Exploration of a modified density dependence in the Skyrme functional

Erler, J.; Klüpfel, P.; Reinhard, P.‐G.

doi:10.1103/physrevc.82.044307

Cited by 32 publications

(50 citation statements)

References 48 publications

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“…Such density dependence in the volume term had also been studied in the context of Skyrme EDF's [31] and found to make not much difference as compared to the form (4). The important new aspect is that the surface term E s Fy has also the form of a Padé approximant involving the gradient of density:…”

Section: The Fayans Functionalmentioning

confidence: 99%

Toward a global description of nuclear charge radii: Exploring the Fayans energy density functional

Reinhard¹,

Nazarewicz²

2017

Phys. Rev. C

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114

102

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Background: Binding energies and charge radii are fundamental properties of atomic nuclei. When inspecting their particle-number dependence, both quantities exhibit pronounced odd-even staggering. While the odd-even effect in binding energy can be attributed to nucleonic pairing, the origin of staggering in charge radii is less straightforward to ascertain.Purpose: In this work, we study the odd-even effect in binding energies and charge radii, and systematic behavior of differential radii, to identify the underlying components of the effective nuclear interaction.Method: We apply nuclear density functional theory using a family of Fayans and Skyrme energy density functionals fitted to similar datasets but using different optimization protocols. We inspect various correlations between differential charge radii, odd-even staggering in energies and radii, and nuclear matter properties. Detailed analysis is carried out for medium-mass and heavy semi-magic nuclei with a particular focus on the Ca chain.Results: By making the surface and pairing terms dependent on density gradients, the Fayans functional offers the superb simultaneous description of odd-even staggering effects in energies and charge radii. Conversely, when the data on differential radii are added to the pool of fit-observables, the coupling constants determining the strengths of the gradient terms of Fayans functional are increased by orders of magnitude. The Skyrme functional optimized in this work with the generalized Fayans pairing term offers results of similar quality. We quantify these findings by performing correlation analysis based on the statistical linear regression technique. The nuclear matter parameters characterizing Fayans and Skyrme functionals optimized to similar datasets are fairly close. Conclusion:Fayans paring functional, with its generalized density dependence, significantly improves description of charge radii in odd and even nuclei. Adding differential charge radii to the set of fit-observables in the optimization protocol is helpful for both description of radii and for improving pairing functional. In particular, Fayans functional constrained in this way is capable of explaining charge radii in the even-even Ca isotopes. However, in order to obtain good description of differential radii data in both medium-mass and heavy nuclei, an A-dependent scaling of Fayans pairing functional is still needed. Various extensions of the current model are envisioned that carry out a promise for the global description.

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Section: The Fayans Functionalmentioning

confidence: 99%

Toward a global description of nuclear charge radii: Exploring the Fayans energy density functional

Reinhard¹,

Nazarewicz²

2017

Phys. Rev. C

Self Cite

114

102

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“…[17] and recently employed in refs. [67,38]. We wish to emphasize that this is the first time that one consistent phenomenological input has been used to constrain SHF and RMF EDFs.…”

Section: Brief Review Of χ 2 Technique and Correlation Analysismentioning

confidence: 99%

“…They are compared with NMP of SHF-RD [67] (employing a modified density dependence and the standard dataset) and SHF-TOV [38] (using neutron star data in addition the standard dataset in the optimization process). As expected, isoscalar effective mass is significantly lowered in RMF as compared to SHF, and the opposite holds for κ TRK .…”

Section: Correlations With Nuclear Matter Propertiesmentioning

confidence: 99%

Symmetry energy in nuclear density functional theory

et al. 2014

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Abstract. The nuclear symmetry energy represents a response to the neutron-proton asymmetry. In this paper we discuss various aspects of symmetry energy in the framework of nuclear density functional theory, considering both non-relativistic and relativistic self-consistent mean-field realizations side by side. Key observables pertaining to bulk nucleonic matter and finite nuclei are reviewed. Constraints on the symmetry energy and correlations between observables and symmetry energy parameters, using statistical covariance analysis, are investigated. Perspectives for future work are outlined in the context of ongoing experimental efforts.

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“…where the normalization factor C 0 = dn/dε F ) −1 = 300 MeV· fm 3 , and the value of r 0 = 0.4 fm was found in [47,48] for the parameter which determines the dependence of the amplitude g ′ on the momentum transfer. To evaluate the PC corrections we need in the vertex g L (r), the creation amplitude of the L-phonon.…”

Section: Self-consistent Tffsmentioning

confidence: 99%

“…It concerns the Hartree-Fock (HF) method with Skyrme force [2,3], the HF method with Gogny force [4], the Relativistic Mean-Field approach [5] and the so-called Generalized Energy Density Functional (EDF) method by Fayans et al [6]. The last approach is essentially close to the selfconsistent Theory of Finite Fermi Systems (TFFS) [7] based on TFFS by Migdal [8] supplemented with the Fayans-Khodel self-consistency relation [9].…”

Section: Introductionmentioning

confidence: 99%

Phonon coupling effects in magnetic moments of magic and semimagic nuclei

et al. 2014

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Phonon coupling (PC) corrections to magnetic moments of odd neighbors of magic and semimagic nuclei are analyzed within the self-consistent Theory of Finite Fermi Systems (TFFS) based on the Energy Density Functional by Fayans et al. The perturbation theory in g 2 L is used where gL is the phonon-particle coupling vertex. A model is developed with separating non-regular PC contributions, the rest is supposed to be regular and included into the standard TFFS parameters. An ansatz is proposed to take into account the so-called tadpole term which ensures the total angular momentum conservation with g 2 L accuracy. An approximate method is suggested to take into account higher order terms in g 2 L . Calculations are carried out for four odd-proton chains, the odd Tl, Bi, In and Sb ones. Different PC corrections strongly cancel each other. In the result, the total PC correction to the magnetic moment in magic nuclei is, as a rule, negligible. In non-magic nuclei considered it is noticeable and, with only one exception, negative. On average it is of the order of −(0.1 ÷ 0.5) µN and improves the agreement of the theory with the data. Simultaneously we calculated the gyromagnetic ratios g ph L of all low-lying phonons in 208 Pb. For the 3 − 1 state it is rather close to the Bohr-Mottelson model prediction whereas for other L-phonons, two 5 − and six positive parity states, the difference from the Bohr-Mottelson values is significant.

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Exploration of a modified density dependence in the Skyrme functional

Cited by 32 publications

References 48 publications

Toward a global description of nuclear charge radii: Exploring the Fayans energy density functional

Toward a global description of nuclear charge radii: Exploring the Fayans energy density functional

Symmetry energy in nuclear density functional theory

Phonon coupling effects in magnetic moments of magic and semimagic nuclei

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