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The methods used in the evaluation of the neutrino-nucleus cross section are reviewed. Results are shown for a variety of targets of practical importance. Many of the described reactions are accessible in future experiments with neutrino sources from the pion and muon decays at rest, which might be available at the neutron spallation facilities. Detailed comparison between the experimental and theoretical results would establish benchmarks needed for verification and/or parameter adjustment of the nuclear models. Having a reliable tool for such calculation is of great importance in a variety of applications, e.g. the neutrino oscillation studies, detection of supernova neutrinos, description of the neutrino transport in supernovae, and description of the r-process nucleosynthesis.
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The prospects of extracting new physics signals in a coherent elastic neutrino-nucleus scattering (CE$ u$NS) process are limited by the precision with which the underlying nuclear structure physics, embedded in the weak nuclear form factor, is known. We present microscopic nuclear structure physics calculations of charge and weak nuclear form factors and CE$ u$NS cross sections on $^{12}$C, $^{16}$O, $^{40}$Ar, $^{56}$Fe and $^{208}$Pb nuclei. We obtain the proton and neutron densities, and charge and weak form factors by solving Hartree-Fock equations with a Skyrme (SkE2) nuclear potential. We validate our approach by comparing $^{208}$Pb and $^{40}$Ar charge form factor predictions with elastic electron scattering data. In view of the worldwide interest in liquid-argon based neutrino and dark matter experiments, we pay special attention to the $^{40}$Ar nucleus and make predictions for the $^{40}$Ar weak form factor and the CE$ u$NS cross sections. Furthermore, we attempt to gauge the level of theoretical uncertainty pertaining to the description of the $^{40}$Ar form factor and CE$ u$NS cross sections by comparing relative differences between recent microscopic nuclear theory and widely-used phenomenological form factor predictions. Future precision measurements of CE$ u$NS will potentially help in constraining these nuclear structure details that will in turn improve prospects of extracting new physics.
Reliable estimates of neutrino-nucleus reactions in the resonance-excitation region play an important role in many of the on-going and planned neutrino oscillation experiments. We study here neutrino-nucleus reactions in the delta-particle excitation region with the use of neutrino pion-production amplitudes calculated in a formalism in which the resonance contributions and the background amplitudes are treated on the same footing. Our approach leads to the neutrino-nucleus reaction cross sections that are significantly different from those obtained in the conventional approach wherein only the pure resonance amplitudes are taken into account. To assess the reliability of our formalism, we calculate the electron-nucleus scattering cross sections in the same theoretical framework; the calculated cross sections agree reasonably well with the existing data.
An accurate description of the nuclear response functions for neutrino scattering in the Gev region is essential for the interpretation of present and future neutrino oscillation experiments. Due to the close similarity of electromagnetic and weak scattering processes, we will review the status of the scaling approach and of relativistic modeling for the inclusive electron scattering response functions in the quasielastic and $Delta$-resonance regions. In particular, recent studies have been focused on scaling violations and the degree to which these imply modifications of existing predictions for neutrino reactions. We will discuss sources and magnitude of such violations, emphasizing similarities and differences between electron and neutrino reactions.
We have constructed an empirical formulae for the fusion and interaction barriers using experimental values available till date. The fusion barriers so obtained have been compared with different model predictions based on the proximity, Woods-Saxon and double folding potentials along with several empirical formulas, time dependent Hartree-Fock theories, and the experimental results. The comparison allows us to find the best model, which is nothing but the present empirical formula only. Most remarkably, the fusion barrier and radius show excellent consonance with the experimental findings for the reactions meant for synthesis of the superheavy elements also. Furthermore, it is seen that substitution of the predicted fusion barrier and radius in classic Wong formula [C. Wong, Phys. Rev. Lett. {31}, 766 (1973)] for the total fusion cross sections satisfies very well with the experiments. Similarly, current interaction barrier predictions have also been compared well with a few experimental results available and Bass potential model meant for the interaction barrier predictions. Importantly, the present formulae for the fusion as well as interaction barrier will have practical implications in carrying out the physics research near the Coulomb barrier energies. Furthermore, present fusion barrier and radius provide us a good nucleus-nucleus potential useful for numerous theoretical applications.
We study the effect of the density-dependent axial and vector form factors on the electro-neutrino ($ u_e$) and anti-neutrino $({bar u}_e)$ reactions for a nucleon in nuclear matter or in $^{12}$C. The nucleon form factors in free space are presumed to be modified for a bound nucleon in a nuclear medium. We adopt the density-dependent form factors calculated by the quark-meson coupling (QMC) model, and apply them to the $ u_e$ and ${bar u}_e$ induced reactions with the initial energy $E = $ 8 $sim$ 80 MeV. We find that the total ${ u}_e$ cross sections on $^{12}$C as well as a nucleon in nuclear matter are reduced by about 5% at the nuclear saturation density, $rho_0$. This reduction is caused by the modification of the nucleon structure in matter. Although the density effect for both cases is relatively small, it is comparable with the effect of Coulomb distortion on the outgoing lepton in the $ u$-reaction. In contrast, the density effect on the ${bar u}_e$ reaction reduces the cross section significantly in both nuclear matter and $^{12}$C cases, and the amount maximally becomes of about 35% around $rho_0$. Such large asymmetry in the $ u_e$ and ${bar u}_e$ cross sections, which seems to be nearly independent of the target, is originated from the difference in the helicities of ${bar u}_e$ and ${ u}_e$. It is expected that the asymmetry influences the r-process and also the neutrino-process nucleosynthesis in core-collapse supernovae.
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