Self-consistent description of finite nuclei based on a relativistic quark model

Relativistic Hartree equations for spherical nuclei have been derived from a relativistic quark model of the structure of bound nucleons which interact through the (self-consistent) exchange of scalar (σ) and vector (ω and ϱ) mesons. The coupling constants and the mass of the σ-meson are determined from the properties of symmetric nuclear matter and the rms charge radius in ⁴⁰Ca. Calculated properties of static, closed-shell nuclei from ¹⁶O to ²⁰⁸Pb are compared with experimental data and with results of Quantum Hadrodynamics (QHD). The dependence of the results on the nucleon size and the quark mass is investigated. Several possible extensions of the model are also discussed.     

Relativistic description of deformed rare earth nuclei

Ground state properties of heavy deformed nuclei in the rare earth region are described in the framework of the relativistic Hartree approximation. Both linear and non-linear parameter sets of the lagrangian are used. The non-linear sets reproduce the experimentally observed binding energies, the charge radii and the quadrupole moments, with the same quality as non-relativistic density dependent mean field calculations with Skyrme forces.     

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.     

Derivation of the effective pion-nucleon Lagrangian within heavy baryon chiral perturbation theory

We develop a method for constructing the heavy baryon chiral perturbation theory (HBChPT) Lagrangian, to a given chiral order, within HBChPT. We work within SU(2) theory, with only the pion field interacting with the nucleon. The main difficulties, which are solved, are to develop techniques for implementing charge conjugation invariance, and for taking the nucleon on shell, both within the non-relativistic formalism. We obtain complete lists of independent terms in L_HBChPT through O(q³) for off-shell nucleons. Then, eliminating equation-of-motion (e.o.m.) terms at the relativistic and non-relativistic level (both within HBChPT), we obtain L_HBChPT for on-shell nucleons, through O(q³). The extension of the method (to obtain on-shell L_HBChPT within HBChPT) to higher orders is also discussed.     

Complex microscopic optical potential between two nuclei based on Dirac-Brueckner theory for nuclear matter

The real and imaginary parts of the optical-model potential between two nuclei are calculated in the energy density formalism. The energy density is derived from the Dirac-Brueckner approach to nuclear matter. In this approach, both free NN scattering and the saturation properties of nuclear matter can be explained starting from a realistic NN interaction. The relativistic features incorporated in the Dirac-Brueckner approach make the real part of the optical potential less attractive than that obtained in a non-relativistic calculation while the imaginary part is enhanced. The comparison of the calculated differential cross section for elastic ¹²C-¹²C scattering with the experimental data suggests that the enhancement of the imaginary part due to the relativistic treatment is favourable while its repulsive contribution to the real part is unfavourable.     

Shape change in Hf,W and Os-isotopes: A non-relativistic Hartree-Fock versus relativistic Hartree approximation

We have investigated the ground-state structures of even-even Hf, W and Os isotopes within the framework of a deformed non-relativistic Hartree-Fock and a relativistic mean field formalism. A majority of the nuclei are predicted to be prolate in shape in the relativistic calculations. On the other hand, contrary to the relativistic results, we predict a shape change in a cyclic order in the non-relativistic calculations. However, in both the cases, the magnitude of the quadrupole deformation parameter agrees well with the experimental data. We also evaluated the hexadecapole deformation parameter for Hf, W and Os isotopes and irrespective of the shape change in quadrupole moments, we find a cyclic change in hexadecapole shape from positive to negative and vice versa in both the relativistic and non-relativistic formalisms.     

相对论核多体研究进展

简要评述了相对论核多体理论最近的发展及其在核物质和有限核的微观描述方面的应用 ,所涉及的理论框架主要是相对论 Brueckner- Hartree- Fock理论和相对论平均场理论 .例举了某些最新的应用领域 ,同时也讨论了若干待解决的问题和可能开展的工作. Relativistic many body methods, which include the relativistic Brueckner Hartree Fock (RBHF) theory and the relativistic mean field (RMF) approach, were introduced, while their progress and application for nuclear matter and finite nuclei were presented. The open questions in this field and the trend in future were also discussed.     

相对论Hartree-Fock研究奇特核的性质

采用相对论Hartree-Fock(RHF)理论来描述奇特核的性质.为了研究Fock项和矢量介子对奇特核性质的贡献和避免有效相互作用的不惟一性,本文推广应用没有自由参数的密度有关的相对论Hartree(RDH)和Hartree-Fock(RDHF)理论来描述奇特核的性质.在RDH和RDHF近似下,计算了钙同位素链的性质,特别研究了Fock交换项和矢量介子的贡献.研究表明交换项和矢量介子对非常丰中子核的性质,如结合能,中子均方根半径,中子密度分布的影响是非常不同于对稳定线附近核性质的影响.同时,对研究滴线奇特核性质的重要性及其理论模型做了简单的讨论.     

Relativistic mean field and some recent applications

The essentials of the Relativistic Mean Field (RMF) theory and some of its recent applications are presented. The explicit calculations are carried out for a few selected isotopic, isotonic and isobaric chains of nuclei covering the entire periodic table. The calculated ground state properties are found to be in good agreement with the corresponding experiment: the binding energies are reproduced within 0.25%, on average, and the charge radii differ only in the second decimal place of fermi. The relativistic origin of the pseudo-spin symmetry is briefly discussed. The density distributions obtained, are found to be in good agreement with the experiment (where available). The peripheral factor, the ratio of neutron and proton densities on the nuclear periphery, extracted in the anti-proton annihilation experiments are well reproduced. The RMF densities are used to calculate the reaction (σ_R) and charge changing (σ_cc) cross sections in the Glauber model, as well as the α (cluster)-daughter interaction energy. The latter is then employed to estimate the decay half lives of Super-Heavy (trans-actinide) nuclei in the WKB approximation. The calculations are found to agree well with the experiment. This success of the RMF in accurately describing the nuclear properties with only a few fixed parameters is indeed remarkable. The text was submitted by the authors in English.     

Electron-nucleon interaction in quasi-free scattering: (II). Non-relativistic Hamiltonian through fourth order

The interaction of non-relativistic nucleons with relativistic electrons can be expressed by a Hamiltonian expanded in a power series of the recoil nucleon velocity. In this paper third- and fourth-order terms are calculated. Free electron-nucleon-scattering and quasi-free electron scattering on ¹²C are studied and results through various orders are compared with the relativistic formulae. A different off-shell behaviour of the relativistic approach is found, which is independent of the higher-order terms and seems responsible for the different results of knock-out reactions.     

Information on three-body interactions from inversion of the energy equations

The inversion of the three energy equations, i.e. for the nuclear total energy, the sum of occupied single-particle state energies and the saturation condition, using the experimental data in ¹⁶O and ⁴⁰Ca, is carried out to determine whether three-body effective interactions are necessary in addition to density independent and dependent two-body interactions. In order to fit the data both in a non-relativistic and a relativistic framework, the three-body interaction energy is found to be large and repulsive. We also show that density-dependent two-body effective interactions, which are another requisite in the non-relativistic potential theory, are not necessarily needed in the relativistic mean field framework but allow to increase the effective nucleon mass.     

Fragmentation of relativistic nuclei in peripheral interactions in nuclear track emulsion

The technique of nuclear track emulsions is used to explore the fragmentation of light relativistic nuclei down to the most peripheral interactions: nuclear “white” stars. A complete pattern of the relativistic dissociation of a 8B nucleus with target fragment accompaniment is presented. Relativistic dissociation ⁹Be → 2α is explored using significant statistics, and a relative contribution of ⁸Be decays from 0+ and 2+ states is established. Target fragment accompaniments are shown for relativistic fragmentation ¹⁴N → 3He +H and ²²Ne → 5He. The leading role of the electromagnetic dissociation on heavy nuclei with respect to breakups on target protons is demonstrated in all these cases. It is possible to conclude that the peripheral dissociation of relativistic nuclei in nuclear track emulsion is a unique tool to study many-body systems composed of the lightest nuclei and nucleons in the energy scale relevant for nuclear astrophysics. The text was submitted by the authors in English.     

On relativistic and non-relativistic approaches to nucleon-nucleus scattering

The impulse approximation to the Dirac theory of nucleon-nucleus scattering is reduced to a non-relativistic formalism. It is shown that relativistic effects can be included on the same footing as the effects of the nuclear medium on the effective interaction. We apply the argument to spin observables in 200 MeV and 500 MeV proton elastic scattering on a ⁴⁰Ca target.     

Relativistic hydrodynamic scaling from the dynamics of quantum field theory

Relativistic hydrodynamic scaling or boost invariance is a particularly important hydrodynamic regime, describing collective flows of relativistic many body systems and is used in the interpretation of experiments from high-energy cosmic rays to relativistic heavy-ion collisions. We show evidence for the emergence of hydrodynamic scaling from the dynamics of relativistic quantum field theory. We consider a scalar lambdaphi(4) model in 1+1 dimensions in the Hartree approximation and study the relativistic collisions of two kinks and the decay of a localized high-energy density region. We find that thermodynamic scalar isosurfaces show approximate boost invariance at high-energy densities.     

Wigner's pseudo-particle relativistic dynamics in external potential field

The Wigner's pseudo-particle formalism has been generalized to describe quantum dynamics of relativistic particle in external potential field. As a simplest application of the developed formalism the time evolution of the 1D relativistic quantum harmonic oscillator been considered. Due to the complex structure of the evolution equation for Wigner function, the only numerical treatment is possible by combining Monte Carlo and molecular dynamics methods. Relativistic dynamics results in appearance of the new physical effects as opposed to non-relativistic case. Interesting is the complete changing of the shape of the momentum and coordinate distribution functions as well as formation of ‘unexpected’ protuberances. To analyze the influence of relativistic effects on average values of quantum operators, the dependencies on time of average momentum, position, their dispersions and energy have been compared for the non-relativistic and relativistic dynamics.     

Quasiparticle relativistic G-matrix interaction

A quasiparticle G-matrix interaction has been constructed from a three-dimensional integral equation which is a relativistic generalization of the conventional non-relativistic Bethe-Goldstone equation. Relativistic dynamical effects have been discussed by comparing the relativistic and the conventional non-relativistic G-matrices. The Landau theory and, in particular, the quasi-particle current have also been discussed within the present relativistic formulation.

As an example of application, the quasiparticle relativistic G-matrix interaction has been used in the RPA calculation which includes 2p-2h processes.     

Ground state properties of 16O, 40Ca and 48Ca in a relativistic Hartree theory of nuclear matter

A relativistic field theory model of nuclear matter is solved in a Hartree approximation for finite nuclei. We show that the theory predicts small shell effects for the charge-density distributions in magic nuclei and is in agreement with recent electron scattering data. The effects of the small component of the relativistic wave function are investigated as well as the role of the isospin-dependent force generated by the rho field.     

Single-particle potential in a relativistic Hartree-Fock mean field approximation

A relativistic Hartree-Fock mean field approximation is investigated in a model in which the nucléon field interacts with scalar and vector meson fields. The Hartree-Fock potential felt by individual nucléons enters in a relativistic Dirac single-particle equation. It is shown that in the case of symmetric nuclear matter one can always find a potential which is fully equivalent to the most general mean field and which is only the sum of a Lorentz scalar, of one component of a Lorentz tensor and of the fourth component of a Lorentz vector. A non-relativistic potential is derived which yields exactly the same single-particle energies and elastic scattering phase shifts as the relativistic Hartree-Fock potential. Analytical results are presented in the case of nuclear matter. A local density approximation is constructed which enables one to consider finite nuclei. The input parameters of the model can be chosen in such a way that the empirical saturation properties of nuclear matter are well reproduced. Good agreement is obtained between the calculated non-relativistic potential and the empirical value of the real part of the optical-model potential at low and at intermediate energy. At intermediate energy, the wine-bottle bottom shape which had previously been found for the potential in the framework of the relativistic Hartree approximation is maintained when the Fock contribution is included.