Mott Effect in Nuclear Matter

Abstract

Nuclear matter consisting of protons and neutrons is an interesting strongly interacting quantum system featuring many-body effects. The equation of state (EoS) of nuclear matter at finite temperature and density with various proton fractions is considered, in particular the region of medium excitation energy given by the temperature range T ≤ 30 MeV and the baryon density range ρ_B ≤ 10^{14. 2} g cm ^{− 3}. In this region (“warm and dilute asymmetric nuclear matter”), the formation of few-body correlations, in particular bound clusters, has to be taken into account. Based on a many-particle Green function approach, the medium modification of the clusters is described by self-energy and Pauli blocking effects, and the cluster-mean field approximation is given. These medium effects lead to a shift of the binding energies as well as a modification of scattering properties. Because of the shift, bound states will merge with the continuum of scattering states at increasing density and are dissolved (Mott effect). Results of the Mott effect for different nuclei embedded in nuclear matter are given.

Thermodynamic properties are influenced by the formation and dissolution of bound states. The nuclear matter EoS is considered within a generalized Beth–Uhlenbeck approach. The connection with the Brueckner Hartree–Fock and Relativistic Mean-Field theory is outlined. Benchmarks such as virial expansion in the low-density limit or the low-temperature limit are considered. An interesting effect is the formation of a two-nucleon quantum condensate, showing the crossover from Cooper pairing to Bose–Einstein condensation. Correlations in the condensate such as quartetting are an interesting issue. The structure of the quantum condensate is determined by the existence of bound states and the Mott effect.

The resulting thermodynamic properties, incorporating the Mott effect, are of interest for heavy-ion collisions and astrophysical applications. The Mott effect is also of relevance for the structure of finite nuclei, especially dilute excited states like the Hoyle state of ¹²C.