Medium modifications for light and heavy nuclear clusters in simulations of core collapse supernovae -- Impact on equation of state and weak interactions

The present article investigates the role of heavy nuclear clusters and weakly bound light nuclear clusters based on a newly developed equation of state for core collapse supernova studies. A novel approach is brought forward for the description of nuclear clusters, taking into account the quasiparticle approach and continuum correlations. It demonstrates that the commonly employed nuclear statistical equilibrium approach, based on non-interacting particles, for the description of light and heavy clusters becomes invalid for warm nuclear matter near the saturation density. This has important consequences for studies of core collapse supernovae. To this end, we implement this nuclear equation of state provided for arbitrary temperature, baryon density and isospin asymmetry, to spherically symmetric core collapse supernova simulations in order to study the impact on the dynamics as well as on the neutrino emission. For the inclusion of a set of weak processes involving light clusters the rate expressions are derived, including medium modifications at the mean field level. A substantial impact from the inclusion of a variety of weak reactions involving light clusters on the post bounce dynamics nor on the neutrino emission could not be found.