Momentum space treatment of inclusive neutrino scattering off the deuteron and trinucleons

TL;DR

This paper develops a momentum space approach to study inclusive neutrino scattering off deuterons and trinucleons, providing cross section predictions and response functions up to 300 MeV energies, and compares results with previous models.

Contribution

It introduces a comprehensive momentum space framework for neutrino-nucleus scattering, including relativistic effects and comparisons with coordinate space calculations.

Findings

Predictions for total cross sections up to 300 MeV.

Analysis of relativistic effects in deuteron reactions.

Discrepancies with previous models due to kinematic and operator differences.

Abstract

The $\bar{\nu}_e + {^2{\rm H}} \rightarrow e^+ + n + n$, $\nu_e + {^2{\rm H}} \rightarrow e^- + p + p$, $\bar{\nu}_l + {^2{\rm H}} \rightarrow \bar{\nu}_l + {^2{\rm H}}$, $\nu_l + {^2{\rm H}} \rightarrow \nu_l + {^2{\rm H}}$, $\bar{\nu}_l + {^2{\rm H}} \rightarrow \bar{\nu}_l + p + n$, $\nu_l + {^2{\rm H}} \rightarrow \nu_l + p + n$, $\bar{\nu}_e + {^3{\rm He}} \rightarrow e^+ + {^3{\rm H}}$, $\bar{\nu}_l + {^3{\rm He}} \rightarrow \bar{\nu}_l + {^3{\rm He}}$, $\nu_l + {^3{\rm He}} \rightarrow \nu_l + {^3{\rm He}}$, $\bar{\nu}_l + {^3{\rm H}} \rightarrow \bar{\nu}_l + {^3{\rm H}}$, $\nu_l + {^3{\rm H}} \rightarrow \nu_l + {^3{\rm H}}$, $\bar{\nu}_e + {^3{\rm He}} \rightarrow e^+ + n + d$, $\bar{\nu}_e + {^3{\rm He}} \rightarrow e^+ + n + n + p$, $\bar{\nu}_l + {^3{\rm He}} \rightarrow \bar{\nu}_l + p + d$, $\bar{\nu}_l + {^3{\rm He}} \rightarrow \bar{\nu}_l + p + p +n$, $\nu_l + {^3{\rm H}} \rightarrow \nu_l + n + d$ and $\nu_l + {^3{\rm H}} \rightarrow \nu_l + n + n + p$ reactions ($l= e, \mu, \tau$) are studied consistently in momentum space for (anti)neutrino energies up to 300 MeV. For most of these processes we provide predictions for the total cross sections and in the case of the (anti)neutrino-$^3$He and (anti)neutrino-$^3$H inelastic scattering we compute examples of essential response functions, using the AV18 nucleon-nucleon potential and a single-nucleon weak current operator. For the reactions with the deuteron we study relativistic effects in the final state kinematics and compare two-nucleon scattering states obtained in momentum and coordinate spaces. Our results from momentum space are compared with the theoretical predictions by G.Shen et al., Phys. Rev. C 86, 035503 (2012). The observed disagreement can be attributed to the differences in kinematics and in the weak current operator.