Light nuclei quasiparticle energy shifts in hot and dense nuclear matter

Abstract

Nuclei in dense matter are influenced by the medium. In the cluster mean-field approximation, an effective Schr\odinger equation for the $A$-particle cluster is obtained accounting for the effects of the correlated medium such as self-energy, Pauli blocking, and Bose enhancement. Similar to the single-baryon states (free neutrons and protons), the light elements ($2\ensuremath{\leqslant}A\ensuremath{\leqslant}4$, internal quantum state \ensuremath{\nu}) are treated as quasiparticles with energies ${E}_{A,\ensuremath{\nu}}(\mathbf{P};T,{n}_{n},{n}_{p})$. These energies depend on the center-of-mass momentum $\mathbf{P}$, as well as temperature $T$ and the total densities ${n}_{n}$, ${n}_{p}$ of neutrons and protons, respectively. No $\ensuremath{\beta}$ equilibrium is considered so that ${n}_{n}$, ${n}_{p}$ (or the corresponding chemical potentials ${\ensuremath{\mu}}_{n}$, ${\ensuremath{\mu}}_{p}$) are fixed independently. For the single-nucleon quasiparticle energy shift, different approximate expressions such as Skyrme or relativistic mean-field approaches are well known. Treating the $A$-particle problem in appropriate approximations, results for the cluster quasiparticle shifts are given. Properties of dense nuclear matter at moderate temperatures in the subsaturation density region considered here are influenced by the composition. This in turn is determined by the cluster quasiparticle energies, in particular the formation of clusters at low densities when the temperature decreases and their dissolution due to Pauli blocking as the density increases. Our finite-temperature Green function approach covers different limiting cases: the low-density region where the model of nuclear statistical equilibrium and virial expansions can be applied and the saturation-density region where a mean-field approach is possible.