# In medium dispersion relation effects in nuclear inclusive reactions at intermediate and low energies

## TL;DR

This paper investigates how spectral functions and RPA correlations influence nuclear response functions and cross sections in neutrino and pion interactions at intermediate and low energies, emphasizing the importance of nuclear corrections for accurate modeling.

## Contribution

It introduces a comprehensive analysis of spectral functions combined with RPA correlations in modeling nuclear reactions, highlighting their impact on cross sections and uncertainties at low energies.

## Key findings

- Nuclear corrections significantly affect cross sections below 400 MeV.
- Errors in the muon/electron cross section ratio are below 5%.
- Spectral functions and RPA effects are crucial for accurate neutrino oscillation experiments.

## Abstract

In a well-established many-body framework, successful in modeling a great variety of nuclear processes, we analyze the role of the spectral functions (SFs) accounting for the modifications of the dispersion relation of nucleons embedded in a nuclear medium. We concentrate in processes mostly governed by one-body mechanisms, and study possible approximations to evaluate the particle-hole propagator using SFs. We also investigate how to include together SFs and long-range RPA-correlation corrections in the evaluation of nuclear response functions, discussing the existing interplay between both type of nuclear effects. At low energy transfers (\le 50 MeV), we compare our predictions for inclusive muon and radiative pion captures in nuclei, and charge-current (CC) neutrino-nucleus cross sections with experimental results. We also present an analysis of intermediate energy quasi-elastic neutrino scattering for various targets and both neutrino and antineutrino CC driven processes. In all cases, we pay special attention to estimate the uncertainties affecting the theoretical predictions. In particular, we show that errors on the \sigma_{\mu}/\sigma_e ratio are much smaller than 5%, and also much smaller than the size of the SF+RPA nuclear corrections, which produce significant effects, not only in the individual cross sections, but also in their ratio for neutrino energies below 400 MeV. These latter nuclear corrections, beyond Pauli blocking, turn out to be thus essential to achieve a correct theoretical understanding of this ratio of cross sections of interest for appearance neutrino oscillation experiments. We also briefly compare our SF and RPA results to predictions obtained within other representative approaches.