Neutrino-nucleus scattering off ${}^{136}\mathrm{Xe}$

Background: Theoretical estimates of the cross sections for the neutrino-nucleus scattering off relevant nuclei for supernova neutrinos are essential for many applications in neutrino physics and astrophysics. The double-$\beta$-decaying nucleus ${}^{136}\mathrm{Xe}$ nucleus is used by the EXO Collaboration in the search for neutrinoless double-$\beta$ decay. A ton-scale experiment based on ${}^{136}\mathrm{Xe}$ could also be used for studies of supernova neutrinos and/or solar neutrinos.

Purpose: The purpose of the present work is, thus, to perform a study of the charged-current and neutral-current nuclear responses to supernova neutrinos for ${}^{136}\mathrm{Xe}$.

Method: The cross sections are computed by using the well-established framework for studies of semileptonic processes in nuclei introduced by O'Connell, Donnelly, and Walecka [Phys. Rev. C 6, 719 (1972)]. The nuclear wave functions of the initial and the final nuclear states for the neutral-current neutrino-nucleus scattering in ${}^{136}\mathrm{Xe}$ are computed by using the quasiparticle random-phase approximation (QRPA). Similarly, the pnQRPA is adopted to construct the initial and final nuclear states which are relevant for the charged-current reactions. The nuclear responses to supernova neutrinos are subsequently computed by folding the cross sections with appropriate energy spectra for the incoming neutrinos.

Results: We present results for the cross sections of the charged-current and neutral-current neutrino and antineutrino scatterings off ${}^{136}\mathrm{Xe}$. Nuclear responses to supernova neutrinos are also given. For the considered scenario for the neutrino mixing we have found that neutrino interactions with matter and so-called collective neutrino oscillations enhance significantly the neutrino and antineutrino flux-averaged cross sections.

Conclusions: We have found that for the charged-current and neutral-current neutrino scatterings off ${}^{136}\mathrm{Xe}$ transitions mediated by the $1^{+}$ multipole are the most important ones. However, for the charged-current antineutrino channel $0^{+}$ and $1^{+}$ transitions are largely suppressed due to the large neutron excess. Transitions to $1^{-}$ and $2^{-}$ final nuclear states are thus relatively more important for the charged-current antineutrino scattering.

Figure 1

Contributions from the dominant multipole channels to the averaged cross section for the CC neutrino scattering off ${}^{136}\mathrm{Xe}$.

Figure 2

Same as Fig. 1 but for the CC antineutrino scattering.

Figure 3

Same as Fig. 1 but for the NC neutrino scattering off ${}^{136}\mathrm{Xe}$.

Figure 4

Cumultative sums of the averaged cross section for the charged-current electron-neutrino scattering (6) off ${}^{136}\mathrm{Xe}$. Results are shown for the two different pnQRPA calculations which are discussed in the text.

Figure 5

Same as Fig. 4 but for the antineutrino reaction (7).

Figure 6

Same as Fig. 4 but for the neutral-current neutrino-nucleus scattering off ${}^{136}\mathrm{Xe}$.

Figure 7

The number of expected CC and NC neutrino scattering events per kiloton of ${}^{136}\mathrm{Xe}$ as functions of the distance from the supernova.

Figure 8

The number of expected CC and NC antineutrino scattering events per kiloton of ${}^{136}\mathrm{Xe}$ as functions of the distance from the supernova.