Symmetry energies, pairing energies, and mass equations

Jänecke, J.; O’Donnell, T.W.

doi:10.1016/j.nuclphysa.2006.11.003

Cited by 12 publications

(18 citation statements)

References 38 publications

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“…Notwithstanding the above considerations, analyses have been carried out in the past leading to a strong dependence of a a on Z, in particular for light systems [8] and for small |N − Z| [29,30], in no particular relation to the Coulomb-symmetry-energy interplay. In addition, claims of proportionality of the symmetry energy to T (T + b) have been made, with b different from 1, such as b ∼ 4 [25,29,30,50]. The latter claims would imply the excitation energy to an IAS of the general form…”

Section: A General Considerationsmentioning

confidence: 99%

Symmetry energy II: Isobaric analog states

2014

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Using excitation energies to isobaric analog states (IAS) and charge invariance, we extract nuclear symmetry coefficients, from a mass formula, on a nucleus-by-nucleus basis. Consistently with charge invariance, the coefficients vary weakly across an isobaric chain. However, they change strongly with nuclear mass and range from a a ∼ 10 MeV at mass A ∼ 10 to a a ∼ 22 MeV at A ∼ 240. Variation with mass can be understood in terms of dependence of nuclear symmetry energy on density and the rise in importance of low densities within nuclear surface in smaller systems. At A 30, the dependence of coefficients on mass can be well described in terms of a macroscopic volume-surface competition formula with a V a ≃ 33.2 MeV and a S a ≃ 10.7 MeV.Our further investigation shows, though, that the fitted surface symmetry coefficient likely significantly underestimates that for the limit of half-infinite matter. Following the considerations of a Hohenberg-Kohn functional for nuclear systems, we determine how to find in practice the symmetry coefficient using neutron and proton densities, even when those densities are simultaneously affected by significant symmetry-energy and Coulomb effects. These results facilitate extracting the symmetry coefficients from Skyrme-Hartree-Fock (SHF) calculations, that we carry out using a variety of Skyrme parametrizations in the literature. For the parametrizations, we catalog novel short-wavelength instabilities. In our further analysis, we retain only those parametrizations which yield systems that are adequately stable both in the long-and short-wavelength limits. In comparing the SHF and IAS results for the symmetry coefficients, we arrive at narrow (±2.4 MeV) constraints on the symmetry energy values S(ρ) at 0.04 ρ 0.13 fm −3 . Towards normal density the constraints significantly widen, but the normal value of energy a V a and the slope parameter L are found to be strongly correlated. To narrow the constraints, we reach for the measurements of Dirac-Bruckner-Hartree-Fock, are consistent with our constraint region on S(ρ).

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Section: A General Considerationsmentioning

confidence: 99%

Symmetry energy II: Isobaric analog states

2014

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“…In addition, the nuclei are divided into regions defined by shells in a similar manner as in ref. [15] in order to see possible related structure changes. In Sec.…”

Section: Detailed Segmented Analysismentioning

confidence: 99%

Global phenomenological descriptions of nuclear odd-even mass staggering

2013

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We examine the general nature of nuclear odd-even mass differences by employing neutron and proton mass relations that emphasize these effects. The most recent mass tables are used. The possibility of a neutron excess dependence of the staggering is examined in detail in separate regions defined by the main nuclear shells, and a clear change in this dependency is found at Z = 50 for both neutrons and protons. A further separation into odd and even neutron (proton) number produces very accurate local descriptions of the mass differences for each type of nucleons. These odd-even effects are combined into a global phenomenological expression, ready to use in a binding energy formula. The results deviate from previous parametrizations, and in particular found to be significantly superior to a recent two term, A −1 dependence.

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“…Then, at some excitation energy ~ or temperature a sharp second-order phase transition occurs to a normal-heated Fermi liquid where the pairing effects are usually neglected [63]. The thermodynamically properties [44][45][46][47][48][49][50], entropy [51][52][53][54][55] and etc have been studied by different authors. The statistical properties of energy levels can be used for investigating the pairing effect on nuclear structures, too.…”

Section: Pairing Hamiltonianmentioning

confidence: 99%

A non-parametric estimation approach in the investigation of spectral statistics

et al. 2013

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In this paper, Kernel Density Estimation (KDE) as a non-parametric estimation method is used to investigate statistical properties of nuclear spectra. The deviation to regular or chaotic dynamics, is exhibited by closer distances to Poisson or Wigner limits respectively which evaluated by Kullback-Leibler Divergence (KLD) measure. Spectral statistics of different sequences prepared by nuclei corresponds to three dynamical symmetry limits of Interaction Boson Model(IBM), oblate and prolate nuclei and also the pairing effect on nuclear level statistics are analyzed (with pure experimental data). KD-based estimated density function, confirm previous predictions with minimum uncertainty (evaluated with Integrate Absolute Error (IAE)) in compare to Maximum Likelihood (ML)-based method. Also, the increasing of regularity degrees of spectra due to pairing effect is reveal.

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Symmetry energies, pairing energies, and mass equations

Cited by 12 publications

References 38 publications

Symmetry energy II: Isobaric analog states

Symmetry energy II: Isobaric analog states

Global phenomenological descriptions of nuclear odd-even mass staggering

A non-parametric estimation approach in the investigation of spectral statistics

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