The nuclear droplet model for arbitrary shapes

Myers, William D.; Świa̧tecki, W.J.

doi:10.1016/0003-4916(74)90299-1

Cited by 392 publications

(205 citation statements)

References 12 publications

(4 reference statements)

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“…5. Once again our calculation agrees fairly well with the results of [5] and at p =Po, with the phenomenological value [15] of E~ym. Very similar results to ours have been obtained [16] in a relativistic calculation at smaller fl values.…”

Section: Symmetry Energy Symmetry Potentialsupporting

confidence: 89%

Neutron matter properties in an extended Brueckner approach

Deneye

Lejeune

1987

Z. Physik A - Atomic Nuclei

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Neutron matter properties are calculated both at zero and finite temperature within an extended Brueckner approach using the Paris potential. The binding energy turns out to be very close to the one calculated variationally with the Urbana v14 potential. Particular emphasis is put on the symmetry energy, on the isospin dependence of the mean field and on the effective mass. As an illustration, the masses of neutron stars are calculated. 21.65. +f PACS: IntroductionA great deal of interest is currently devoted to the nuclear matter equation of state. The present situation is however rather confuse. To describe it very shortly, conventional analysis of giant monopole in nuclei [1,2], early analysis of heavy-ion collisions neglecting effective mass effects [3,4] and microscopic calculations based on potential models, be them performed in a variational [5] or in a (nonrelativistic [6] or relativistic [7]) perturbative scheme, seem to point to a so-called stiff nuclear matter equation of state, i.e. a sharp increase of the binding energy per particle between P0 and ,-~4po (P0 =normal nuclear matter equilibrium density). On the other hand, reanalysis of nuclear properties in the spirit of the Landau sum rules for Fermi liquids [8], and recent calculations on supernovae explosions [9] seem, on the contrary, to suggest that the equation of state would be much softer. Finally, the masses of known neutron stars favour [10] a stiff nuclear matter equation of state. The last considerations involve asymmetric nuclear matter, for which the theoretical investigations are much less numerous in comparison with the symmetric case. In fact, for purely neutronic matter, there is practically only one very sophisticated microscopic * Work supported by the NATO Grant 025.81 calculation [5], based on the variational method. Here, we want to study the same system by a detailed Brueckner type approach, both at zero and at low temperature, extending so our previous investigations of symmetric nuclear matter [6]. Actually, our purpose is fourfold. First, we want to calculate the binding energy of neutron matter, in order to check whether the agreement between variational and perturbative approaches, observed for N =Z [6], also holds for Z = 0. Second, we want to calculate microscopically the symmetry energy. Third, we investigate the single-particle properties of neutron matter both at T= 0 and T+ 0, especially the neutron effective mass, which can play an important role in supernovae explosions. Fourth, we propose ourselves to use our results to calculate the neutron star mass spectrum. This is for illustrative purpose mainly, since this calculation requires the detailed knowledge of the equation of state at large densities, for which the perturbative approach is inadequate or, at least, on less safe grounds than the variational approach.The paper is organized as follows. Section 2 shortly describes the theoretical frame. Section 3 contains the numerical results for the binding energy, the average nucleon field, the effective mass and...

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Section: Symmetry Energy Symmetry Potentialsupporting

confidence: 89%

Neutron matter properties in an extended Brueckner approach

Deneye

Lejeune

1987

Z. Physik A - Atomic Nuclei

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“…where r 2 is the mean-square radius of the nucleus and Q is the surface stiffness coefficient that measures the resistance of the system to the formation of a neutron skin [31]. In keeping with the fact that the ratio J/Q and the slope parameter L display a strong correlation [33], this semi-classical result clearly indicates that the electric dipole polarizability is related to properties of the nuclear symmetry energy [34].…”

Section: A Theoretical Conceptsmentioning

confidence: 59%

“…In the particular case of the electric dipole polarizability, the m −1 moment may be obtained from a constrained calculation based on Eq. (3) using the droplet model of Myers and Swiatecki [31]. In this case the semi-classical approximation to the electric dipole polarizability reads [32]:…”

Section: A Theoretical Conceptsmentioning

confidence: 99%

Neutron skin thickness from the measured electric dipole polarizability inNi68,Sn120, and
Roca-Maza
¹
,
Viñas
²
,
Centelles
³

et al. 2015
Phys. Rev. C
233
32
256
3
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The information on the symmetry energy and its density dependence is deduced by comparing the available data on the electric dipole polarizability αD of 68 Ni, 120 Sn, and 208 Pb with the predictions of Random Phase Approximation, using a representative set of nuclear energy density functionals.The calculated values of αD are used to validate different correlations involving αD, the symmetry energy at the saturation density J, corresponding slope parameter L and the neutron skin thickness ∆rnp, as suggested by the Droplet Model. A subset of models that reproduce simultaneously the measured polarizabilities in 68 Ni, 120 Sn, and 208 Pb are employed to predict the values of symmetry energy parameters at saturation density and ∆rnp. The resulting intervals are: J = 30-35 MeV, L = 20-66 MeV; and the values for ∆rnp in 68 Ni, 120 Sn, and 208 Pb are in the ranges: 0.15-0.19 fm, 0.12-0.16 fm, and 0.13-0.19 fm, respectively. The strong correlation between the electric dipole polarizabilities of two nuclei is instrumental to predict the values of electric dipole polarizabilities in other nuclei.

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“…The ETF method smoothes out quanta! effects and one is left with the average part of the HF energy, which is similar in spirit to the droplet model [My69,My74]. The remaining part of the energy, much smaller, is of pure quanta!…”

Section: 2)mentioning

confidence: 98%

A semiclassical approach to relativistic nuclear mean field theory

1992

Annals of Physics

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The nuclear droplet model for arbitrary shapes

Cited by 392 publications

References 12 publications

Neutron matter properties in an extended Brueckner approach

Neutron matter properties in an extended Brueckner approach

Neutron skin thickness from the measured electric dipole polarizability inNi68,Sn120, and
Roca-Maza
¹
,
Viñas
²
,
Centelles
³

et al. 2015
Phys. Rev. C
233
32
256
3
View full text Add to dashboard Cite

A semiclassical approach to relativistic nuclear mean field theory

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The nuclear droplet model for arbitrary shapes

Cited by 392 publications

References 12 publications

Neutron matter properties in an extended Brueckner approach

Neutron matter properties in an extended Brueckner approach

Neutron skin thickness from the measured electric dipole polarizability inNi68,Sn120, andRoca-Maza1, Viñas2, Centelles3 et al. 2015Phys. Rev. C233322563View full textAdd to dashboardCite

A semiclassical approach to relativistic nuclear mean field theory

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About

Neutron skin thickness from the measured electric dipole polarizability inNi68,Sn120, and
Roca-Maza
¹
,
Viñas
²
,
Centelles
³

et al. 2015
Phys. Rev. C
233
32
256
3
View full text Add to dashboard Cite