Description of nuclear systems within the relativistic Hartree-Fock method with zero range self-interactions of the scalar field

An exact method is suggested to treat the nonlinear self-interactions (NLSI) in the relativistic Hartree-Fock (RHF) approach for nuclear systems. We consider here the NLSI constructed from the relativistic scalar nucleon densities and including products of six and eight fermion fields. This type of NLSI corresponds to the zero range limit of the standard cubic and quartic self-interactions of the scalar field. The method to treat the NLSI uses the Fierz transformation, which enables one to express the exchange (Fock) components in terms of the direct (Hartree) ones. The method is applied to nuclear matter and finite nuclei. It is shown that, in the RHF formalism, the NLSI, which are explicitly isovector-independent, generate scalar, vector and tensor nucleon self-energies strongly density-dependent. This strong isovector structure of the self-energies is due to the exchange terms of the RHF method. Calculations are carried out with a parametrization containing five free parameters. The model allows a description of both types of systems compatible with experimental data.Comment: 23 pages, 14 figures (v2: major quantitative changes

On the relativistic origin of the kink effect in the chain of Pb isotopes

We investigate the origin of the kink effect (KE) in the relativistic mean field theory by transforming the single-particle Dirac equation into a Schrodinger-like equation. It is found that relativistic self-consistent effects as well as contributions from the rho meson determine the actual structure of the KE. However, the spin-orbit force generated by the rho meson has no significant influence on the KE.Comment: 11 pages, RevTeX, 3 postscript figs., Phys. Lett.

Spin-Orbit Splitting in Non-Relativistic and Relativistic Self-Consistent Models

The splitting of single-particle energies between spin-orbit partners in nuclei is examined in the framework of different self-consistent approachs, non-relativistic as well as relativistic. Analytical expressions of spin-orbit potentials are given for various cases. Proton spin-orbit splittings are calculated along some isotopic chains (O, Ca, Sn) and they are compared with existing data. It is found that the isotopic dependence of the relativistic mean field predictions is similar to that of some Skyrme forces while the relativistic Hartree-Fock approach leads to a very different dependence due to the strong non-locality.Comment: 12 pages, RevTeX, 4 new figs.in .zip format, unchanged conclusions, Phys. ReV.

Spin symmetry in Dirac negative energy spectrum in density-dependent relativistic Hartree-Fock theory

The spin symmetry in the Dirac negative energy spectrum and its origin are investigated for the first time within the density-dependent relativistic Hartree-Fock (DDRHF) theory. Taking the nucleus $^{16}$O as an example, the spin symmetry in the negative energy spectrum is found to be a good approximation and the dominant components of the Dirac wave functions for the spin doublets are nearly identical. In comparison with the relativistic Hartree approximation where the origin of spin symmetry lies in the equality of the scalar and vector potentials, in DDRHF the cancellation between the Hartree and Fock terms is responsible for the better spin symmetry properties and determines the subtle spin-orbit splitting. These conclusions hold even in the case when significant deviations from the G-parity values of the meson-antinucleon couplings occur.Comment: 13 pages, 7 figures, 1 table, accepted by Eur. Phys. J.

Correction: Atlantic Bluefin Tuna (Thunnus thynnus) Biometrics and Condition

Correction: Atlantic Bluefin Tuna (Thunnus thynnus) Biometrics and ConditionPostprint4,411

Atlantic Bluefin Tuna (Thunnus thynnus) Biometrics and Condition

The compiled data for this study represents the first Atlantic and Mediterranean-wide effort to pool all available biometric data for Atlantic bluefin tuna (Thunnus thynnus) with the collaboration of many countries and scientific groups. Biometric relationships were based on an extensive sampling (over 140,000 fish sampled), covering most of the fishing areas for this species in the North Atlantic Ocean and Mediterranean Sea. Sensitivity analyses were carried out to evaluate the representativeness of sampling and explore the most adequate procedure to fit the weight-length relationship (WLR). The selected model for the WLRs by stock included standardized data series (common measurement types) weighted by the inverse variability. There was little difference between annual stock-specific round weight-straight fork length relationships, with an overall difference of 6% in weight. The predicted weight by month was estimated as an additional component in the exponent of the weight-length function. The analyses of monthly variations of fish condition by stock, maturity state and geographic area reflect annual cycles of spawning and feeding behavior. We update and improve upon the biometric relationships for bluefin currently used by the International Commission for the Conservation of Atlantic Tunas, by incorporating substantially larger datasets than ever previously compiled, providing complete documentation of sources and employing robust statistical fitting.WLRs and other conversion factors estimated in this study differ from the ones used in previous bluefin stock assessments.Postprint4,411

Nuclear Tensor Force and Effective Pions in the Relativistic Hartree-Fock Formalism

In the framework of nonlinear nuclear models based on the relativistic Hartree-Fock approximation, we have isolated the contribution of the tensor force of pions in the effective NN interaction, by means of two different approximate methods, recently developed by us, in order to dilucidate its role in a variety of nuclear properties. Results show that a reduction of the contribution of this tensor force considerably influences the spin-orbit splittings and magic gaps in the spin-unsaturated midweight 56Ni nucleus as well as the behaviour of the total binding energies with A in heavy nuclei. Both methods give similar results. We also study the evolution of the splitting of the proton 1d spin-orbit doublet in the chain Z=14, from N=20 to N=28, and the neutron 2p − 1f shell in the chain N=28, from the 48Ca nucleus to the 42Si nucleus. Whereas, in the first case, the pion tensor force (PTF) plays an important role and its reduction is needed to reproduce the corresponding experimental results; in the second case, the quenching of the neutron 2p3/2 − 1f7/2 gap in the mentioned isotonic chain N=28 is hardly affected by the PTF

Pseudospin symmetry in the Dirac phenomenology

In the phenomenological relativistic framework of the Dirac equation for spherical nuclei, we use different kinds of single-particle central potentials ( ΣS + Σ0 to investigate certain aspects of the spin and pseudospin (PS) symmetries. Neither the splitting of PS doublets (PSDs) nor the similarity of the radial parts of the small components (F/r of the corresponding Dirac spinors have been found related with the magnitude of ΣS + Σ0 , in the sense predicted by several authors in the last decade. This conclusion is shown to be valid, in particular, for a potential of Coulomb type. We give a simple explanation for the strong correlation established in the relativistic calculations between the similarity of the radial parts of the big (small) components of the Dirac spinors of two spin (pseudospin) partners and the number of their nodes. The direct effects of the so-called PS symmetry-breaking term (and its singularity point) on the F functions of the PSDs are also analysed

Origin of the pseudospin symmetry in the relativistic formalism

The grounds on which the nuclear pseudospin symmetry (PSS) is supposed to be based are analysed within the relativistic mean-field framework. A connection between the mechanisms responsible for the spin-orbit and pseudospin-orbit splittings is shown. The nature of the PSS is investigated through an extended Dirac equation which allows a generalization of the PSS breaking term. It is shown that the PSS breaking in real nuclei can be explained as a result of a non-perturbative transformation from non-physical solutions of the Dirac equation, which satisfy exactly the PSS, to the physical ones. The PSS breaking term produces important, though qualitatively similar, effects on both states of a pseudospin-orbit doublet. The similarity of these effects increases with the number of nodes of the small component of the Dirac spinor of these states

Pseudospin symmetry as an accidental symmetry in the relativistic framework

We analyse the arguments used in the relativistic context to base the quasi-degeneracy of pseudospin doublets (PSDs) observed in atomic nuclei on the smallness of the single-particle central potential (Σ S + Σ0), discussing, especially, the implications of the results obtained in the limit (Σ S + Σ0 = 0. We study also the transition from a relativistic model, where Σ S + Σ0 is a harmonic-oscillator potential and exhibits degenerate PSDs, to a more realistic one with broken pseudospin symmetry. We examine, in particular, the effect of the corresponding pseudospin symmetry-breaking term on the Dirac spinors of the PSDs. An extension of the Nilsson model to the relativistic case is also considered