Spin-orbit splitting in nonrelativistic and relativistic self-consistent models

López−Quelle, M.; Giai, Nguyen Van; Marcos, S.; Savushkin, L. N.

doi:10.1103/physrevc.61.064321

Cited by 28 publications

(35 citation statements)

References 26 publications

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“…Earlier it was already noted that all standard Skyrme interactions, including the SLy parametrizations that share our fit protocol, have an unresolved trend that overestimates the spin-orbit splittings in heavy nuclei [14,29,98]. Adding the tensor terms, however, further deteriorates the overall description of spin-orbit splittings, instead of improving it.…”

Section: Connection Between Tensor and Spin-orbit Termsmentioning

confidence: 81%

Tensor part of the Skyrme energy density functional: Spherical nuclei

Lesinski

Bender²,

Bennaceur³

et al. 2007

Phys. Rev. C

345

659

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We perform a systematic study of the impact of the J 2 tensor term in the Skyrme energy functional on properties of spherical nuclei. In the Skyrme energy functional, the tensor terms originate from both zero-range central and tensor forces. We build a set of 36 parametrizations, covering a wide range of the parameter space of the isoscalar and isovector tensor term coupling constants with a fit protocol very similar to that of the successful SLy parametrizations. We analyze the impact of the tensor terms on a large variety of observables in spherical mean-field calculations, such as the spin-orbit splittings and single-particle spectra of doubly-magic nuclei, the evolution of spin-orbit splittings along chains of semi-magic nuclei, mass residuals of spherical nuclei, and known anomalies of radii. The major findings of our study are as follows: (i) Tensor terms should not be added perturbatively to existing parametrizations; a complete refit of the entire parameter set is imperative. (ii) The free variation of the tensor terms does not lower the χ 2 within a standard Skyrme energy functional. (iii) For certain regions of the parameter space of their coupling constants, the tensor terms lead to instabilities of the spherical shell structure, or even to the coexistence of two configurations with different spherical shell structures. (iv) The standard spin-orbit interaction does not scale properly with the principal quantum number, such that single-particle states with one or several nodes have too large spin-orbit splittings, whereas those of nodeless intruder levels are tentatively too small. Tensor terms with realistic coupling constants cannot cure this problem.(v) Positive values of the coupling constants of proton-neutron and like-particle tensor terms allow for a qualitative description of the evolution of spin-orbit splittings in chains of Ca, Ni, and Sn isotopes. (vi) For the same values of the tensor term coupling constants, however, the overall agreement of the single-particle spectra in doubly-magic nuclei is deteriorated, which can be traced back to features of the single-particle spectra that are not related to the tensor terms. We conclude that the currently used central and spin-orbit parts of the Skyrme energy density functional are not flexible enough to allow for the presence of large tensor terms.well-defined transformation properties under rotations: (7) where δ µν is the Kronecker symbol and µνκ is the Levi-Civita tensor. The pseudoscalar, vector, and pseudotensor parts expressed in terms of the Cartesian tensor are given byν=x κµν J µν (r), 014312-6 TENSOR PART OF THE SKYRME ENERGY DENSITY . . . PHYSICAL REVIEW C 76, 014312 (2007) some authors [59]: z µ,ν=x J t,µν J t,µν = 1 3 J (0) t 2 + 1 2 J 2 t + z µ,ν=x J (2) t,µν J (2) t,µν , (24) 1 2 z µ=x J t,µµ 2 + z µ,ν=x J t,µν J t,νµ = 2 3 J (0) t 2 − 1 4 J 2 t + 1 2 z µ,ν=x J (2) t,µν J (2) t,µν . (25)

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Section: Connection Between Tensor and Spin-orbit Termsmentioning

confidence: 81%

Tensor part of the Skyrme energy density functional: Spherical nuclei

Lesinski

Bender²,

Bennaceur³

et al. 2007

Phys. Rev. C

345

659

View full text Add to dashboard Cite

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“…The neutron and proton spin-orbit splittings E SO = E n,l,j=l−1/2 −E n,l,j=l+1/2 are examined in Fig.5 Various experimental data [23,24] are also shown in Table.1, respectively. The upper and lower triangles are taken from Ref.…”

Section: Finite Nucleimentioning

confidence: 99%

Effective Dirac Brueckner-Hartree-Fock method for asymmetric nuclear matter and finite nuclei

Liu

2002

Phys. Rev. C

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A new decomposition of the Dirac structure of nucleon self-energies in the Dirac Brueckner-Hartree-Fock (DBHF) approach is adopted to investigate the equation of state for asymmetric nuclear matter. The effective coupling constants of σ, ω, δ and ρ mesons with a density dependence in the relativistic mean field approach are deduced by reproducing the nucleon self-energy resulting from the DBHF at each density for symmetric and asymmetric nuclear matter. With these couplings the properties of finite nuclei are investigated.The agreement of charge radii and binding energies of finite nuclei with the experimental data are improved simultaneously in comparison with the projection method. It seems that the properties of finite nuclei are sensitive to the scheme used for the DBHF self-energy extraction. We may conclude that the properties of the asymmetric nuclear matter and finite nuclei could be well described by the new decomposition approach of the G matrix.

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“…It is found that the Fock terms of the σ and ω μ fields strongly contribute to the symmetry energy and increase somewhat the value of K. In contrast, the contribution of pions and, mainly, the contribution of the tensor coupling of the ρ meson produce a major reduction of this magnitude, although, for the coupling constants chosen in [18], K still remains too large (∼460 MeV). Nevertheless, the increase of the KE appears to be quite sensitive to the reduction of K. Further, with the experimental value of the coupling constant f 2 π /4π = 0.08 used, pions produce unrealistic spin-orbit splittings [26] and gaps in the shell model [13,14], which restricts the applicability of the RHFA [18].…”

Section: Results On the Anomalous Ke With Published Relativistic Modelsmentioning

confidence: 95%

“…This can be done, quite simply, in the RHFA [18]. However, if one uses the experimental coupling constant for the Nπ vertex obtained from the NN scattering data (f 2 π /4π ≈ 0.08), the spin-orbit splittings in a family of isotopes seem to exhibit a too strong dependence on A [26]. For example, to fit the experimental results for the splitting of the 1d states of the 48 Ca nucleus, one should reduce the value of f 2 π /4π about 40−60% from its experimental value, i.e., down to f 2 π /4π ≈ 0.05−0.03 (notice that the experimental uncertainty of the spin-orbit splitting for this 1d doublet is not small [26]).…”

Section: Pion Contributionmentioning

confidence: 97%

Isotopic dependence of the nuclear charge radii and binding energies in the relativistic Hartree-Fock formalism

et al. 2012

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Relativistic nonlinear models based on the Hartree and Hartree-Fock approximations, including the σ, ω, π, and ρ mesons, are worked out to explore the behavior of the nuclear charge radii and the binding energies of several isotopic chains. We find a correlation between the magnitude of the anomalous kink effect (KE) in the Pb isotopic family and the compressibility modulus (K) of nuclear matter. The KE appears to be sensitive, in particular, to the mechanisms which control the K value. The influence of the symmetry energy on the Ca isotopic chain is also studied. The behavior of the charge radii of single-particle states for some special cases and its repercussion on the nuclear charge radius is analyzed. The effect of pairing correlations on the models improves considerably the quality of the results in both binding energy and KE.

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Spin-orbit splitting in nonrelativistic and relativistic self-consistent models

Cited by 28 publications

References 26 publications

Tensor part of the Skyrme energy density functional: Spherical nuclei

Tensor part of the Skyrme energy density functional: Spherical nuclei

Effective Dirac Brueckner-Hartree-Fock method for asymmetric nuclear matter and finite nuclei

Isotopic dependence of the nuclear charge radii and binding energies in the relativistic Hartree-Fock formalism

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