Density-dependent Form Factors Research Articles

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.

Density dependence of parity violation in electron quasi-elastic scattering

Within the framework of a relativistic single-particle model, we investigate the effect of the density dependent form factor on parity violating electron scattering from a heavy nucleus in the quasielastic region through the leading order of the interference of the electromagnetic current and the electro-weak neutral current. 208Pb is used as a target nucleus in the incident electron energy range up to 1 GeV. The density-dependent form factors are obtained from a quark-meson coupling model. The sensitivities of the density-dependence are studied separately for each Dirac (F 1), Pauli (F 2), and axial (G A ) form factors. The density enhances the parity violation asymmetry, in particular, in the forward angle region, and the density dependence turns out to be most sensitive to the Pauli form factor.

In-medium effect with muon-neutrino and anti-muon-neutrino quasi-elastic scattering from 12C nucleons

We investigated the in-medium effect by density-dependent axial and weak-vector form factors on muon-neutrino () and anti-muon-neutrino scattering in the quasi-elastic (QE) region from nucleons (N*) bound in a nucleus or immersed in a nuclear medium via neutral current (NC) and charged current (CC). For the density-dependent form factors, we exploited a quark–meson-coupling (QMC) model. We found that the scattering cross sections via NC in the QE region usually decrease with an increased medium density, while those using CC were increased. However, their rate of change was sensitive to the four-momentum transfer given to a bound nucleon through scattering. We compared these results obtained by the elementary process corrected by the in-medium effect to the BNL and MiniBooNE data, which measured scattering cross sections per nucleon through – 12C scattering in 12C composite targets. The incident energy range was 550 3000 MeV. We increased the energy up to 100 GeV to compare our results to the NOMAD experimental data. In order to study the density effects on a nucleon embedded in 12C, we exploited the QMC form factors evaluated at , where the normal density . The strangeness contributions in NC scattering are also incorporated into the form factors for comparison with experimental data. Our numerical results show that most of the experimental data can be explained in a satisfactory manner by the density-dependent elementary process, but there are some remaining deviations resulting from the nuclear structure, particularly in the low and high momentum-transfer regions.

Effect of Density-Dependent Form Factors on Coulomb Sum Rule in the Quasi-Elastic Region

Within the framework of a relativistic single particle model, we study the effects of density-dependent electromagnetic form factors on the inclusive (e,e′) reaction in the quasi-elastic region. The density-dependent form factors generated by a quark-meson coupling model are applied into the (e,e′) reaction. We calculate the differential cross sections, and extract the longitudinal and transverse structure functions. Furthermore the Coulomb sum is calculated in terms of three momentum transfer from 40Ca. The effects of the density-dependent form factors reduce the longitudinal structure function by amount of a few percent but increase the transverse structure function about 10%, consequently the (e,e′) differential cross sections are enhanced.

Effects of density-dependent weak form factors on charged-current neutrino-nucleus scattering in the quasi-elastic region

We study the effects of density-dependent electromagnetic, axial, and weak vector form factors on the inclusive $(e,{e}^{\ensuremath{'}})$ reaction and the charged-current neutrino-nucleus scattering in the quasi-elastic region within the framework of a relativistic single-particle model. The density-dependent form factors obtained from a quark-meson coupling model are applied into the $(e,{e}^{\ensuremath{'}})$ reaction and the neutrino-nucleus scattering via charged current. The effects of the density-dependent form factors increase the $(e,{e}^{\ensuremath{'}})$ cross sections by a few percent. However, the effects may reduce the differential cross sections up to 20% (60%) at $\ensuremath{\rho}=1.0{\ensuremath{\rho}}_{0}\phantom{\rule{4pt}{0ex}}(2.0{\ensuremath{\rho}}_{0})$ for the antineutrino scattering and also reduce the cross section up to 20% (30%) at $\ensuremath{\rho}=1.0{\ensuremath{\rho}}_{0}\phantom{\rule{4pt}{0ex}}(2.0{\ensuremath{\rho}}_{0})$ for the neutrino scattering around the peak positions, where the normal density is ${\ensuremath{\rho}}_{0}\ensuremath{\sim}0.15$ ${\mathrm{fm}}^{\ensuremath{-}3}$. For the density of finite nuclei such as $^{12}\mathrm{C}$, $^{40}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$ as 0.6, 0.7, and 1.0 of ${\ensuremath{\rho}}_{0}$, the in-medium effects are 20% to 30%, even in the antineutrino case. Our theoretical double-differential and total cross sections are compared with the recent MiniBooNE data for $^{12}\mathrm{C}({\ensuremath{\nu}}_{\ensuremath{\mu}},{\ensuremath{\mu}}^{\ensuremath{-}})$ scattering.

Asymmetry in the neutrino and anti-neutrino reactions in a nuclear medium

We study the effect of the density-dependent axial and vector form factors on the electron–neutrino (νe) and anti-neutrino (ν¯e) reactions for a nucleon in nuclear matter or in 12C. 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 νe and ν¯e induced reactions with the initial energy E=8–80 MeV. We find that the total νe cross sections on 12C as well as on a nucleon in nuclear matter are reduced by about 5% at the nuclear saturation density, ρ0. 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 ν-reaction. In contrast, the density effect on the ν¯e reaction reduces the cross section significantly in both nuclear matter and 12C cases, and the amount maximally becomes of about 35% around ρ0. Such large asymmetry in the νe and ν¯e cross sections, which seems to be nearly independent of the target, is originated from the differences in the helicities of ν¯e and νe. It is expected that the asymmetry influences the r-process and also the neutrino-process nucleosynthesis in core-collapse supernovae.

Off-shell and medium effects on the electromagnetic nucleon current

Ambiguities in the nuclear electromagnetic current operator within the nuclear medium are used to examine the significance of the off-shell form of the current operator for the case of40Ca. The standard form of the electromagnetic current operator and two alternate forms, one of which is the popular de Forest prescription, are used to study current operator ambiguities in the context of the quasi-elastic (e, e′) and (e, e′p) reactions in the presence of realistic final-state interactions. Nucleons may themselves be modified in the nuclear medium and the associated modification of the current operator, which has been modelled through the use of density-dependent form factors, is studied here in the (e, e′p) reaction. For the quasi-elastic inclusive reaction we find large current-operator-dependent effects in both the longitudinal and transverse response. For the transverse response these effects are clearly linked to the nature of the final-state interactions and are traced to virtual pair processes present in the relativistic case. In particular, the de Forest current yields a greatly enhanced transverse response and a large high-energy tail in the relativistic case. Current operator ambiguities do not seriously affect Coulomb Sum Rule saturation trends and produce less dramatic effects for the exclusive (e, e′p) reaction. Our results suggest that present knowledge of the nucleon electromagnetic current operator is insufficient to allow firm predictions of the electronuclear reactions to be made to the precision required to resolve other physical issues.