Comparison of the Nilsson and Skyrme Hartree-Fock results for the properties of highly deformed states in nuclei

Zamick, Larry; Zheng, D. C.; Lee, S. J.; Caballero, J. A.; Guerra, E. Moya de

doi:10.1016/0003-4916(91)90121-n

Cited by 10 publications

(9 citation statements)

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“…These rates, in turn, are greatly influenced by accurate measurements and theoretical predictions of several important low-lying states in 12 C, including the second 0 + 2 (Hoyle) state and its 2 + excitation that has fostered long-lasting debate in experimental studies [114][115][116][117][118][119][120]. Further challenges relate to the α-cluster substructure of these states that has been explored within clustertailored [121][122][123][124][125][126] or self-consistent [127,128] framework, but has hitherto precluded a fully microscopic ab initio no-core shell-model description [129] (see, e.g., detailed reviews on the topic [130,131]). Only recently, first ab initio state-of-the-art calculations have been attempted using lattice effective field theory (EFT) [17,132].…”

Section: No-core Symplectic Shell Model (Ncspm) and The Elusive Hoylementioning

confidence: 99%

Symmetry-guided large-scale shell-model theory

Launey

Dytrych

Draayer

2016

Progress in Particle and Nuclear Physics

131

173

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In this review, we present a symmetry-guided strategy that utilizes exact as well as partial symmetries for enabling a deeper understanding of and advancing ab initio studies for determining the microscopic structure of atomic nuclei. These symmetries expose physically relevant degrees of freedom that, for large-scale calculations with QCD-inspired interactions, allow the model space size to be reduced through a very structured selection of the basis states to physically relevant subspaces. This can guide explorations of simple patterns in nuclei and how they emerge from first principles, as well as extensions of the theory beyond current limitations toward heavier nuclei and larger model spaces. This is illustrated for the ab initio symmetry-adapted no-core shell model (SA-NCSM) and two significant underlying symmetries, the symplectic Sp(3, R) group and its deformation-related SU(3) subgroup. We review the broad scope of nuclei, where these symmetries have been found to play a key role -from the light p-shell systems, such as 6 Li, 8 B, 8 Be, 12 C, and 16 O, and sd-shell nuclei exemplified by 20 Ne, based on first-principle explorations; through the Hoyle state in 12 C and enhanced collectivity in intermediate-mass nuclei, within a no-core shell-model perspective; up to strongly deformed species of the rare-earth and actinide regions, as investigated in earlier studies. A complementary picture, driven by symmetries dual to Sp(3, R), is also discussed. We briefly review symmetry-guided techniques that prove useful in various nuclear-theory models, such as Elliott model, ab initio SA-NCSM, symplectic model, pseudo-SU(3) and pseudo-symplectic models, ab initio hyperspherical harmonics method, ab initio lattice effective field theory, exact pairing -plusshell model approaches, and cluster models, including the resonating-group method. Important implications of these approaches that have deepened our understanding of emergent phenomena in nuclei, such as enhanced collectivity, giant resonances, pairing, halo, and clustering, are discussed, with a focus on emergent patterns in the framework of the ab initio SA-NCSM with no a priori assumptions.

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Section: No-core Symplectic Shell Model (Ncspm) and The Elusive Hoylementioning

confidence: 99%

Symmetry-guided large-scale shell-model theory

Launey

Dytrych

Draayer

2016

Progress in Particle and Nuclear Physics

131

173

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“…However the usage of the relativistic mean field approach is mostly limited to spherical or moderately deformed nuclei since the RMF failed in describing highly deformed nuclei unless using a nonlinear meson field [24,25,26]. On the other hand the nonrelativistic Hartree-Fock (HF) approach using empirical Skyrme interaction can describe highly deformed nuclei moderately well [29,30] as well as describing spherical nuclei. Thus we use nonrelativistic HF approach here in describing structures of He and Be isotopes.…”

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confidence: 99%

Mean-Field Theoretical Structure of He and Be Isotopes

Lee¹,

Son²,

Park³

2007

J. Korean Phy. Soc.

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The structures of He and Be even-even isotopes are investigated using an axially symmetric Hartree-Fock approach with a Skyrme-IIIls mean field potential. In these simple HF calculations, He and Be isotopes appear to be prolate in their ground states and Be isotopes have oblate shape isomeric states. It is also shown that there exists a level crossing when the nuclear shape changes from the prolate state to the oblate state. The single neutron levels of Be isotopes exhibit a neutron magic number 6 instead of 8 and show that the level inversion between 1/2 − and 1/2 + levels occurs only for a largely deformed isotope. Protons are bound stronger in the isotope with more neutrons while neutron levels are somewhat insensitive to the number of neutrons and thus the nuclear size and also the neutron skin become larger as the neutron number increases. In these simple calculations with Skyrme-IIIls interaction no system with a clear indication of neutron halo was found among He and Be isotopes. Owing to the progress of experimental techniques, information concerning the ground state and the excited states of light unstable nuclei has rapidly increased. Furthermore radioactive ion beam accelerator will produce various unstable nuclei far from β-stability line. In light stable nuclei, it has already been known that clustering is one of the essential features of nuclear dynamics not only in excited states but also in ground states. Thus we may expect cluster structures in light unstable nuclei. Pioneering theoretical studies have suggested the development of cluster structures with a 2α core in Be and B isotopes [1,2,3,4,5]. The α chain structures of 8 Be and 12 C was investigated using a relativistic mean field (RMF) approximation [6]. In the case of 12 Be, the existence of cluster states was suggested in experimental measurements of the excited states [7] and in experiments of 6 He+ 6 He and 8 He+ 4 He breakup reactions [8]. The measured spin-parities of excited states indicate a rotational band with a large moment of inertia. These states are candidates of states with cluster structure. It is an interesting subject to investigate clustering aspects in Be isotopes. The cluster structures of 12 Be were studied with a potential model with He clusters [9] and with an algebraic version of resonating group model [10] using α particles as inert clusters. To eliminate the model assumption of inert α cluster an antisymmetrized molecular dynamics (AMD) [11] is used in study of Be isotopes. However this study uses inert Gaussian wave packets to represent nucleons. These studies treat α particles as inert clusters or nucleon as a fixed Gaussian packet, and thus miss any detailed structure of nuclei and any change of the internal structure of α particles in a nucleus. For a study of the detailed nuclear structure (such as size, shape, quadrupole moment, single nucleon levels) of these unstable nuclei, we need to use a self-consistent mean field approach in terms of nucleon itself. Mean field approaches have been applied successfully...

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“…The energy is E=hO)xXx + hgOyZy + hgO~Z~, (2) where X x = ~, (N x + 89 (0, 1, 0), (0, 0, 1). The energy is E=hO)xXx + hgOyZy + hgO~Z~, (2) where X x = ~, (N x + 89 (0, 1, 0), (0, 0, 1).…”

Section: :(2--m-t-2mgoxx2)+(p~ +2 Mgoxymentioning

confidence: 99%

“…The energy is E=hO)xXx + hgOyZy + hgO~Z~, (2) where X x = ~, (N x + 89 (0, 1, 0), (0, 0, 1). To get the deformation we must supplement the above with the Mottelson condition: gOx_ 227z gOz Xx+Zy (3) This condition leads to a minimization of the energy (2) provided that the volume is conserved, i.e., o) 3= gox goy go~ is fixed. To get the deformation we must supplement the above with the Mottelson condition: gOx_ 227z gOz Xx+Zy (3) This condition leads to a minimization of the energy (2) provided that the volume is conserved, i.e., o) 3= gox goy go~ is fixed.…”

Section: :(2--m-t-2mgoxx2)+(p~ +2 Mgoxymentioning

confidence: 99%

“…The linear chain state is obtained by Brink's prescription of "putting all the quanta in the z direction" [ 1 ], so for 160, the occupying states are (0, 0, 0), (0, 0, 1), (0, 0, 2) and (0, 0, 3). For the chain states, it is easy to show that [2] Echai n = h gO ~ A + h gO A 2 2A4/3 (4) and that gox/goz = A/4, where A is the mass number. For the chain states, it is easy to show that [2] Echai n = h gO ~ A + h gO A 2 2A4/3 (4) and that gox/goz = A/4, where A is the mass number.…”

Section: :(2--m-t-2mgoxx2)+(p~ +2 Mgoxymentioning

confidence: 99%

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