.15$ fm^-3 or at the lower density, $ 0.5\rho_0$ . Then these cross sections are analyzed in the two different kinematics: One is that the momentum of the outgoing nucleon is along the momentum transfer. The other is that the angle between the momentum of the outgoing nucleon and the momentum transfer is varied at fixed magnitude of the momentum of the outgoing nucleon. Our theoretical differential reduced cross sections are compared with the NIKHEF data for the 208 Pb(e, e’p) reaction, which is related to the probability that a bound nucleon from a given orbit can be knocked-out of the nucleus. The effects of the density-dependent form factors increase the differential cross sections for both knocked-out proton and neutron by an amount of a few percent. Moreover they are shown to be almost the same within only a few percent, i.e., nearly independent of the shell location of knockout nucleons. These results are quite consistent with the characteristics of double magic nuclei which have relatively sharp smearing in the density distribution.