Correlations and Clustering in Dilute Matter

Abstract

Nuclear systems are treated within a quantum statistical approach. Correlations and cluster formation are relevant for the properties of warm dense matter, but the description is challenging and different approximations are discussed. The equation of state, the composition, Bose condensation of bound fermions, the disappearance of bound states at increasing density because of Pauli blocking are of relevance for different applications in astrophysics, heavy ion collisions, and nuclear structure. I. BOUND STATES IN A FERMION SYSTEMS: THE CHEMICAL PICTUREA. Structure of matterOur investigation refers to a fundamental property of matter: We can define elementary constituents (indivisible particles, Greek ) ατ oµoς) that interact. Then, the macroscopic properties are calculated within a quantum statistical approach. The interaction may lead to bound states, which can influence the properties in an essential manner and new properties may emerge. A well known example is the formation of atoms from charged particles, the electrons and the atomic nuclei. While unbound electrons and nuclei form a plasma which conducts electricity, the formation of charge-neutral atoms results in non-conducting dielectric matter. Another example is Bose-Einstein condensation which may occur when bosonic bound states are formed in a fermionic system. A well-known bosonic bound state is Helium-4, consisting of two electrons, two protons, and two neutrons. It shows superfluidity at low temperatures. Nuclear systems where Bose-Einstein condensation of α particles may occur are discussed below.Here, we consider nuclear systems consisting of neutrons and protons (and possibly electrons for charge neutrality) as constituting "elementary" particles. As a consequence of the nucleon-nucleon (N − N ) interaction, bound states, the nuclei, are formed. Examples are the light nuclei 2 H (deuteron, d), 3 H (triton, t), 3 He (helion, h), and 4 He (α particle). The fundamental interaction is the strong interaction, as described by QCD. Because the deduction of the N − N interaction from QCD is not solved at present, effective interactions are introduced which reproduce measured properties such as binding energies and scattering phase shifts. Examples are the Yukawa, Reid, Bonn, Paris, Argonne, etc., interactions, but also the separable (Yamaguchi, PEST, BEST, etc.) parametrization of the N − N interaction are available. The optimum form of the effective N − N interaction is widely discussed in nuclear physics but will not addressed in the present work.The appearance of bound states is a general feature of the structure of matter. For example, quarks form hadrons, hadrons form nuclei, nuclei together with electrons form atoms and ions, atoms form molecules. The new bound states may be considered as the elements of a statistical description of matter, what is possible as long as the energies considered are small enough so that the internal structure of the bound states is not excited. A description where the "elementary" particles and the composed bound stat...

Towards a Unified Quark-Hadron-Matter Equation of State for Applications in Astrophysics and Heavy-Ion Collisions

“…We emphasize that the subdivision of the intrinsic partition function into a bound and a scattering contribution is artificial and not of physical relevance. The summations over A, c and P of (16) remain to be done for the EOS (13), and Z may be included in c. The region in the parameter space, in particular P, where bound states exist, may be restricted what is expressed by the step function Θ(x) = 1, x ≥ 0; = 0 else. The continuum edge of scattering states is denoted by E cont A,c (P; T, µ n , µ p ).…”

“…A strict quantum statistical approach to this nonequilibrium process is not available at present. A possible method is the Zubarev nonequilibrium statistical operator which is able to describe the formation of correlations in the expanding hot and dense matter [13,114]. First steps to describe cluster formation (A < 4) in expanding matter have been performed [115], but have to be worked out further, in particular to include larger clusters (A ≥ 4).…”

“…To give some systematics with respect to the different approximations calculating the self-energy and the corresponding approximation for the EoS, in Ref. [13] the following overview was presented.…”

Unification of Thermo Field Kinetic and Hydrodynamics Approaches in the Theory of Dense Quantum–Field Systems

“…The problem of accounting for the bound states (clusters) [1,2] formed by particles is particularly important in the development of the theories of nonequilibrium processes of thermal quantum field systems, such as nuclear matter [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Kinetic and hydrodynamic processes in a hot, compressed nuclear matter, which appears after ultrarelativistic collisions of heavy nuclei [7,14,[16][17][18][19][20][21], are mutually connected, and therefore, the bound states between nucleons should be considered.…”

“…In his recent works [1,2,19], G. Röpke noted the importance of constructing a nonequilibrium theory in which along with hydrodynamic parameters, a cluster distribution function is taken into account, similarly to the case of the classical theory of non-equilibrium processes of dense gases and liquids [28][29][30][31].…”