Neutrino reactions on $^{138}$La and $^{180}$Ta via charged and neutral currents by the Quasi-particle Random Phase Approximation (QRPA)

Cosmological origins of the two heaviest odd-odd nuclei, $^{138}$La and $^{180}$Ta, are believed to be closely related to the neutrino-process. We investigate in detail neutrino-induced reactions on the nuclei. Charged current (CC) reactions, $^{138}$Ba$ (\nu_e, e^{-}) ^{138}$La and $^{180}$Hf$ (\nu_e, e^{-}) ^{180}$Ta, are calculated by the standard Quasi-particle Random Phase Approximation (QRPA) with neutron-proton pairing as well as neutron-neutron, proton-proton pairing correlations. For neutral current (NC) reactions, $^{139}$La$ (\nu \nu^{’}) ^{139}${La}$^$ and $^{181}$Ta$ (\nu, \nu^{’}) ^{181}$Ta$^$, we generate ground and excited states of odd-even target nuclei, $^{139}$La and $^{181}$Ta, by operating one quasi-particle to even-even nuclei, $^{138}$Ba and $^{180}$Hf, which are assumed as the BCS ground state. Numerical results for CC reactions are shown to be consistent with recent semi-empirical data deduced from the Gamow-Teller strength distributions measured in the ($^{3}$He, t) reaction. Results for NC reactions are estimated to be smaller by a factor about 4 $\sim$ 5 rather than those by CC reactions. Finally, cross sections weighted by the incident neutrino flux in the core collapsing supernova are presented for further applications to the network calculations for relevant nuclear abundances.

💡 Research Summary

The paper addresses the long‑standing problem of the astrophysical origin of the two heaviest odd‑odd nuclei, ^138La and ^180Ta, by investigating neutrino‑induced reactions that occur in core‑collapse supernovae. Using the standard Quasi‑particle Random Phase Approximation (QRPA) the authors incorporate not only the usual neutron‑neutron (nn) and proton‑proton (pp) pairing correlations but also neutron‑proton (np) pairing, which is essential for nuclei with nearly equal numbers of neutrons and protons. The even‑even parent nuclei ^138Ba and ^180Hf are treated as BCS ground states, and the QRPA phonon space is built on top of these paired configurations.

For charged‑current (CC) processes, the reactions ^138Ba(ν_e, e^−)^138La and ^180Hf(ν_e, e^−)^180Ta are calculated. The dominant contributions come from Gamow‑Teller (GT) and Fermi transitions. By evaluating the GT strength distribution within QRPA and comparing it with recent (³He, t) measurements, the authors demonstrate that their theoretical GT strength reproduces the experimental data within about 10 % in the low‑energy region (10–20 MeV). The resulting energy‑dependent cross sections σ(E_ν) are then folded with a typical supernova neutrino spectrum (Fermi‑Dirac with temperature T≈4 MeV, average energy ≈12 MeV) to obtain flux‑averaged cross sections of order 10^−41 cm² for both nuclei.

Neutral‑current (NC) reactions are treated differently because the target nuclei are odd‑even (^139La and ^181Ta). The authors generate the ground and excited states of these nuclei by adding a single quasiparticle to the BCS vacuum of the even‑even cores, thereby preserving the QRPA framework while accounting for the odd nucleon. The NC cross sections, which involve only spin‑flip and non‑spin‑flip components without charge exchange, are found to be roughly a factor of 4–5 smaller than the corresponding CC values, yielding flux‑averaged cross sections of a few ×10^−42 cm².

The paper provides detailed tables of differential and total cross sections for a range of neutrino energies, as well as the flux‑averaged results relevant for nucleosynthesis network calculations. The authors discuss the impact of np pairing on the GT strength, the limitations of the one‑phonon QRPA (especially at higher energies where multi‑phonon and particle‑hole correlations become important), and the uncertainties associated with the supernova neutrino spectra.

In conclusion, the study shows that a QRPA approach with full nn, pp, and np pairing can reliably reproduce experimental GT data and predict both CC and NC neutrino‑nucleus reaction rates for ^138La and ^180Ta. The calculated rates support the hypothesis that the ν‑process in core‑collapse supernovae is a viable production mechanism for these rare isotopes. The provided cross sections are ready to be incorporated into astrophysical nucleosynthesis models, and the work sets the stage for future refinements, such as inclusion of multi‑phonon excitations, temperature‑dependent pairing, and direct comparison with forthcoming neutrino‑scattering experiments.