Isotope shifts within the energy-density functional approach with density dependent pairing

Fayans, S.A.; Tolokonnikov, S. V.; Trykov, E.L.; Zawischa, D.

doi:10.1016/0370-2693(94)91334-x

Cited by 45 publications

(25 citation statements)

References 19 publications

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“…The obtained relations can be used to estimate the influence of pairing on the charge radii for heavy nuclei as was done in Ref. [22]. It was shown that pairing interaction with strong ρ-dependence at x ≈ 1 might significantly change the equilibrium density.…”

mentioning

confidence: 88%

“…In all these calculations the functional parameter set of Ref. [22] have been used. These results are presented in Table 2 strong phonons which contribute significantly to the mean square radii.…”

Section: Ground State Fluctuationsmentioning

confidence: 99%

“…First results obtained mainly in diagonal-pairing approximation (i.e. with a HF-BCS formalism) have already been given in a few short publications [22][23][24] (the paper [23] gives the first application of the EDF approach to deformed nuclei and contains the results of a HFB-type calculation for dysprosium isotopes). In the present paper we give the results of more elaborate calculations based on the coordinate-space technique developed in [25] which allows us, for a local pairing field ∆( r), to solve the Gor'kov equations in spherical finite systems without any approximations [26].…”

Section: Introductionmentioning

confidence: 99%

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Nuclear isotope shifts within the local energy-density functional approach

et al. 2000

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The foundation of the local energy-density functional method to describe the nuclear ground-state properties is given. The method is used to investigate differential observables such as the odd-even mass differences and odd-even effects in charge radii. For a few isotope chains of spherical nuclei, the calculations are performed with an exact treatment of the Gor'kov equations in the coordinate-space representation. A zero-range cutoff density-dependent pairing interaction with a density-gradient term is used. The evolution of charge radii and nucleon separation energies is reproduced reasonably well including kinks at magic neutron numbers and sizes of staggering. It is shown that the density-dependent pairing may also induce sizeable staggering and kinks in the evolution of the mean energies of multipole excitations. The results are compared with the conventional mean field Skyrme-HFB and relativistic Hartree-BCS calculations. With the formulated approach, an extrapolation from the pairing properties of finite nuclei to pairing in infinite matter is considered, and the dilute limit near the critical point, at which the regime changes from weak to strong pairing, is discussed. 21.65.+f; 21.90.+f; 24.10.Cn PACS

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confidence: 88%

Section: Ground State Fluctuationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nuclear isotope shifts within the local energy-density functional approach

et al. 2000

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“…and, thirdly, the contact interaction depending on the total (isoscalar) density of particles ρ(r) [23][24][25][26],…”

Section: Pairing Interactionsmentioning

confidence: 99%

Closed shells at drip-line nuclei

Dobaczewski¹,

Nazarewicz²,

Werner³

1995

Phys. Scr.

101

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“…In this context, the EDF developed by S.A. Fayans and collaborators [14][15][16][17][18] stands out as it has demonstrated a rare ability to describe charge radii in isotopic chains of semi-magic spherical nuclei, including the challenging Ca chain. A notable achievement of the Fayans model has been to explain the odd-even staggering effect in charge radii in terms of the density-dependent nucleonic pairing [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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

Reinhard¹,

Nazarewicz²

2017

Phys. Rev. C

112

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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Isotope shifts within the energy-density functional approach with density dependent pairing

Cited by 45 publications

References 19 publications

Nuclear isotope shifts within the local energy-density functional approach

Nuclear isotope shifts within the local energy-density functional approach

Closed shells at drip-line nuclei

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

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