Global relativistic folding optical potential and the relativistic Green's function model

Optical potentials provide critical input for calculations on a wide variety of nuclear reactions, in particular, for neutrino-nucleus reactions, which are of great interest in the light of the new neutrino oscillation experiments. We present the global relativistic folding optical potential (GRFOP) fits to elastic proton scattering data from ${}^{12}\mathrm{C}$ nucleus at energies between 20 and 1040 MeV. We estimate observables, such as the differential cross section, the analyzing power, and the spin rotation parameter, in elastic proton scattering within the relativistic impulse approximation. The new GRFOP potential is employed within the relativistic Green's function model for inclusive quasielastic electron scattering and for (anti)neutrino-nucleus scattering at MiniBooNE kinematics.

Figure 1

(a) The proton and neutron scalar and vector densities obtained and used in our analysis. (b) The elastic electron scattering cross sections from ${}^{12}\mathrm{C}$ in DWBA. The experimental data are from Refs. [76, 77].

Figure 2

Differential cross section for the elastic scattering of protons with $T_p=20–1040$ MeV from ${}^{12}\mathrm{C}$. The dash-dotted curves display our predictions obtained using the GRFOP. The results obtained with EDAI (dashed line) and EDAD1 (solid line) are also shown for a comparison.

Figure 3

Analyzing power for the elastic scattering of protons with $T_p=20–800$ MeV from ${}^{12}\mathrm{C}$. Line convention is as in Fig. 2.

Figure 4

Spin rotation parameter for the elastic scattering of protons with $T_p=20–800$ MeV from ${}^{12}\mathrm{C}$. Line convention is as in Fig. 2.

Figure 5

The real scalar and vector optical potentials for ${}^{12}\mathrm{C}$ at $T_p=50$ MeV (a), 200 MeV (b) 500 MeV (c), and 1000 MeV (d): EDAI, dashed lines; EDAD1, solid lines; and GRFOP, dash-dotted lines. The corresponding imaginary parts are shown in panels $\left({\mathrm{a}}^{\prime }\right)–\left({\mathrm{d}}^{\prime }\right)$.

Figure 6

Differential cross section of the ${}^{12}\mathrm{C}(e,e^{\prime })$ reaction for different beam energies and electron scattering angles. Experimental data are from Refs. [89, 90, 91].

Figure 7

Longitudinal contributions to the scaling function for $q=500$ and 1000 MeV/$c$ compared with the averaged experimental scaling function.

Figure 8

Flux-averaged double-differential cross section per target nucleon for the CCQE ${}^{12}\mathrm{C}({\nu }_{\mu },{\mu }^{-})$ reaction as a function of the muon kinetic energy $T_{\mu }$ for three bins of the muon scattering angle $cos\vartheta$ calculated with the RGF-GRFOP (dot-dashed lines), the RGF-EDAD1 (solid lines), and the RGF-EDAI (dashed lines). The experimental data are from the MiniBooNE Collaboration [57].

Figure 9

The same as in Fig. 8, but for ${\overline{\nu }}_{\mu }$ scattering. The experimental data are from the MiniBooNE Collaboration [55].

Figure 10

Total CCQE cross section per target nucleon as a function of the neutrino energy $E_{\nu }$ (upper panel) and of the antineutrino energy $E_{\overline{\nu }}$ (lower panel) calculated with the RGF-GRFOP (dot-dashed lines), the RGF-EDAD1 (solid lines), and the RGF-EDAI (dashed lines). The experimental data are from the MiniBooNE Collaboration [55, 57].

Figure 11

Neutrino and antineutrino NCE flux-averaged cross section per target nucleon as a function of $Q^2$ calculated with the RGF-GRFOP (dot-dashed lines), the RGF-EDAD1 (solid lines), and the RGF-EDAI (dashed lines). The experimental data are from the MiniBooNE Collaboration [56, 58].

Figure 12

Ratio of the antineutrino to neutrino NCE scattering cross section in MiniBooNE with total error. The experimental data are from the MiniBooNE Collaboration [56, 58].