Theory Of Nuclear Matter Research Articles

RELATIVISTIC URCA PROCESSES IN NEUTRON STARS WITH AN ANTIKAON CONDESATE

A recently developed effective relativistic theory for nuclear matter is applied to the description of the cooling process of baryon degenerate neutron star matter through neutrino emission considering direct URCA processes. In our approach nucleons and antikaon condensates interact with σ, ω, ρ, δ and ς meson fields. Our results indicate a substantial decrease of the critical threshold density for the URCA process. This is because the presence of these interacting degrees of freedom increase the proportion of protons, producing simultaneously the reduction of the isospin asymmetry in nuclear matter. Our results also indicate that neutron stars with larger masses than MNE ~ 0.9M⊙, which represents the stellar critical threshold (the mass of the neutron star whose baryon central density reached the critical density) would be cooled efficiently and be outside the possibility of observation by heat radiation in a few years.

Nonlinear statistical effects in relativistic mean field theory

We investigate the relativistic mean field theory of nuclear matter at finite temperature and baryon density taking into account of nonlinear statistical effects, characterized by power-law quantum distributions. The analysis is performed by requiring the Gibbs conditions on the global conservation of baryon number and electric charge fraction. We show that such nonlinear statistical effects play a crucial role in the equation of state and in the formation of mixed phase also for small deviations from the standard Boltzmann-Gibbs statistics.

Non-perturbative methods for a chiral effective field theory of finite density nuclear systems

Recently we have developed a novel chiral power counting scheme for an effective field theory of nuclear matter with nucleons and pions as degrees of freedom [1]. It allows for a systematic expansion taking into account both local as well as pion-mediated multi-nucleon interactions. We apply this power counting in the present study to the evaluation of the pion self-energy and the energy density in nuclear and neutron matter at next-to-leading order. To implement this power counting in actual calculations we develop here a non-perturbative method based on Unitary Chiral Perturbation Theory for performing the required resummations. We show explicitly that the contributions to the pion self-energy with in-medium nucleon–nucleon interactions to this order cancel. The main trends for the energy density of symmetric nuclear and neutron matter are already reproduced at next-to-leading order. In addition, an accurate description of the neutron matter equation of state, as compared with sophisticated many-body calculations, is obtained by varying only slightly a subtraction constant around its expected value. The case of symmetric nuclear matter requires the introduction of an additional fine-tuned subtraction constant, parameterizing the effects from higher order contributions. With that, the empirical saturation point and the nuclear matter compressibility are well reproduced while the energy per nucleon as a function of density closely agrees with sophisticated calculations in the literature.

NATURALNESS, ISOSPIN BREAKING IN NUCLEAR MATTER AND THE OKAMOTO–NOLEN–SCHIFFER ANOMALY

A recently developed relativistic theory for nuclear matter, which shows consistency with the concept of naturalness and conservation of chiral symmetry, is applied to the description of the Okamoto–Nolen–Schiffer anomaly. The results of our study show significant improvements in the description of the anomaly when compared to the corresponding results of other authors. In particular, our predictions for the Okamoto–Nolen–Schiffer anomaly include the known anomalous growth, namely that the anomaly not necessarily grow with the nuclear mass, since the anomaly is lower, for instance, for the nuclei 39 C and 39 K when compared to the 17 F and 17 O nuclei. As far as we know, this trend was not described by any other model found in the literature.

Isospin-dependent pairing interaction from nuclear matter calculations

The isospin dependence of the effective pairing interaction is discussed on the basis of the Bardeen, Cooper, and Schrieffer theory of superfluid asymmetric nuclear matter. It is shown that the energy gap, calculated within the mean field approximation in the range from symmetric nuclear matter to pure neutron matter, is not linearly dependent on the symmetry parameter owing to the nonlinear structure of the gap equation. Moreover, the construction of a zero-range effective pairing interaction compatible with the neutron and proton gaps in homogeneous matter is investigated, along with some recent proposals of isospin dependence tested on the nuclear data table.

Chiral effective field theory for nuclear matter including long- and short-range multi-nucleon interactions

We review on a novel chiral power counting scheme for in-medium chiral perturbation theory with nucleons and pions as degrees of freedom. It allows for a systematic expansion taking into account local as well as pion-mediated inter-nucleon interactions. Based on this power counting, one can identify classes of nonperturbative diagrams that require a resummation. As a method for performing those resummations we review on the techniques of Unitary Chiral Pertubation Theory for nucleon-nucleon interactions. We then apply both power counting and non-perturbative methods to the example of calculating the pion self-energy in asymmetric nuclear matter up-to-and-including next-to-leading order. It is shown that the leading corrections involving in-medium nucleon-nucleon interactions cancel between each other at given chiral orders.

Isospin splitting of the nucleon-nucleus optical potential

The volume component of the phenomenological optical potential is traced to the microscopic theory of nuclear matter. The latter is based on the Brueckner-Hartree-Fock approach with three-body force, which recently has proved to be able to reproduce the empirical saturation properties of nuclear matter. The self-energy is calculated and its on-shell matrix elements are related to the volume part of the optical potential. A previous investigation, where the real part of the microscopic potential was compared with an empirical one, which is a fit of the experimental nucleon-nucleus elastic scattering, is here extended to the absorptive component. Moreover, the isospin splitting of the optical potential is discussed in connection with the proton and neutron effective masses of isospin asymmetric nuclear systems.

Chiral effective field theory for nuclear matter with long- and short-range multi-nucleon interactions

We derive a novel chiral power counting scheme for in-medium chiral perturbation theory with explicit nucleonic and pionic degrees of freedom coupled to external sources. It allows for a systematic expansion taking into account local as well as pion-mediated inter-nucleon interactions. Based on this power counting, one can identify classes of non-perturbative diagrams that require a resummation. Within this scheme, the pion self-energy in asymmetric nuclear matter is analyzed and calculated up-to-and-including next-to-leading order (NLO). It is shown that the corrections involving in-medium nucleon–nucleon interactions cancel between each other at NLO. As a result, there are no corrections up to this order to the linear density approximation for the in-medium pion self-energy.

Constraints for weakly interacting light bosons from existence of massive neutron stars

Theories beyond the standard model include a number of new particles some of which might be light and weakly coupled to ordinary matter. Such particles affect equation of state of nuclear matter and can shift admissible masses of neutron stars to higher values. The internal structure of neutron stars is modified provided the ratio between coupling strength and mass squared of a weakly interacting light boson is above $g^2/\mu^2 \sim 25 ~\mathrm{GeV}^{-2}$. We provide limits on the couplings with the strange sector, which cannot be achieved from laboratory experiments analysis. When the couplings to the first family of quarks is considered the limits imposed by the neutron stars are not more stringent than the existing laboratory ones. The observations on neutron stars give evidence that equation of state of the $\beta$-equilibrated nuclear matter is stiffer than expected from many-body theory of nuclei and nuclear matter. A weakly interacting light vector boson coupled predominantly to the second family of the quarks can produce the required stiffening.

Isovector component of the optical potential

The volume part of the phenomenological optical potential is interpreted in terms of the microscopic theory of nuclear matter. The latter is based on the Brueckner-Hartree-Fock approach with a new version of three-body force, reproducing the empirical saturation properties of nuclear matter. The self-energy is calculated and its on-shell matrix elements are related to the volume part of the optical potential. A comparison is made with a recent parametrization of the optical model potential fitting the experimental nucleon-nucleus elastic scattering. The isospin effects and Coulomb corrections are emphasized.

Relativistic chiral Hartree-Fock description of nuclear matter with constraints from nucleon structure and confinement

We present a relativistic chiral effective theory for symmetric and asymmetric nuclear matter taken in the Hartree-Fock scheme. The nuclear binding is ensured by a background chiral invariant scalar field associated with the radial fluctuations of the chiral quark condensate. Nuclear matter saturation is obtained once the scalar response of the nucleon-generating three-body repulsive forces is incorporated. For those parameters related to the scalar sector and quark confinement mechanism inside the nucleon we make use of an analysis of lattice results on nucleon mass evolution with quark mass. The other parameters are constrained as much as possible by standard hadron and nuclear phenomenology. Special attention is paid to the treatment of the propagation of the scalar fluctuations. The rearrangement terms associated with in-medium modified mass and coupling constants are explicitly included to satisfy the Hugenholtz-Van Hove theorem. We point out the important role of the tensor piece of the rho exchange Fock term to reproduce the asymmetry energy of nuclear matter. We also discuss the isospin dependence of the Landau nucleon effective mass.

SHORT RANGE CORRELATIONS IN RELATIVISTIC NUCLEAR MODELS

Short range correlations are introduced using the unitary operator method in a relativistic theory of nuclear matter based on the Hartree-Fock approximation. Pion exchange, including the tensor contribution, is taken into account. It is found that both the tensor contribution of pion exchange and short range correlations soften the equation of state. The neutron matter equation of state is also discussed.

Variational theory of hot nucleon matter

We develop a variational theory of hot nuclear matter in neutron stars and supernovae. It can also be used to study charged, hot nuclear matter which may be produced in heavy-ion collisions. This theory is a generalization of the variational theory of cold nuclear and neutron star matter based on realistic models of nuclear forces and pair correlation operators. The present approach uses microcanonical ensembles and the variational principle obeyed by the free energy. In this paper we show that the correlated states of the microcanonical ensemble at a given temperature $T$ and density \ensuremath{\rho} can be orthonormalized preserving their diagonal matrix elements of the Hamiltonian. This allows for the minimization of the free energy without corrections from the nonorthogonality of the correlated basis states, similar to that of the ground state energy. Samples of the microcanonical ensemble can be used to study the response, and the neutrino luminosities and opacities of hot matter. We present methods to orthonormalize the correlated states that contribute to the response of hot matter.

From QCD to Nuclear Matter Saturation

We discuss a relativistic chiral theory of nuclear matter with σ and ω exchange using a formulation of the σ model in which all the chiral constraints are automatically fulfilled. We establish a relation between the nuclear response to the scalar field and the QCD one which includes the nucleonic parts. It allows a comparison between nuclear and QCD information. Going beyond the mean field approach we introduce the effects of the pion loops supplemented by the short-range interaction. The corresponding Landau-Migdal parameters are taken from spin-isospin physics results. The parameters linked to the scalar meson exchange are extracted from lattice QCD results. These inputs lead to a reasonable description of the saturation properties, illustrating the link between QCD and nuclear physics. We also derive from the corresponding equation of state the density dependence of the quark condensate and of the QCD susceptibilities.

Quark Matter 2005 – Theoretical Summary

This is a review of the latest developments in the theory of superdense nuclear matter, formed in relativistic heavy ion collisions or in the core of collapsed stars, as they were reported and discussed at the Quark Matter 2005 conference in Budapest (Hungary).

QCD susceptibilities and nuclear-matter saturation in a relativistic chiral theory

We investigate the evolutions with density of the QCD scalar susceptibility and of the sigma mass in a chiral relativistic theory of nuclear matter, in the mean-field approximation. In order to reach saturation we need to introduce the scalar response of the nucleons. The consequences are a quite mild density dependence of the sigma mass and the progressive decoupling of the quark density fluctuations from the nucleonic ones at large densities.

Gauge invariance and the κ–gl relation

The connection between the enhancement factor of the photonuclear E1 sum rule and the orbital angular momentum g-factor of a bound nucleon is discussed in the framework of the Landau–Migdal theory for isospin asymmetric nuclear matter, and compared to empirical informations.

The relation between the photonuclear E1 sum rule and the effective orbital g-factor

The connection between the enhancement factor (1+ κ) of the photonuclear E1 sum rule and the orbital angular momentum g-factor ( g ℓ) of a bound nucleon is investigated in the framework of the Landau–Migdal theory for isospin asymmetric nuclear matter. Special emphasis is put on the role of gauge invariance to establish the κ– g ℓ relation. By identifying the physical processes which are taken into account in κ and g ℓ, the validity and limitations of this relation will be discussed. The connections to the collective excitations and to nuclear Compton scattering are also shown.

String theory meets QCD

String theory began life in the late 1960s as an attempt to understand the properties of nuclear matter such as protons and neutrons. Although it was not successful as a theory of quarks and gluons, it has since developed a life of its own as a possible theory of everything – with the potential to incorporate quantum gravity as well as the other forces of nature. However, in a remarkable about face in the last five years, it has now been discovered that string theory and the standard theory of nuclear matter – QCD – might in fact describe the same physics. These exciting developments were the topic of discussion at a major workshop in Seattle in February.

Nuclear Level Structure, B(E2) Gamma-transitions and Nucleon Interaction Data for 56Fe by a Unified Soft-rotator Model and Coupled-Channels Framework

The soft-rotator model (SRM) and a coupled-channels method based on the coupling scheme built on the wave functions of the SRM were applied for a consistent analysis of the nuclear level structure, B(E2) and the nucleon interaction data of 56Fe. The model could describe the experimental collective levels of 56Fe up to the excitation energy of 5.5 MeV successfully. Relativistickinematics and global optical potential form, consistent with nuclear matter theory and Dirac phenomenology, were used in coupled-channels optical model approach to overcome problems left in our previous work. The available nucleon interaction experimental data up to 160 MeV and B(E2) γ-transitions were described satisfactorily.