Properties of nuclear matter

An account is given of recent theories by Brueckner, Eden, Swiatecki, Bethe, and co-workers about the properties of nuclear matter, which is identical in content, but different in its method of presentation. This presentation tries to clarify the reasons for the applicability of the independent-particle model and to determine what particular features of the nuclear forces are responsible for the validity of this model.     

Properties of nuclear matter andN=Z closed-shell nuclei

A simple three-parameter density dependent effective interaction is used to study the properties of nuclear matter, neutron matter and some bulk properties such as ground state energies and rms charge radii of three double-closed shell nuclei⁴He,¹⁶O and⁴⁰Ca. The three parameters of the effective interaction are determined by requiring to fit the binding energy and density of infinite nuclear matter at saturation density as well as ground state energy of¹⁶O in the first order perturbation theory. This interaction gives correct saturation in nuclear matter with a value of 283 MeV for compressibility. The symmetry coefficienta _T atk _F=1·36 fm^–1 is 28·58 MeV. The energy per particle in neutron matter is calculated in the range of nuclear matter densities and it compares well with those ofNemeth andSprung. Groundstate energies and rms charge radii of⁴He,¹⁶O and⁴⁰Ca are calculated using oscillator eigen functions as single particle wave functions. Results for ground state energies are in good agreement with empirical values and rms charge radii are slightly better than those obtained byMoszkowski with the MDI.The authors are thankful to the Computer Centre, Utkal University, Bhubaneswar for providing computational facilities for this work.     

Properties of nuclear and neutron matter in a relativistic Hartree-Fock theory

Relativistic Hartree-Fock (HF) equations are derived for an infinite system of mesons and baryons in the framework of a renormalizable relativistic quantum field theory. The derivation is based on a diagrammatic approach and Dyson's equation for the baryon propagator. The result is a set of coupled, nonlinear integral equations for the baryon self-energy with a self-consistency condition on the single-particle spectrum. The HF equations are solved for nuclear and neutron matter in the Walecka model, which contains neutral scalar and vector mesons. After renormalizing model parameters to reproduce nuclear matter saturation properties, HF results at low to moderate densities are similar to those in the mean-field (Hartree) approximation. Self-consistent exchange corrections to the Hartree equation of state become negligible at high densities. Rho- and pi-meson exchanges are incorporated using a renormalizable gauge-theory model. A chiral transformation of the lagrangian is used to replace the pseudoscalar πN coupling with a pseudovector coupling, for which one-pion exchange is a reasonable first approximation. This transformation maintains the model's renormalizability so that corrections may be evaluated. Pion exchange has a small effect on the HF results of the Walecka model and brings HF results in closer agreement with the mean-field theory. The diagrammatic techniques used here retain the mesonic degrees of freedom and are simple enough to be extended to more refined self-consistent approximations.     

Properties of hot and dense nuclear matter in a mixed phase

The QCD phase transition is treated within a statistical model taking into account the coexistence of interacting quark-gluon and hadron phases. Being in agreement with the recent lattice QCD data, this statistical mixed phase model predicts that the “softest point” of the equation of state, resulting in the longest-lived fireball effect, is atε _{sp ≈ 0.35}GeV/fm³. It is shown that this “softest point” is washed out at the baryon densities higher than the normal nuclear density. The approach is extended to include strangeness. Attention is drawn to the study of signatures for forming the mixed quark-hadron phase of nuclear matter in the collision energy rangeE _lab ≈ 2–10 GeV/A.     

Properties of nuclear matter using the velocity-dependent effective potential ofs-wave interaction

Two forms of a velocity-dependent effective potential are used. The binding energy and the incompressibility of the nuclear matter are calculated. These are found to be in a good agreement with those obtained by others and with the experimental results. The single-particle potential, the effective massM ^* and the nuclear surface energy are also discussed and compared with those obtained by the others.     

Properties of nuclear matter in the Λ00-approximation for local potentials

In the Λ⁰⁰-approximation of the Green's function theory the nuclear matter properties have been calculated for several local potentials. All these potentials contain a hard core repulsion and match the experimentalS-wave phase-shifts. Due to the analytical form of these potentials one can obtain many results analytically. Thus the whole structure of this approximation becomes relatively transparent and can easily be calculated. Therefore this model can be used as an input for more complicated approximations. Furthermore one can also treat the optical potential problem. Te results for nuclear matter are comparable with the results for nonlocal potentials. The momentum distribution deviates more strongly from the independent particle model as in the case of nonlocal potentials.     

Rotating nuclear matter

Rotating nuclear matter is defined as the system of infinitely many nucleons in a rotating frame neglecting the electrostatic interaction and centrifugal single-nucleon potential. We study the ground state of this system as a function of the densities of neutrons and protons. In the limit where the angular velocity is much smaller than the Fermi energy, the structure of the single-nucleon density corresponds to anisotropic spin distributions at the surfaces of local neutron and proton Fermi spheres. The anisotropy results from the non-central terms in the effective two-nucleon interaction. Contrary to the situation in a system of non-interacting nucleons, the spin asymmetry induced by rotation is a strongly non-linear function of the Fermi momentum. In symmetric nuclear matter at normal density it equals roughly that of the non-interacting system due to mutually cancelling contributions from the spin-orbit and central parts of the effective two-nucleon interaction. The volume contributions to the moments of inertia and single-nucleon Routhian of finite nuclei are calculated, and estimates obtained of certain surface contributions to the moment of inertia.     

Superfluid nuclear matter calculations

We present a method to calculate nuclear matter properties in the superfluid phase. The method is based on the use of self-consistent off-shell nucleon propagators in the T-matrix equation. Such a complete treatment of the spectral function is required below and around T_c due to a pseudogap formation in the spectral function. In the superfluid phase we introduce the anomalous self-energy in the fermion propagators and in the T-matrix equation, consistently with the strong coupling BCS equations. The equations for the nucleon spectral function include both a contribution of condensed and scattering pairs. The method is illustrated by numerical calculations. Above T_c pseudogap formation is visible in the spectral function and below T_c a superfluid gap also appears.     

Towards exotic nuclear matter

In this article I would like to describe what I am doing right now. First, introductory remarks on nuclear matter at high densities and/or high temperatures are presented. Then, I report our recent data obtained at the Brookhaven AGS. Finally, I describe briefly our future RHIC experiment, PHENIX.     

Skyrmion in nuclear matter

The properties of Skyrmions in finite nuclei are considered. The deformation effect is taken into account through the external-field-induced distortion of the profile function of a chiral field. The masses of classical Skyrmions and the distribution of their baryon number versus the Skyrmion position within a nucleus are discussed.     

The disassembly of nuclear matter

A statistical model is applied for multi-fragment final states in nuclear collisions with bombarding energies E/A ≈ 100 MeV. A portion of the intermediate system formed is assumed to decay according to the available classical non-relativistic phase space, calculated in a grand canonical ensemble. The model correlates and predicts many experimental observables in terms of three parameters: the available energy per nucleon, the isospin asymmetry, and the effective interaction volume.     

Collective excitations of nuclear matter

It has been shown that in a renormalizable gauge-invariant field-theory model, besides the usual factorizable contribution to the parity-violating vector-meson-exchange potential there is a nonseparable contribution which is equally important. Both contributions have been calculated in the model based on the Bethe-Salpeter equation which describes vector mesons as bound quark-antiquark states. Complete expressions for parity-violating nuclear potentials have been given for the Cabibbo and the Weinberg-Salam models, including the asymptotically-free field-theory version of the latter, which employs coloured quarks and vector gluons.     

The theory of nuclear matter

This article is an account of the present position of theories of nuclear matter initiated some years ago mainly by Jastrow and Brueckner. Section 1 introduces the basic ideas. Section 2 discusses the variational approach. Section 3 develops methods involving partial summations in perturbation theory. The difficulties confronting the latter approach, and their partial resolution by ideas from superconductivity theory, are analysed in § 4.

Much of the formalism is relevant also in the theory of individual nuclei (see for example the review by Eden 1959) and in fields other than nuclear physics (see for example The Many Body Problem, Les Houches, 1958). However, in the selection of material our criterion has been relevance for the ground state of nuclear matter.     

Quasi-lattice model of nuclear matter

Brueckner and others have applied an extension of the self-consistent method of Hartree-Fock to the determination of the properties of a hypothetical nuclear matter consisting of roughly equal numbers of neutrons and protons, the electrical forces between protons being “turned off”. Taking the nucleon-nucleon interaction potentials to be those of Gammel and Thaler, we have applied the well-known Wigner-Seitz method for crystal lattices to a quasi-lattice model of nuclear matter. This method gives the energy of the lowest single particle state as a function of the internucleonic separation. Good agreement is obtained with the experimental values for the nuclear density and binding energy per nucleon.     

Static viscosity of nuclear matter

The static shear viscosity η₀ of symmetric nuclear matter is estimated. It is found, that for reasonable nuclear temperatures the mean free path connected with η_o is considerably larger than the nuclear radii. We therefore conclude, that the concept of viscosity cannot be applied to nuclear fission and heavy ion collisions without taking into account the nuclear surface.     

Many-body theory of nuclear matter

We combine the many-body theory and the low-density expansion developed by Brueckner, Bethe and others to investigate several properties of the ground state and of single-particle excited states of symmetric nuclear matter. We calculate the following quantities from Reid's hard core nucleon-nucleon interaction: strength, energy-dependence, nonlocality and density-dependence of the real and of the imaginary parts of the optical-model potential, momentum distribution in the interacting ground state, dependence on density and momentum of the norm of a quasiparticle and of the effective mass, spectral function for particle states, saturation density and average binding energy per nucleon. No free parameter is adjusted in the calculation; good agreement is obtained with empirical values. It is shown that the effective mass has a narrow maximum at the Fermi surface; this is investigated in the framework of analytical models.     

Quantum condensates in nuclear matter

Nonrelativistic nuclear matter is considered as a special example of a many-particle system. Quantum statistical methods are applied to treat the formation and dissolution of bound states in dense matter. The formation of quantum condensates is investigated. Special aspects are the transition from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer (BCS) pairing as well as the occurrence of quartetting. Consequences for the structure of nuclei are compared with experimental data. Exercises to illustrate the main features of in-medium effects in nuclear matter are given. The text was submitted by the author in English.