Light $p$-shell nuclei with cluster structures ($4 \le A \le 16$) in nuclear matter

The composition of hot and dense nuclear matter is calculated including the $1p$-shell nuclei $4 \le A \le 16$. In-medium shifts, in particular Pauli blocking, are determined by the intrinsic wave function of the nuclei. Results are given within a shell-model approach for the nucleon wave function. Light nuclei are not always well described by the shell model. The 'clustered' nucleus $^8$Be exhibits strong correlation effects because of $\alpha$-like clustering. Intrinsic cluster structures are also significant for the nuclei $^6$Li, $^7$Li, $^7$Be, and $^9$Be. The contribution of the relatively rare elements Li, Be, and B, to the equation of state (EoS) of matter near the saturation density is overestimated in simple approaches such as the nuclear statistical equilibrium (NSE) model. Both, the treatment of continuum correlations and the account of in-medium modifications are considered for the contribution of $^5$He and $^4$H clusters. Compared to the extended NSE including unstable nuclei, the contributions of the corresponding P$_{3/2}$ channel with $A=5, Z=2$ and P$_{2}$ channel with $A=4, Z=1$, respectively, to the EoS are strongly suppressed at high densities owing to Pauli blocking effects. For the shifts of the binding energies of the light $p$-shell nuclei, simple fit formula are given to calculate the composition of hot and dense matter in a wide parameter range.