Uncertainties in modeling low-energy neutrino-induced reactions on iron-group nuclei

Charged-current neutrino-nucleus cross sections for ${}^{54,56}$Fe and ${}^{58,60}$Ni are calculated and compared using frameworks based on relativistic and Skyrme energy-density functionals and on the shell model. The current theoretical uncertainties in modeling neutrino-nucleus cross sections are assessed in relation to the predicted Gamow-Teller transition strength and available data, to multipole decomposition of the cross sections, and to cross sections averaged over the Michel flux and Fermi-Dirac distribution. By employing different microscopic approaches and models, the decay-at-rest (DAR) neutrino-${}^{56}$Fe cross section and its theoretical uncertainty are estimated to be ${\langle \sigma \rangle }_{\mathrm{th}}=(258\pm 57)\times {10}^{-42}{\mathrm{cm}}^2$, in very good agreement with the experimental value ${\langle \sigma \rangle }_{\exp }=(256\pm 108\pm 43)\times {10}^{-42}{\mathrm{cm}}^2$.

Figure 1

GT${}^{-}$ transition strength in ${}^{56}$Fe, calculated using the RQRPA (DD-ME2) and the shell model (GXPF1J).

Figure 2

GT${}^{-}$ transition strengths calculated with the Skyrme RPA (SGII, SLy5) and the RQRPA (DD-ME2), in comparison to the shell model (GXPF1J) [13] and experimental values [29]. (Q)RPA calculations include a quenching factor of 0.8 in the axial-vector coupling constant $g_A$.

Figure 3

Same as described in the caption to Fig. 2 but for the GT${}^{+}$ transitions. Experimental values are from Refs. [30, 31, 32].

Figure 4

Contributions of the multipole transitions ${\lambda }^{\pi }=0^{\pm }$–$4^{\pm }$ to the inclusive cross section for the ${}^{56}$Fe(${\nu }_e,e^{-}$)${}^{56}$Co reaction, at $E_{{\nu }_e}$ $=$ 40, 60, and 807nbsp;MeV. Calculations include RHB + RQRPA (DD-ME2) and the shell model (GXPF1J) (for the $1^{+}$ transition) plus the RPA (SGII) for higher multipoles. The quenching factors in $g_A$ are denoted in the figure.

Figure 5

Inclusive neutrino-nucleus cross sections in the $1^{+}$ channel for the ${}^{54,56}$Fe and ${}^{58,60}$Ni target nuclei, at incoming neutrino energies $E_{{\nu }_e}$ $=$ 40, 60, and 80 MeV. The results are obtained using the RHB + RQRPA (DD-ME2) framework and the shell model (GXPF1J). The axial-vector coupling $g_A^{*}$ includes a quenching factor as denoted in the figure.

Figure 6

Neutrino-${}^{56}$Fe cross sections averaged over the Fermi-Dirac distribution. The RHB+RQRPA (DD-ME2) calculations, including the standard (0.8) and enhanced (0.74) quenching factors of the axial-vector coupling $g_A$, are compared to shell-model $+$ RPA results [13] and to those obtained using a hybrid model [33].