Effect of energy conservation on in-medium \(\mbox{NN}\to \mbox{N}\Delta\) cross section in isospin-asymmetric nuclear matter

• Published in: arXiv.org
• Main Authors: Cui, Ying, Zhang, Yingxun, Li, Zhuxia
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 18.10.2018
• Subjects: Beams (radiation); Channels; Cross-sections; Dependence; Energy conservation; Exchanging; Nuclear matter; Potential energy; Rho-mesons
• ISSN: 2331-8422

In this paper, the in-medium \(NN\rightarrow N\Delta\) cross section is calculated in the framework of the one-boson exchange model by including the isovector mesons, i.e. \(\delta\) and \(\rho\) mesons. Due to the isospin exchange in the \(NN\rightarrow N\Delta\) process, the vector self-energies of the outgoing particles are modified relative to the incoming particles in isospin asymmetric nuclear matter, and it leads to the effective energies of the incoming \(NN\) pair being different from the outgoing \(N\Delta\) pair. This effect is investigated in the calculation of the in-medium \(NN\rightarrow N\Delta\) cross section. With the corrected energy conservation, the cross sections of the \(\Delta^{++}\) and \(\Delta^+\) channels are suppressed, and the cross sections of the \(\Delta^0\) and \(\Delta^-\) channels are enhanced relative to the results obtained without properly considering the potential energy changes. Our results further confirm the dependence of medium correction factor, \(R=\sigma_{ NN\rightarrow N\Delta}^*/\sigma_{NN\rightarrow N\Delta}^{\text{free}}\), on the charge state of \(NN\rightarrow N\Delta\) especially around the threshold energy, but the isospin splitting of medium correction factor \(R\) becomes weak at high beam energies.