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.

Figure 1

Electromagnetic response functions of ${}^{40}\mathrm{Ar}$ in the SRFG and ARFG for momentum transfer $q=300$ (left column) and 800 (right column) $\mathrm{MeV}/c$. The separate contributions of protons and neutrons are also displayed.

Figure 2

Electromagnetic response functions of ${}^{208}\mathrm{Pb}$ in the SRFG and ARFG. The separate contributions of protons and neutrons are also displayed.

Figure 3

Weak NC response functions for $\nu \text{−}{}^{40}\mathrm{Ar}$ in the SRFG and ARFG. The separate contributions of protons and neutrons are also displayed.

Figure 4

Weak NC response functions for $\nu \text{−}{}^{208}\mathrm{Pb}$ in the SRFG and ARFG. The separate contributions of protons and neutrons are also displayed.

Figure 5

Neutrino charged-current weak response functions per neutron of ${}^{12}\mathrm{C}$ in the SRFG and ARFG. The ARFG results with no energy shift (see text) are also shown. Each column corresponds to a fixed value of the momentum transfer $q$.

Figure 6

Same as Fig. 5, but for the antineutrino functions.

Figure 7

Neutrino CC weak response functions per neutron of ${}^{40}\mathrm{Ar}$ in the SRFG and ARFG. The ARFG results with no energy shift (see text) are also shown. Each column corresponds to a fixed value of the momentum transfer $q$.

Figure 8

Same as Fig. 7, but for the antineutrino functions.

Figure 9

Neutrino CC weak response functions per neutron of ${}^{208}\mathrm{Pb}$ in the SRFG and ARFG. The ARFG results with no energy shift (see text) are also shown. Each column corresponds to a fixed value of the momentum transfer $q$.

Figure 10

Same as Fig. 9, but for antineutrino functions.