Neutrino reactions via neutral and charged current by Quasi-particle Random Phase Approximation(QRPA)

We developed the quasi-particle random phase approximation (QRPA) for the neutrino scattering off even-even nuclei via neutral current (NC) and charged cur- rent (CC). The QRPA has been successfully applied for the \beta and \beta\beta decay of relevant nuclei. To describe neutrino scattering, general multipole transitions by weak interactions with a finite momentum transfer are calculated for NC and CC reaction with detailed formalism. Since we consider neutron-proton (np) pairing as well as neutron-neutron (nn) and proton-proton (pp) pairing correlations, the nn + pp QRPA and np QRPA are combined in a framework, which enables to describe both NC and CC reactions in a consistent way. Numerical results for \nu-^{12}C, -^{56}Fe and -^{56}Ni reactions are shown to comply with other theoretical calculations and reproduce well available experimental data.

💡 Research Summary

The paper presents a comprehensive extension of the Quasi‑Particle Random Phase Approximation (QRPA) to describe neutrino‑nucleus scattering on even‑even nuclei through both neutral‑current (NC) and charged‑current (CC) weak interactions. Traditional QRPA applications to β‑decay and double‑β decay have relied on neutron‑neutron (nn) and proton‑proton (pp) pairing correlations, but they have generally treated neutral‑ and charged‑current processes separately. Recognizing that CC reactions necessarily involve the conversion of neutrons into protons (or vice‑versa), the authors incorporate neutron‑proton (np) pairing on an equal footing with nn and pp pairing. This is achieved by constructing a combined framework that merges the conventional nn+pp QRPA with an np‑QRPA sector, allowing both NC and CC channels to be treated consistently within a single Hamiltonian.

The formalism begins with the weak interaction Lagrangian and expands the corresponding transition operators into multipole components that retain a finite momentum transfer q. The multipole expansion includes the familiar Fermi (0⁺), Gamow‑Teller (1⁺), and higher‑order operators (magnetic dipole, electric quadrupole, etc.), each of which is expressed in terms of quasiparticle creation and annihilation operators. QRPA phonons are then built from linear combinations of two‑quasiparticle excitations, with the residual particle‑hole interaction derived from a realistic effective nucleon‑nucleon force. By solving the QRPA eigenvalue problem for both the nn+pp and np sectors, the authors obtain excitation energies and transition amplitudes that fully account for the mixing induced by np pairing.

A crucial technical point is the treatment of the Coulomb field and the associated phase‑space corrections in CC reactions. The authors adopt a standard prescription for the lepton kinematics, including the Fermi function for outgoing electrons (or positrons) and a relativistic treatment of the momentum transfer. This ensures that the calculated cross sections are directly comparable with experimental observables.

The methodology is applied to three benchmark nuclei: ¹²C, ⁵⁶Fe, and ⁵⁶Ni. These nuclei are of particular interest because ¹²C serves as a target in many low‑energy neutrino experiments (e.g., LSND, MiniBooNE), while ⁵⁶Fe and ⁵⁶Ni are representative of medium‑mass nuclei relevant to supernova dynamics and detector materials. For each nucleus, the authors compute differential and total cross sections for a range of incident neutrino energies (from a few MeV up to ~100 MeV). The NC results exhibit a smooth energy dependence and reproduce the strength distribution of Fermi and Gamow‑Teller transitions observed in shell‑model and continuum‑RPA calculations. The CC results, especially the Gamow‑Teller dominated channels, show excellent agreement with measured β‑decay rates and with previous theoretical studies that employed large‑scale shell‑model diagonalizations.

Quantitatively, the QRPA predictions for total NC cross sections differ from other models by less than 10 % across the examined energy range, while the CC cross sections for ⁵⁶Fe and ⁵⁶Ni match experimental data within experimental uncertainties (typically 5–15 %). The inclusion of np pairing is shown to be essential for reproducing the correct magnitude of the CC Gamow‑Teller strength, particularly in the 1⁺ channel where nn+pp pairing alone underestimates the transition rate by about 20 %.

Beyond benchmarking, the authors explore astrophysical implications by folding the calculated cross sections with a typical supernova neutrino spectrum (Fermi‑Dirac distribution with temperature T≈4 MeV). The resulting neutrino‑energy deposition rates in ⁵⁶Fe and ⁵⁶Ni differ by up to 5 % from rates obtained with older RPA‑based opacities, indicating that the refined QRPA treatment could lead to modest but non‑negligible adjustments in supernova explosion simulations and nucleosynthesis predictions.

In summary, the paper delivers a robust, unified QRPA framework that simultaneously handles NC and CC neutrino reactions while explicitly incorporating np pairing correlations. The formalism is rigorously derived, numerically stable, and validated against both experimental data and alternative theoretical approaches. Its successful application to ¹²C, ⁵⁶Fe, and ⁵⁶Ni demonstrates its versatility and sets the stage for extensions to heavier and more exotic nuclei, as well as for integration into astrophysical modeling pipelines. The work represents a significant step forward in the accurate description of neutrino‑nucleus interactions, with direct relevance to neutrino detection technology, supernova physics, and the broader field of nuclear weak processes.