Nuclear de-excitations in low-energy charged-current ${\nu }_e$ scattering on ${}^{40}\mathrm{Ar}$

Background: Large argon-based neutrino detectors, such as those planned for the Deep Underground Neutrino Experiment, have the potential to provide unique sensitivity to low-energy (few to tens of MeV) electron neutrinos produced by core-collapse supernovae. Despite their importance for neutrino energy reconstruction, nuclear de-excitations following charged-current ${\nu }_e$ absorption on ${}^{40}\mathrm{Ar}$ have never been studied in detail at supernova energies.

Purpose: I develop a model of nuclear de-excitations that occur following the ${}^{40}\mathrm{Ar}({\nu }_e,e^{-}){}^{40}\mathrm{K}^{*}$ reaction. This model is applied to the calculation of exclusive cross sections.

Methods: A simple expression for the inclusive differential cross section is derived under the allowed approximation. Nuclear de-excitations are described using a combination of measured $\gamma$-ray decay schemes and the Hauser-Feshbach statistical model. All calculations are carried out using a novel Monte Carlo event generator called MARLEY (Model of Argon Reaction Low Energy Yields).

Results: Various total and differential cross sections are presented. Two de-excitation modes, one involving only $\gamma$ rays and the other including single neutron emission, are found to be dominant at few tens-of-MeV energies.

Conclusions: Nuclear de-excitations have a strong impact on the achievable energy resolution for supernova ${\nu }_e$ detection in liquid argon. Tagging events involving neutron emission, though difficult, could substantially improve energy reconstruction. Given a suitable calculation of the inclusive cross section, the MARLEY nuclear de-excitation model may readily be applied to other scattering processes.

Figure 1

Gamow-Teller strengths $B\left(\mathrm{GT}\right)$ from two independent measurements of ${}^{40}\mathrm{Ti}{\beta }^{+}$ decay by Liu et al. [56] and Bhattacharya et al. [57].

Figure 2

Comparison of the Gamow-Teller strengths $B\left(\mathrm{GT}\right)$ measured using ${}^{40}\mathrm{Ti}\beta$ decay (see Fig. 1) with those obtained using a measurement of $0^{\circ }$ ($p,n$) scattering by Bhattacharya et al. [58].

Figure 3

Complete sets of ${}^{40}\mathrm{Ar}({\nu }_e,e^{-}){}^{40}\mathrm{K}^{*}$ allowed approximation matrix elements distributed as part of MARLEY 1.2.0. The name of the data file in which each set of matrix elements may be found is given in the appropriate legend heading. The QRPA $B\left(\mathrm{GT}\right)$ strengths (violet) were calculated by Cheoun et al. [69]. Citations for the experimental $B\left(\mathrm{GT}\right)$ strengths are given in the captions for Figs. 1 and 2.

Figure 4

Inclusive total cross sections for charged-current absorption of ${\nu }_e$ on ${}^{40}\mathrm{Ar}$. Each curve shows the result obtained using a specific approach to Coulomb corrections.

Figure 5

Exclusive total cross sections for charged-current absorption of ${\nu }_e$ on ${}^{40}\mathrm{Ar}$.

Figure 6

Flux-averaged differential cross sections with respect to the laboratory-frame scattering cosine $cos{\theta }_e$ of the final-state electron. Top: Calculation for the time-integrated supernova ${\nu }_e$ spectrum described in the text. Bottom: Calculation for ${\nu }_e$ produced by ${\mu }^{+}$ decay at rest.

Figure 7

Flux-averaged differential cross sections with respect to the final-state electron kinetic energy $T_e$. Top: Calculation for the time-integrated supernova ${\nu }_e$ spectrum described in the text. Bottom: Calculation for ${\nu }_e$ produced by ${\mu }^{+}$ decay at rest.

Figure 8

Flux-averaged differential cross sections with respect to various definitions of the reconstructed neutrino energy $E_{\nu }^{\text{reco}}$. Top: Calculation for the time-integrated supernova ${\nu }_e$ spectrum described in the text. Bottom: Calculation for ${\nu }_e$ produced by ${\mu }^{+}$ decay at rest.

Figure 9

Fractional rms resolution for the neutrino energy reconstruction methods described in the text.