In-medium $\Delta(1232)$ potential, pion production in heavy-ion collisions and the symmetry energy

Understand

Using the dcQMD transport model, the isoscalar and isovector in-medium potentials of the $\Delta$(1232) baryon are studied and information regarding their effective strength is obtained from a comparison to experimental pion production data in heavy-ion collisions below 800 MeV/nucleon impact energy.

• The best description is achieved for an isoscalar potential moderately more attractive than the nucleon optical potential and a rather small isoscalar relative effective mass m$^*_\Delta \approx$ 0.45.
• For the isovector component only a constraint between the potential's strength at saturation and the isovector effective mass difference can be extracted, which depends on quantities such as the slope of the symmetry energy and the neutron-proton effective mass difference.
• These results are incompatible with the usual assumption, in transport models, that the $\Delta$(1232) and nucleon potentials are equal.