Shell-model computed cross sections for charged-current scattering of astrophysical neutrinos off ${}^{40}\mathrm{Ar}$

Charged-current (anti)neutrino-${}^{40}\mathrm{Ar}$ cross sections for astrophysical neutrinos have been calculated. The initial and final nuclear states were calculated using the nuclear shell model. The folded solar-neutrino scattering cross section was found to be $1.78\left(23\right)\times {10}^{-42}{\mathrm{cm}}^2$, which is higher than what the previous papers have reported. The contributions from the $1^{-}$ and $2^{-}$ multipoles were found to be significant at supernova-neutrino energies, confirming the random-phase approximation (RPA) result of a previous study. The effects of neutrino flavor conversions in dense stellar matter (matter oscillations) were found to enhance the neutrino-scattering cross sections significantly for both the normal and inverted mass hierarchies. For the antineutrino scattering, only a small difference between the nonoscillating and inverted-hierarchy cross sections was found, while the normal-hierarchy cross section was 2–3 times larger than that of the nonoscillating cross section, depending on the adopted parametrization of the Fermi-Dirac distribution. This property of the supernova-antineutrino signal could probably be used to distinguish between the two hierarchies in megaton LAr detectors.

Figure 1

Experimental and shell-model excitation spectra of ${}^{40}\mathrm{K}$. The observed states with uncertain spin parities or angular momenta above 4 are not shown. The experimental spectrum is from Ref. [13].

Figure 2

Experimental and shell-model excitation spectra of ${}^{40}\mathrm{Cl}$. The observed states with uncertain spin parities or angular momenta above 4 are not shown. The experimental spectrum is from Ref. [13].

Figure 3

Unfolded cross sections for the charged-current ${}^{40}\mathrm{Ar}(\nu ,e^{-}){}^{40}\mathrm{K}$ scattering as functions of the energy of the incident neutrino.

Figure 4

Unfolded cross sections for the charged-current ${}^{40}\mathrm{Ar}(\overline{\nu },e^{+}){}^{40}\mathrm{Cl}$ scattering as functions of the energy of the incident neutrino.

Figure 5

Differential cross section for the CC supernova-neutrino scattering to final nuclear states at excitation energies $E_{\mathrm{exc}}$. The total cross section is normalized to unity. Panel (a) is folded with the solar neutrino spectrum, panel (b) with Fermi-Dirac distribution with parametrization (I), and panel (c) with parametrization (II) (see Table 3). Here the effects of flavor conversions are not included.

Figure 6

Differential cross section for the CC supernova-antineutrino scattering to final nuclear states at excitation energies $E_{\mathrm{exc}}$. The total cross section is normalized to unity. Panel (a) with Fermi-Dirac distribution with parametrization (I) and panel (b) with parametrization (II) (see Table 3). Here the effects of flavor conversions are not included.

Figure 7

The total shell-model cross section and a quadratic fit.