Charged-current neutrino-nucleus scattering off ${}^{127}\mathrm{I}$ and ${}^{133}\mathrm{Cs}$

Calculations of (anti)neutrino-nucleus scattering cross sections are vital since experimental results for these cross sections for terrestrial-based (anti)neutrino sources in the low-to-intermediate energy ranges are exceedingly rare. A recent measurement of the scattering of stopped-pion neutrinos off ${}^{127}\mathrm{I}$ by the COHERENT Collaboration yielded a cross section that was only $41\%$ of the expected theoretical prediction. Inspired by this, we have computed the cross sections for (anti)neutrino scatterings off ${}^{127}\mathrm{I}$ and ${}^{133}\mathrm{Cs}$ by considering also the effect of the quenching of the weak axial coupling $g_{\text{A}}$ on the results. Two quenching schemes, a conservative and a radical estimate, were considered. The cross sections as functions of the neutrino energy are presented along with folded cross sections for stopped-pion and supernova (anti)neutrino spectra. The nuclear model used was the microscopic quasiparticle-phonon model based on large single-particle model spaces and realistic $G$-matrix-based effective two-body interactions. The obtained inclusive cross sections for stopped-pion neutrino scattering off ${}^{127}\mathrm{I}$ are in good agreement with the experimental results. The results indicate that discrepancy between the experimental and theoretical results could be at least partly explained by the quenching of $g_{\text{A}}$.

Figure 1

Feynman diagram illustrating the reaction where an incoming (anti)neutrino $\left(\overline{\nu }\right)\nu$ scatters off an atomic nucleus $N(A,Z)$ via the exchange of a charged $W^{\mp }$ boson, producing the final state lepton $l^{\mp }$ and the daughter nucleus $N{(A,Z\pm 1)}^{*}$, which may be in an excited state. The four-momenta of the lepton and nucleus prior to the scattering are denoted by $k_{\mu }$ and $K_{\mu }$, and after the scattering by $k_{\mu }^{\prime }$ and $K_{\mu }^{\prime }$, respectively. The transferred 4-momentum is denoted by $q_{\mu }=k_{\mu }^{\prime }-k_{\mu }=K_{\mu }-K_{\mu }^{\prime }$.

Figure 2

The energies and spin-parities of the grounds states of the nuclei involved in the scattering reactions considered in this paper. The energies are normalized to the energy of the ground states of the initial nuclei.

Figure 3

Experimental and MQPM-computed energy spectra of ${}^{127}\mathrm{Xe}$ and ${}^{127}\mathrm{Te}$ from the reference nuclei ${}^{128}\mathrm{Xe}$ and ${}^{126}\mathrm{Te}$, respectively.

Figure 4

Experimental and MQPM-computed energy spectra of ${}^{133}\mathrm{Ba}$ and ${}^{133}\mathrm{Xe}$ from the reference nuclei ${}^{134}\mathrm{Ba}$ and ${}^{132}\mathrm{Xe}$, respectively.

Figure 5

Total cross section as function of the incoming (anti)neutrino energy for all the scattering reactions of interest.

Figure 6

Contributions of different multipoles to the total folded stopped-pion neutrino cross section for scattering off ${}^{127}\mathrm{I}$ (left) and ${}^{133}\mathrm{Cs}$ (right). The parts with different tensorial character (vector, axial-vector, interference) for each individual multipole contribution are also visualized. Higher multipoles not present in the graphs have vanishingly small contributions.

Figure 7

Contributions to the total folded stopped-pion neutrino cross section from individual final nuclear states with energies $E_{\text{exc}}$, normalized to the total folded cross section.

Figure 8

Contributions of different multipoles to the total folded supernova-neutrino scattering cross section off ${}^{127}\mathrm{I}$ (top) and ${}^{133}\mathrm{Cs}$ (bottom) with $\alpha =3$ for charged-current (anti)neutrinos on the (right) left. The parts with different tensorial character (vector, axial-vector, interference) for each individual multipole contribution for neutrinos and contributions from Coulomb-longitudinal and transverse parts for antineutrinos are also visualized. Higher multipoles not presented in the graphs have vanishingly small contributions.

Figure 9

Contributions to the total folded supernova neutrino cross section with $\alpha =3$ from individual final nuclear states with energies $E_{\text{exc}}$, normalized to the total folded cross section.