Neutral-current neutrino-nucleus cross sections based on relativistic nuclear energy density functional

Background: Inelastic neutrino-nucleus scattering through the weak neutral-current plays an important role in a stellar environment where the transport of neutrinos determines the rate of cooling. Since there are no direct experimental data on neutral-current neutrino-nucleus cross sections available, only the modeling of these reactions provides the relevant input for supernova simulations.

Purpose: To establish a fully self-consistent framework for neutral-current neutrino-nucleus reactions based on a relativistic nuclear energy density functional.

Methods: Neutrino-nucleus cross sections are calculated using a weak Hamiltonian and nuclear properties of initial and excited states are obtained with a relativistic Hartree-Bogoliubov model and a relativistic quasiparticle random phase approximation that is extended to include pion contributions for unnatural parity transitions.

Results: Inelastic neutral-current neutrino-nucleus cross sections for ${}^{12}$C, ${}^{16}$O, ${}^{56}$Fe, ${}^{56}$Ni, and even isotopes ${}^{92-100}$Mo as well as respective cross sections averaged over distribution of supernova neutrinos.

Conclusions: The present study provides insight into neutrino-nucleus scattering cross sections in the neutral channel, their theoretical uncertainty in view of recently developed microscopic models, and paves the way for systematic self-consistent large-scale calculations involving open-shell target nuclei.

Figure 1

Dependence of the neutrino-nucleus cross sections for the scattering process ${}^{12}$C${({\nu }_e,{\nu }_e^{\prime })}^{12}$C${}^{*}$ on the incoming neutrino energy. The cross sections with separate contributions from various multipoles $J_{\pi }=0^{\pm }$–$3^{\pm }$ and the total cross sections, including $J_{\pi }=0^{\pm }$–$5^{\pm }$ states, are shown. The overall cross sections (stars) are shown in comparison to the QRPA based results (full circles) from Ref. [38].

Figure 2

The same as in Fig. 1, but for the scattering process ${}^{40}$Ar${({\nu }_e,{\nu }_e^{\prime })}^{40}$Ar${}^{*}$. The overall cross sections (stars) are shown in comparison to the QRPA based results (full circles) from Ref. [40].

Figure 3

The same as in Fig. 1, but for the scattering process ${}^{56}$Fe${({\nu }_e,{\nu }_e^{\prime })}^{56}$Fe${}^{*}$.

Figure 4

The same as in Fig. 1, but for the scattering process ${}^{56}$Ni${({\nu }_e,{\nu }_e^{\prime })}^{56}$Ni${}^{*}$.

Figure 5

The same as in Fig. 1, but for the scattering process ${}^{98}$Mo${({\nu }_e,{\nu }_e^{\prime })}^{98}$Mo${}^{*}$.

Figure 6

Contributions of multipole transitions $J^{\pi }=0^{\pm }$–$5^{\pm }$ in the cross sections for the reaction ${}^{96}$Mo${({\nu }_e,{\nu }_e^{\prime })}^{96}$Mo${}^{*}$ at incoming electron neutrino energy $E_{{\nu }_e}=20$ MeV. The results of the present analysis (RQRPA) are compared with QRPA based calculations (Balasi et al., Ref. [37]).

Figure 7

The same as in Fig. 6, but for the neutrino energy $E_{{\nu }_e}=100$ MeV.

Figure 8

Neutral-current neutrino-nucleus cross sections averaged over the supernova neutrino flux in the temperature interval $T_{\nu }=2$–10 MeV. Results are shown for ${}^{12}$C, ${}^{40}$Ar, ${}^{56}$Fe, ${}^{56}$Ni, and ${}^{98}$Mo target nuclei.

Figure 9

The same as in Fig. 8 but for ${}^{92,94,96,98,100}$Mo target nuclei.