Understand
The momentum dependence of the nucleon mean-field potential in a wide momentum range can be an important factor to determine the $\Delta$ resonance and pion production in intermediate-energy heavy-ion collisions.
- In particular, in neutron-rich systems such as ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ collisions, we need to carefully treat the momentum dependence because the neutron and proton potentials can have different momentum dependence, as characterized at low momenta by effective masses.
- In the present work, we rigorously calculate the collision terms of $NN \leftrightarrow N \Delta$ and $\Delta \leftrightarrow N \pi$ processes with the precise conservation of energy and momentum under the presence of momentum-dependent potentials for the initial and final particles of the process.
- The potentials affect not only the threshold condition for the process but also the cross section in general as a function of the momenta of the initial particles, which is treated in a natural way in the present work.