Microscopic-macroscopic approach for binding energies with the Wigner-Kirkwood method

Bhagwat, A.; Viñas, X.; Centelles, M.; Schuck, Peter; Wyss, R.

doi:10.1103/physrevc.81.044321

Cited by 51 publications

(96 citation statements)

References 70 publications

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“…Next, we calculate single-particle (SP) levels in each nucleus by using a Woods-Saxon potential, whose parameters are taken from Ref. [10]. Note that, in principle, the SP potential depends on temperature.…”

Section: Finite-temperature Shell-correction Methodsmentioning

confidence: 99%

Shell effects in hot nuclei and their influence on nuclear composition in supernova matter

Nishimura¹,

Takano²

2014

AIP Conference Proceedings

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Abstract. We calculate nuclear composition in supernova (SN) matter explicitly taking into account the temperature dependence of nuclear shell effects. The abundance of nuclei in SN matter is important in the dynamics of core-collapse supernovae and, in recently constructed equations of state (EOS) for SN matter, the composition of nuclei are calculated assuming nuclear statistical equilibrium wherein the nuclear internal free energies govern the composition. However, in these EOS, thermal effects on the shell energy are not explicitly taken into account. To address this shortfall, we calculate herein the shell energies of hot nuclei and examine their influence on the composition of SN matter. Following a simplified macroscopic-microscopic approach, we first calculate single-particle (SP) energies by using a spherical Woods-Saxon potential. Then we extract shell energies at finite temperatures using Strutinsky method with the Fermi distribution as the average occupation probability of the SP levels. The results show that at relatively low temperatures, shell effects are still important and magic nuclei are abundant. However, at temperatures above approximately 2 MeV, shell effects are almost negligible, and the mass fractions with shell energies including the thermal effect are close to those obtained from a simple liquid drop model at finite temperatures.

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Section: Finite-temperature Shell-correction Methodsmentioning

confidence: 99%

Shell effects in hot nuclei and their influence on nuclear composition in supernova matter

Nishimura¹,

Takano²

2014

AIP Conference Proceedings

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“…In our previous works [6,7], we have demonstrated that the Strutinsky average can be replaced by the semiclassical energy computed by means of the Wigner-Kirkwood (WK)h expansion of the one-body partition function [8][9][10][11][12][13][14][15], in order to evaluate the shell corrections of a system of N neutrons and Z protons at zero temperature in an external potential. There are some reasons supporting this choice as we have discussed in Ref.…”

Section: Introductionmentioning

confidence: 99%

Microscopic-macroscopic approach for binding energies with the Wigner-Kirkwood method. II. Deformed nuclei

et al. 2012

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The binding energies of deformed even-even nuclei have been analyzed within the framework of a recently proposed microscopic-macroscopic model. We have used the semiclassical Wigner-Kirkwoodh expansion up to fourth order, instead of the usual Strutinsky averaging scheme, to compute the shell corrections in a deformed Woods-Saxon potential including the spin-orbit contribution. For a large set of 561 even-even nuclei with Z 8 and N 8, we find an rms deviation from the experiment of 610 keV in binding energies, comparable to the one found for the same set of nuclei using the finite range droplet model of Möller and Nix (656 keV). As applications of our model, we explore its predictive power near the proton and neutron drip lines as well as in the superheavy mass region. Next, we systematically explore the fourth-order Wigner-Kirkwood corrections to the smooth part of the energy. It is found that the ratio of the fourth-order to the second-order corrections behaves in a very regular manner as a function of the asymmetry parameter I = (N − Z)/A. This allows us to absorb the fourth-order corrections into the second-order contributions to the binding energy, which enables us to simplify and speed up the calculation of deformed nuclei.

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“…Thus ETF energy functional embodies the macroscopic models; it is more general and powerful. Some of the macroscopic models with microscopic corrections [48,50,54,55,60, and 81] also suffer from the inconsistency problem mentioned earlier. Exceptions being the Duflo-Zuker…”

Section: Further Discussionmentioning

confidence: 99%

“…These are the same set of nuclei considered by Bhagwat et al [54]. The electronic binding energy 1.433x10 −5 Z 2.39 MeV has been subtracted from the binding energies of Ref [38].…”

Section: A Calculations For Nucleimentioning

confidence: 99%

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Nuclear matter properties, phenomenological theory of clustering at the nuclear surface, and symmetry energy

et al. 2011

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We present a phenomenological theory of nuclei that incorporates clustering at the nuclear surface in a general form. The theory explains the recently extracted large symmetry energy by Natowitz et al. at low densities of nuclear matter and is fully consistent with the static properties of nuclei. In phenomenological way clusters of all sizes, shapes along with medium modifications are included. Symmetric nuclear matter properties are discussed in detail. Arguments are given that lead to an equation of state of nuclear matter consistent with clustering in the low density region. We also discuss properties of asymmetric nuclear matter. Because of clustering, an interesting interpretation of the equation of state of asymmetric nuclear matter emerges. As a framework, an extended version of Thomas Fermi theory is adopted for nuclei which also contain phenomenological pairing and Wigner contributions. This theory connects the nuclear matter equation of state, which incorporate clustering at low densities, with clustering in nuclei at the nuclear surface. Calculations are performed for various equation of state of nuclear matter. We consider measured binding energies of 2149 nuclei for N, Z ≥ 8. The importance of quartic term in symmetry energy is demonstrated at and below the saturation density of nuclear matter. It is shown that it is largely related to the use of, ab initio, realistic equation of state of neutron matter, particularly the contribution arising from the three neutron interaction and somewhat to clustering.Reasons for these are discussed. Because of clustering the neutron skin thickness in nuclei is found to reduce significantly. Theory predicts new situations and regimes to be explored both theoretically and experimentally. *

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Microscopic-macroscopic approach for binding energies with the Wigner-Kirkwood method

Cited by 51 publications

References 70 publications

Shell effects in hot nuclei and their influence on nuclear composition in supernova matter

Shell effects in hot nuclei and their influence on nuclear composition in supernova matter

Microscopic-macroscopic approach for binding energies with the Wigner-Kirkwood method. II. Deformed nuclei

Nuclear matter properties, phenomenological theory of clustering at the nuclear surface, and symmetry energy

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