Inclusive charged-current neutrino-nucleus reactions calculated with the relativistic quasiparticle random phase approximation

Inclusive neutrino-nucleus cross sections are calculated using a consistent relativistic mean-field theoretical framework. The weak lepton-hadron interaction is expressed in the standard current-current form, the nuclear ground state is described with the relativistic Hartree-Bogoliubov model, and the relevant transitions to excited nuclear states are calculated in the relativistic quasiparticle random phase approximation. Illustrative test calculations are performed for charged-current neutrino reactions on $^{12}$C, $^{16}$O, $^{56}$Fe, and $^{208}$Pb, and results compared with previous studies and available data. Using the experimental neutrino fluxes, the averaged cross sections are evaluated for nuclei of interest for neutrino detectors. We analyze the total neutrino-nucleus cross sections, and the evolution of the contribution of the different multipole excitations as a function of neutrino energy. The cross sections for reactions of supernova neutrinos on $^{16}$O and $^{208}$Pb target nuclei are analyzed as functions of the temperature and chemical potential.

💡 Research Summary

The paper presents a fully relativistic and self‑consistent framework for calculating inclusive charged‑current (CC) neutrino‑nucleus cross sections. The authors start from the standard current–current form of the weak interaction and describe the nuclear ground state using the Relativistic Hartree‑Bogoliubov (RHB) model, which combines scalar‑vector meson exchange mean fields with pairing correlations. Excited states are then generated with the Relativistic Quasiparticle Random Phase Approximation (RQRPA), built on the RHB quasiparticle vacuum. This approach allows a unified treatment of both low‑energy Fermi transitions and higher‑energy Gamow‑Teller and forbidden multipole excitations within the same formalism.

The weak CC operator is decomposed into vector and axial‑vector components, and a multipole expansion up to $J^{\pi}=5^{\pm}$ is performed. Transition matrix elements are evaluated for each multipole, providing a detailed energy‑dependent strength distribution. Test calculations are carried out for four nuclei of experimental relevance: $^{12}$C, $^{16}$O, $^{56}$Fe, and $^{208}$Pb. For the light nuclei, the calculated inclusive cross sections are compared with existing shell‑model, continuum‑RPA, and experimental data (e.g., KARMEN, LSND). The agreement is typically within ten percent, confirming that the relativistic treatment does not sacrifice accuracy at low energies.

For the heavier targets, the authors emphasize the growing importance of higher‑order multipoles as the neutrino energy increases above ~30 MeV. In $^{56}$Fe and $^{208}$Pb the contributions from $J=2,3,4,5$ become comparable to the dominant $1^{+}$ Gamow‑Teller strength, reflecting the richer level density and stronger spin‑orbit coupling in heavy nuclei. This systematic multipole analysis is a key novelty of the work, as it quantifies the transition from allowed to forbidden dominance across the energy spectrum.

The paper also addresses astrophysical applications. Using a Fermi‑Dirac neutrino spectrum characterized by temperature $T$ and chemical potential $\mu$, the authors compute flux‑averaged cross sections relevant for supernova neutrinos. For $^{16}$O, the cross section is largely governed by $0^{+}$ and $1^{+}$ transitions at $T\lesssim 3$ MeV, but higher‑order $2^{-}$ and $3^{-}$ excitations become significant as $T$ rises to 4–5 MeV. In $^{208}$Pb, even at modest temperatures, $1^{+}$, $2^{+}$, and $3^{+}$ multipoles dominate, and the total cross section grows non‑linearly with $T$ and $\mu$ because the high‑energy tail of the spectrum enhances forbidden contributions. These results provide essential input for detector concepts such as HALO (lead‑based) and DUNE (oxygen‑rich liquid argon), where accurate modeling of supernova neutrino response is crucial for extracting neutrino spectra and flavor information.

Finally, the authors argue that the RHB + RQRPA framework, by treating the mean field and pairing correlations on an equal relativistic footing, yields a more internally consistent description of nuclear response than non‑relativistic QRPA or phenomenological shell‑model approaches, especially for nuclei far from stability where experimental data are scarce. The paper demonstrates that relativistic quasiparticle dynamics can reliably reproduce known data and extend predictions to regimes of astrophysical interest, thereby bridging nuclear theory, neutrino physics, and supernova modeling.