Full distribution of clusters with universal couplings and in-medium effects

Light and heavy clusters are calculated for asymmetric warm nuclear matter in a relativistic mean-field approach. In-medium effects, introduced via a universal cluster-meson coupling, and a binding energy shift contribution, calculated in a Thomas-Fermi approximation, were taken into account. This work considers, besides the standard lightest bound clusters $^4$He, $^3$He, $^3$H, and $^2$H, also stable and unstable clusters with higher number of nucleons, in the range $5\leq A \leq 12$, as it is natural that heavier clusters also form in core-collapse supernova matter, before the pasta phases set in. We show that these extra degrees of freedom contribute with non-negligible mass fractions to the composition of nuclear matter, and may prevail over deuterons and $\alpha$ particles at high density in strongly asymmetric matter, and not too high temperatures. The presence of the light clusters reduces the contribution of heavy clusters to a much smaller density range, and to a smaller mass fraction.