Figure 1

Diagrammatic representation of the neutrino self-energy in nuclear matter.Reuse & Permissions

Figure 2

Diagrammatic representation of some diagrams contributing to the $W^{+}$ self-energy.Reuse & Permissions

Figure 3

Set of irreducible diagrams responsible for the polarization (RPA) effects in the 1p1h contribution to the $W$ self-energy.Reuse & Permissions

Figure 4

$W^{+}$ self-energy diagram obtained from the first diagram depicted in Fig. 2 by dressing up the nucleon propagator of the particle state in the ph excitation.Reuse & Permissions

Figure 5

Insertion of the nucleon self-energy on the nucleon line of the particle state.Reuse & Permissions

Figure 6

Diagrammatic representation of the muon (at rest) self-energy in nuclear matter.Reuse & Permissions

Figure 7

Predictions for the LSND measurement of the ${}^{12}\mathrm{C}$ $({\nu }_{\mu },{\mu }^{-})X$ reaction (left panels) and the ${}^{12}\mathrm{C}$ $({\nu }_e,e^{-})X$ reaction near threshold (right panels). Results have been obtained by using nonrelativistic kinematics for the nucleons and without FSI. Top: ${\nu }_{\mu }$ and ${\nu }_e$ cross sections multiplied by the neutrino fluxes, as a function of the neutrino energy. In addition to the RPA calculation (solid line), we show results without RPA correlations and Coulomb corrections (dotted line), and also (dashed line) the low-density limit of Eq. (31). Middle: Differential muon and electron neutrino cross sections at $E_{{\nu }_{\mu }}=179.5\mathrm{MeV}$ (left) and $E_{{\nu }_e}=46.2\mathrm{MeV}$ (right), as a function of the energy transfer. Bottom: Neutrino spectra from Ref. 50 (left) and Eq. (65) (right).Reuse & Permissions

Figure 8

Inclusive muon capture differential width from ${}^{12}\mathrm{C}$, as a function of the outgoing neutrino energy (top axis) and of the energy transfer (bottom axis). Nonrelativistic kinematics has been used for the nucleons. The two calculations are labeled as in Table .Reuse & Permissions

Figure 9

RPA and Coulomb (CB) corrections to electron and muon neutrino and antineutrino QE cross sections for different nuclei, as a function of the neutrino energy. A relativistic treatment of the nucleons is undertaken and FSI effects are not considered. $R_{\mathrm{RPA}+\mathrm{CB}}$ is defined as $({\sigma }_{\mathrm{RPA}+\mathrm{CB}}-{\sigma }_0)∕{\sigma }_0$, where ${\sigma }_0$ does not include RPA and Coulomb corrections, while ${\sigma }_{\mathrm{RPA}+\mathrm{CB}}$ includes these nuclear effects.Reuse & Permissions

Figure 10

Electron and muon neutrino and antineutrino inclusive QE cross sections and ratios for different nuclei, at intermediate energies. Results have been obtained with the full model without FSI, and using relativistic kinematics for the nucleons. For comparison we also show results obtained in the free space [low-density limit, LDT, Eq. (31)].Reuse & Permissions

Figure 11

Muon neutrino and antineutrino relativistic QE differential cross sections from different nuclei and several ${\nu }_{\mu },{\overline{\nu }}_{\mu }$ energies. Results, denoted as “$\text{Pauli}+Q$” or “$\text{Pauli}+\overline{Q}$” have been obtained in ${}^{12}\mathrm{C}$ and do not include RPA, FSI, and Coulomb effects, while the rest of the results have been obtained with the full model without FSI.Reuse & Permissions

Figure 12

Muon neutrino differential cross sections in calcium as a function of the lepton scattering angle (top) and of the momentum transfer (bottom). The neutrino energy is $371.8\mathrm{MeV}$. Top: Cross sections, without FSI and using relativistic kinematics for the nucleons, at different muon energies. Crosses have been obtained without RPA and Coulomb effects, while the curves have been obtained with the full model (up to FSI effects). Bottom: Cross sections, for a muon energy of $228.6\mathrm{MeV}$, obtained by using relativistic (long dashed line REL) and nonrelativistic nucleon kinematics. In this latter case, we present results with (solid line, FSI) and without (short dashed line, NOREL) FSI effects. For the three cases, we also show the effect of taking into account RPA and Coulomb corrections (lower lines at the peak). The areas (in units of ${10}^{-40}{\mathrm{cm}}^2∕\mathrm{MeV}$) below the curves are 3.50 (REL), 3.87 (NOREL), and 3.77 (FSI) when RPA and Coulomb corrections are not considered, and 3.13 (REL), 3.49 (NOREL), and 3.53 (FSI) when these nuclear effects are taken into account.Reuse & Permissions

Figure 13

${\nu }_e$ and ${\overline{\nu }}_e$ differential cross sections in ${}^{16}\mathrm{O}$ as a function of the excitation energy, for fixed values of the momentum transfer and $E_{\nu ,\overline{\nu }}=400\mathrm{MeV}$. Top: Results obtained from the full relativistic model without FSI, with (RPA) and without RPA and Coulomb corrections ($\text{Pauli}+Q\left(\overline{Q}\right)$). Bottom: Results obtained by using relativistic (long dashed line, REL) and nonrelativistic nucleon kinematics. In this latter case, we present results with (solid line, FSI) and without (short dashed line, NOREL) FSI effects. For the three cases, we also show the effect of taking into account RPA and Coulomb corrections (lower lines at the peak). The areas (in units of ${10}^{-40}{\mathrm{cm}}^2∕\mathrm{MeV}$) below the curves are 1.02 (REL), 1.13 (NOREL), and 1.01 (FSI) when RPA and Coulomb corrections are not considered, and 0.79 (REL), 0.90 (NOREL), and 0.85 (FSI) when these nuclear effects are taken into account.Reuse & Permissions

Figure 14

Muon neutrino QE differential cross sections in oxygen as a function of the energy transfer. The neutrino energy is $375\mathrm{MeV}$. We show results for relativistic (long dashed line, REL) and nonrelativistic nucleon kinematics. In this latter case, we present results with (solid line, FSI) and without (short dashed line, NOREL) FSI effects. We also show the effect of RPA and Coulomb corrections (lower lines at the peak). The integrated cross sections can be found in Table .Reuse & Permissions