Error estimates for the Skyrme–Hartree–Fock model

Erler, J.; Reinhard, P.‐G.

doi:10.1088/0954-3899/42/3/034026

Cited by 42 publications

(51 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As a consequence, the charge radius of 44 Ca is increased, and that of 48 Ca is reduced, with respect to the Fy(std) prediction. While the properties of the charge form factor of 48 Ca are well reproduced by Fy(∆r), this is not the case for of 44 Ca, where a good agreement for r ch is obtained at the cost of underestimating σ ch and overestimating of R diff . Another interesting lesson offered by Fig.…”

Section: Ca Andmentioning

confidence: 79%

“…The functionals with the full Fayans pairing, namely Fy(∆r), Fy(∆r, ∆r oe ), and Sk+PFy, perform well up to 48 Ca. However, the δ⟨r 2 ⟩ values in 49−52 Ca are underestimated in all models except for Fy(∆r).…”

Section: Ca Andmentioning

confidence: 98%

“…Another key structural indicator is the odd-even staggering of charge radii along isotopic chains. In particular, the intricate behavior of charge radii along the Ca chain -the almost equal values of charge radii in 40 Ca and 48 Ca, an appreciable oddeven staggering, and unexpectedly large charge radius in 52 Ca [6] -constitute a long-standing challenge for nuclear theory [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Reinhard¹,

Nazarewicz²

2017

Phys. Rev. C

117

102

View full text Add to dashboard Cite

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.

show abstract

Section: Ca Andmentioning

confidence: 79%

Section: Ca Andmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Reinhard¹,

Nazarewicz²

2017

Phys. Rev. C

117

102

View full text Add to dashboard Cite

show abstract

“…One can omit a group from the pool of fit data. Comparison with the full fit allows to explore the impact of the omitted group, see [94] and section 6.2.…”

Section: Variations Of Fit Datamentioning

confidence: 99%

“…An analysis following this strategy was already given in [94]. We repeat part of that material for a reduced set of variations and, on the other hand, add new variations.…”

Section: Impact Of Groups Of Datamentioning

confidence: 99%

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

Reinhard

2015

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Fission barriers and probabilities of spontaneous fission for elements with Z≥ 100

et al. 2015

View full text Add to dashboard Cite

This is a short review of methods and results of calculations of fission barriers and fission halflives of even-even superheavy nuclei. An approvable agreement of the following approaches is shown and discussed: The macroscopic-microscopic approach based on the stratagem of the shell correction to the liquid drop model and a vantage point of microscopic energy density functionals of Skyrme and Gogny type selfconsistently calculated within Hartree-Fock-Bogoliubov method. Mass parameters are calculated in the Hartree-Fock-Bogoliubov cranking approximation. A short part of the paper is devoted to the nuclear fission dynamics. We also discuss the predictive power of Skyrme functionals applied to key properties of the fission path of 266 Hs. It applies the standard techniques of error estimates in the framework of a χ 2 analysis.

show abstract

Error estimates for the Skyrme–Hartree–Fock model

Cited by 42 publications

References 37 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

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

Fission barriers and probabilities of spontaneous fission for elements with Z≥ 100

Contact Info

Product

Resources

About