Systematics of collective correlation energies from self-consistent mean-field calculations

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

doi:10.1140/epja/i2008-10633-3

Cited by 57 publications

(98 citation statements)

References 57 publications

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“…[23]. The adopted errors for ∆E ee were derived by estimating the effect of ground state correlations as in [45]. Experimental nuclear masses and charge radii were taken from Refs.…”

Section: F Optimization Strategies and Variantsmentioning

confidence: 99%

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

Reinhard¹,

Nazarewicz²

2017

Phys. Rev. C

117

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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“…[23]. The adopted errors for ∆E ee were derived by estimating the effect of ground state correlations as in [45]. Experimental nuclear masses and charge radii were taken from Refs.…”

Section: F Optimization Strategies and Variantsmentioning

confidence: 99%

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

Reinhard¹,

Nazarewicz²

2017

Phys. Rev. C

117

102

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“…[22]. These fits were done to a large pool of semi-magic nuclei that were checked to have negligible correlation effects [27]. The observables included in the SV optimization database are: binding energy (70 entries), rms charge radius (50 entries), charge diffraction radius (28 entries), charge surface thickness (26 entries), neutron and proton pairing gaps (37 entries), and spinorbit splittings of single-particle energies (7 entries).…”

Section: A Scmf Modelsmentioning

confidence: 99%

Information content of the weak-charge form factor

et al. 2013

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Background: Parity-violating electron scattering provides a model-independent determination of the nuclear weak-charge form factor that has widespread implications across such diverse areas as fundamental symmetries, nuclear structure, heavy-ion collisions, and neutron-star structure.Purpose: We assess the impact of precise measurements of the weak-charge form factor of 48 Ca and 208 Pb on a variety of nuclear observables, such as the neutron skin and the electric-dipole polarizability.Methods: We use the nuclear Density Functional Theory with several accurately calibrated non-relativistic and relativistic energy density functionals. To assess the degree of correlation between nuclear observables and to explore systematic and statistical uncertainties on theoretical predictions, we employ the chi-square statistical covariance technique.Results: We find a strong correlation between the weak-charge form factor and the neutron radius, that allows for an accurate determination of the neutron skin of neutron-rich nuclei. We determine the optimal range of the momentum transfer q that maximizes the information content of the measured weak-charge form factor and quantify the uncertainties associated with the strange quark contribution. Moreover, we confirm the role of the electric-dipole polarizability as a strong isovector indicator.Conclusions: Accurate measurements of the weak-charge form factor of 48 Ca and 208 Pb will have a profound impact on many aspects of nuclear theory and hadronic measurements of neutron skins of exotic nuclei at radioactivebeam facilities.

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“…Its evaluation is very involved, for details see [41,44,45]. We will include the full correlation energies only once in the introductory overview in section 6.0.1.…”

Section: Correlation Energymentioning

confidence: 99%

“…This together defines a collective Schrödinger equation whose solution then yields the collective excitation energies and associated B(E2) values. For details of this rather involved formal framework see, e.g., [41,46]. remain open.…”

Section: Finite Nucleimentioning

confidence: 99%

“…The set of fit data includes the bulk properties E B , r rms , R diffr , and σ plus pairing gaps and some spin-orbit splittings (see section 3.2). The nuclei are restricted to be spherical and carefully selected to have small ground-state correlations [41]. This guarantees that we deal with nuclei which can reliably well be described by a mean-field model.…”

Section: Finite Nucleimentioning

confidence: 99%

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Estimating the relevance of predictions from the Skyrme–Hartree–Fock model

Reinhard

2015

Phys. Scr.

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This contribution reviews the present status of the Skyrme-HartreeFock (SHF) approach as one of the leading self-consistent mean-field models in the physics of atomic nuclei. It starts with a brief summary of the formalism and strategy for proper calibration of the SHF functional. The main emphasis lies on an exploration of the reliability of predictions, particularly in the regime of extrapolations. Various strategies are discussed to explore the statistical and systematic errors of SHF. The strategies are illustrated on examples from actual applications. Variations of model and fit data are used to get an idea about systematic errors. The statistical error is evaluated in straightforward manner by statistical analysis based on χ 2 fits. This also allows also to evaluate the correlations (covariances) between observables which provides useful insights into the structure of the model and of the fitting strategy.

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Systematics of collective correlation energies from self-consistent mean-field calculations

Cited by 57 publications

References 57 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

Information content of the weak-charge form factor

Estimating the relevance of predictions from the Skyrme–Hartree–Fock model

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