The influence of $\delta$ meson on the isospin splitting of in-medium $NN\to N\Delta$ cross sections

TL;DR

This study examines how the $oldsymbol{ ext{delta}}$ meson affects the isospin-dependent in-medium nucleon-nucleon to nucleon-delta cross sections using a one-boson exchange model, revealing significant changes in medium correction factors.

Contribution

It introduces the inclusion of the $oldsymbol{ ext{delta}}$ meson in the model, showing its impact on the isospin splitting of in-medium $oldsymbol{NN o N riangle}$ cross sections, which was not considered before.

Findings

Medium correction factors differ for various channels without $oldsymbol{ ext{delta}}$$

Including $oldsymbol{ ext{delta}}$$ reverses the isospin splitting pattern

Results highlight the importance of $oldsymbol{ ext{delta}}$ meson in in-medium cross section calculations

Abstract

The isospin splitting of the in-medium $NN\rightarrow N\Delta$ cross sections in asymmetric nuclear medium are investigated in the framework of the one-boson exchange model by including $\delta$ and $\rho$ mesons. Our results show that the medium correction factors $R=\sigma_{ NN\rightarrow N\Delta}^*/\sigma_{NN\rightarrow N\Delta}^{\text{free}}$ have $R_{pp \to n\Delta ^{++}} < R_{nn \to p\Delta ^{-}}$ and $R_{NN \to N\Delta ^{+}} <R_{NN \to N\Delta ^{0}}$ by using the without-$\delta$ sets. By including the $\delta$ meson, it appears the totally opposite results in the $R$ for different channels, i.e., $R_{pp \to n\Delta ^{++}} > R_{nn \to p\Delta ^{-}}$ and $R_{NN \to N\Delta ^{+}} >R_{NN \to N\Delta ^{0}}$.