Self-consistent hartree description of finite nuclei in a relativistic quantum field theory

Relativistic Hartree equations for spherical nuclei are derived from a relativistic nuclear quantum field theory using a coordinate-space Green function approach. The renormalizable field theory lagrangian includes the interaction of nucleons with σ, ω, ρ and π mesons and the photon. The Hartree equations represent the “mean-field” approximation for a finite nuclear system. Coupling constants and the σ-meson mass are determined from the properties of nuclear matter and the rms charge radius in ⁴⁰Ca, and pionic contributions are absent for static, closed-shell nuclei. Calculated charge densities, neutron densities, rms radii, and single-nucleon energy levels throughout the periodic table are compared with data and with results of non-relativistic calculations. Relativistic Hartree results agree with experiment at a level comparable to that of the most sophisticated non-relativistic calculations to date. It is shown that the Lorentz covariance of the relativistic formalism leads naturally to density-dependent interactions between nucleons. Furthermore, non-relativistic reduction reveals non-central and non-local aspects inherent in the Hartree formalism. The success of this simple relativistic Hartree approach is attributed to these features of the interaction.     

Quasiparticle excitations in relativistic quantum field theory

We analyze the particle-like excitations arising in relativistic field theories in states different than the vacuum. The basic properties characterizing the quasiparticle propagation are studied using two different complementary methods. First we introduce a frequency-based approach, wherein the quasiparticle properties are deduced from the spectral analysis of the two-point propagators. Second, we put forward a real-time approach, wherein the quantum state corresponding to the quasiparticle excitation is explicitly constructed, and the time-evolution is followed. Both methods lead to the same result: the energy and decay rate of the quasiparticles are determined by the real and imaginary parts of the retarded self-energy, respectively. Both approaches are compared, on the one hand, with the standard field-theoretic analysis of particles in the vacuum and, on the other hand, with the mean-field-based techniques in general backgrounds.     

Mass splitting in relativistic quantum field theory

Null plane integrals of certain classes of tensor densities, conserved or non-conserved, may define symmetric operators on dense subspaces of the in and out states. These operators annihilate the vacuum and may satisfy a Lie algebra. In particular, the possibility that a finite number of null plane charges, which includes the Poincaré generators, close on an algebra whose irreducible representations contain particles with different masses is considered. The situation in which the Lie algebra is defined on a dense domain which is not from the in and out states is discussed. Some algebraic hypotheses other than that of a Lie algebra in the usual sense are briefly considered; in these cases there can be no mass splitting.Supported in part by the U.S.-Israel Binational Science Foundation (B.S.F.), Jerusalem, Israel.     

Renormalization effects in a field theory of finite nuclei

In case of thep-α system, the Coulomb exchange potential of the resonating group model and of the fish bone optical model are compared with each other. It is seen that the difference between the two approximations arises mainly from the unrealistic shortdistance behaviour of the proton-protone ²/r potential, which has been assumed in both models. In case of the α-¹⁶O system, it is demonstrated that the importance of the Coulomb exchange potential can be very much reduced by an off-shell transformation.     

Renormalized Hartree-Fock equations in a nuclear relativistic quantum field theory

Renormalized Hartree-Fock equations are derived for an infinite system of mesons and baryons in the framework of a relativistic quantum field theory. Direct and exchange diagrams in the baryon propagator are summed self-consistently to all orders, and the effects of occupied negative-energy states in the Dirac sea are included. The required counterterm subtractions are defined by conventional renormalization conditions, but they need not be evaluated explicitly. The result is a set of finite nonlinear integral equations for the baryon self-energy that includes vacuum fluctuation effects from virtual N$\text{N}$ pairs in the many-body wavefunction at finite density.     

Properties and structure of N=Z nuclei within relativistic mean field theory

The axially deformed relativistic mean field theory with the force NLSH has been performed in the blocked BCS approximation to investigate the properties and structure of N=Z nuclei from Z=20 to Z=48. Some ground state quantities such as binding energies, quadrupole deformations, one/two-nucleon separation energies, root-mean-square （rms） radii of charge and neutron, and shell gaps have been calculated. The results suggest that large deformations can be found in medium-heavy nuclei with N=Z=38-42. The charge and neutron rms radii increase rapidly beyond the magic number N=Z=28 until Z=42 with increasing nucleon number, which is similar to isotope shift, yet beyond Z=42, they decrease dramatically as the structure changes greatly from Z=42 to Z=43. The evolution of shell gaps with proton number Z can be clearly observed. Besides the appearance of possible new shell closures, some conventional shell closures have been found to disappear in some region. In addition, we found that the Coulomb interaction is not strong enough to breakdown the shell structure of protons in the current region.     

Properties and structure of N=Z nuclei within relativistic mean field theory

The axially deformed relativistic mean field theory with the force NLSH has been performed in the blocked BCS approximation to investigate the properties and structure of N=Z nuclei from Z=20 to Z=48.Some ground state quantities such as binding energies, quadrupole deformations, one/two-nucleon separation energies, root-mean-square (rms) radii of charge and neutron, and shell gaps have been calculated.The results suggest that large deformations can be found in medium-heavy nuclei with N=Z=38-42.The charge and neutron rms radii increase rapidly beyond the magic number N=Z=28 until Z=42 with increasing nucleon number, which is similar to isotope shift, yet beyond Z=42, they decrease dramatically as the structure changes greatly from Z=42 to Z=43.The evolution of shell gaps with proton number Z can be clearly observed.Besides the appearance of possible new shell closures, some conventional shell closures have been found to disappear in some region.In addition, we found that the Coulomb interaction is not strong enough to breakdown the shell structure of protons in the current region.     

Additive conservation laws in local relativistic quantum field theory

We consider generatorsQ of symmetry transformations acting additively on asymptotic particle states according to (1.1). [This equation can be derived forQ defined as integral over a conserved local current!]. For simplicity, we consider only the case that all asymptotic fields are scalar. Assuming that elastic scattering occurs at least in an open subset of the scattering manifold we show thatQ is at most alinear combination of generators of the Poincaré group and internal symmetries.     

On the geometric structure of a parity-conserving relativistic quantum field theory

Wheeler's conjecture that there might exist a ‘principle’ which rules out parity-non-conserving spaces is analysed. The following result has been obtained: A local relativistic quantum field theory is parity-conserving if the following conditions hold:

1. The fields are derived from geometry, i.e. they are represented by quantised currents (in the sense of de Rham); and
2. The theory may be defined on a connected and, under certain restrictions, on a disconnected orientable space-time continuumM ⁴.

     

On stochastic Einstein locality in algebraic relativistic quantum field theory

This paper assesses Miklós Rédei's [1991] proof of the proposition that algebraic relativistic quantum field theory is stochastic Einstein local. The conclusion is that either Rédei's proof is spurious, in that it does not really prove what it intends to establish, or that the proof is fallacious. The paper is self-contained in the sense that the few ingredients of algebraic quantum theory that go into Rédei's proof are first summed up. Then Hellman's definition of stochastic Einstein locality is discussed, a detailed exposition is offered of Rédei's proof, and finally the author's refutation is explicated.     

A relativistic quantum field theory for rotating nuclear matter

The relativistic quantum field theory of Walecka is extended to rotating nuclear systems using a mean-field Thomas-Fermi approximation. Self-bound systems exhibit centrifugal stretching and a maximum angular frequency. Systems constrained to a cylindrical box develop central holes for large angular frequencies.     

Systematics of nuclear matter and finite nuclei properties in a non-linear relativistic mean field approach

A phenomenological non-linear relativistic mean field approach is used to investigate primarily the properties of nuclear matter. The dimensionless parameters are adjusted using different empirical quantities which are discussed in detail: saturation conditions, the incompressibility parameter, symmetry energy and surface energy. Particular attention is paid to the cubic and quartic terms in the self-interaction part of the scalar field. The effective parameters are then used to study doubly magic finite nuclei in the Dirac-Hartree approximation. Different ground-state properties, binding energies, rms radii, density distributions, are then systematically analyzed and discussed. A remarkable agreement with experimental quantities is found and further possibilities are suggested.     

Properties of hydrodynamic nuclei for quantum field models

The transition to the hydrodynamic limit for a many-particle quantum system withN local conservation laws is made in a specified class of external effects. It is shown that the hydrodynamic equations are nonlocal in time and space and the hydrodynamic model is equivalent to the initial quantum statistical model. The nuclei appearing in the material relations are expressed in terms of the Green functions for the currents. It follows from the properties of the Green functions that the hydrodynamic model satisfies the dissipation conditions. When the quantum field model isT-invariant, the nuclei are related by reciprocal relations (analogous to the Onsager relations).Institute of Earth Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 34–38, July, 1995.     

Infinite-component fields as a basis for a finite quantum field theory

A quantum field theory based on infinite-component fields is developed in which the spectrum of particles for all spins is composed of infinite sums of finite, non-unitary representations of the Lorentz group. This leads to a field theory free of causality problems. The problem of gauging away all unphysical modes in the infinite-component field theory is achieved by using infinite-parameter gauge fields which remove all unphysical modes, independently of the number of space-time dimensions. A model of an infinite-component quantum field theory is formulated, using perturbation theory, in which there are no ultraviolet divergences and the S-matrix is causal and unitary.     

Comments on lightlike translations and applications in relativistic quantum field theory

In the algebraic framework of quantum field theory we consider one parameter subgroups of lightlike translations. After establishing a few preliminary properties we prove a certain cluster property and then exhibit the close connection between such subgroups and a class of type III factors. A few applications of this connection are also discussed.     

Collective excitations of nuclei in a relativistic mean-field theory

Collective excitations of finite nuclei are discussed in a model relativistic baryon-meson field theory. Eigenvalue equations for small amplitude motion about the static mean-field solutions assuming irrotational flow are derived. Variational estimates of the lowest modes are obtained.     

Compression properties of finite nuclei in a semi-classical relativistic approach

Skyrme type potentials are known to lead — in the framework of the scaling model — to a finite-nucleus incompressibility valueK _A where the volume coefficientK _v equals roughly the negative surface coefficient K_s. This is found for Skyrme interactions with K_v between 200 and 360 MeV. In a semi-classical relativistic approach on the basis of the — model (linear as well as non-linear) using in addition local density approximations, we findK _s to depend in particular on the surface energy coefficienta _s , and not so much on the value ofK _v . For a realistic value of a_s, both the linear and the non-linear — model (with NL1 parameter set) yield a ratio ¦K _s K _v ¦ of approximately 1. We discuss implications of this finding with a particular view on recent empirical results onK _v andK _s .Dedicated to Prof. Dr. H. J. Mang on the occasion of his 60th birthday     

A real-time approach to nonequilibrium quantum field theory of relativistic fields

Summary The basic ingredients of a real-time nonequilibrium quantumfield theoretical approach, based on a generalization of thermofield dynamics, are briefly reviewed. In particular, the possible advantages of its application to relativistic models, as the φ⁴-model for the Higgs field are pointed out. Also the differences between the above approach and others using the Feynman's path integral method are underlined. ?Angelo della Riccia? Fellow.     

Candidate chiral nuclei in bromine isotopes based on triaxial relativistic mean field theory

Following the observation of candidate chiral doublet bands in ~(78,80)Br, triaxial deformations with corresponding configurations in odd-odd bromine isotopes have been investigated using adiabatic and configuration-fixed constrained triaxial relativistic-meanfield calculations with an aim of finding the boundary of chirality in the chain of Br isotopes. Several minima with triaxial deformation and the proper particle-hole configuration were obtained in ~(74,76,78,80,82)Br, where the chiral doublet bands have the possibility of occurrence. Furthermore, the possible existence of multiple chiral doublet(MχD) bands is demonstrated in ~(74,76,78,80,82)Br.Experiments to explore the chirality and MχD properties of Br isotopes are conducted to verify the predictions.