Nuclear Structure

Bohr, Aage; Mottelson, Ben R.

doi:10.1142/3530-vol1

Cited by 786 publications

(1,406 citation statements)

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“…Such SB is beyond the CMF picture and, while negligible in the ground state of the He atom ͑whose study was central to the development of the quantum theory of matter due to the failure of the Bohr-type models 6 ͒, it is similar in nature to the SB found 6 in the 1970s in doubly excited He, where the formation of an e-He 2ϩ -e ''triatomic'' molecule was invoked. Furthermore, we show that symmetry breaking at Bϭ0 of the self-consistent field associated with the triplet excited state of the 2e QD originates from a Jahn-Teller distortion of the CMF, similar to that underlying formation of nonspherical open-shell nuclei 7,8 and metal clusters. 9,10 Along with a unification of concepts pertaining to spontaneous SB in a variety of finite fermionic systems ͑from nuclei, metal clusters, and natural atoms, to 2D QD's͒, we demonstrate the ability to control the orientation and to manipulate ͑i.e., to enhance, but also to counteract and even to void͒ the formation of the electron molecules in 2e QD's via impurity and/or magnetic-field effects.…”

Section: Introductionmentioning

confidence: 77%

Formation and control of electron molecules in artificial atoms: Impurity and magnetic-field effects

Yannouleas

Landman

2000

Phys. Rev. B

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Interelectron interactions and correlations in quantum dots can lead to spontaneous symmetry breaking of the self-consistent mean field, resulting in the formation of Wigner molecules. With the use of spin-and-space unrestricted Hartree-Fock ͑sS-UHF͒ calculations, such symmetry breaking is discussed for field-free conditions, as well as under the influence of an external magnetic field. Using as paradigms impurity-doped ͑as well as the limiting case of clean͒ two-electron quantum dots ͑which are analogs to heliumlike atoms͒, it is shown that the interplay between the interelectron repulsion and the electronic zero-point kinetic energy leads, for a broad range of impurity parameters, to the formation of a singlet ground-state electron molecule, reminiscent of the molecular picture of doubly excited helium. A comparative analysis of the conditional probability distributions for the sS-UHF and exact solutions for the ground state of two interacting electrons in a clean parabolic quantum dot reveals that both of them describe the formation of an electron molecule with similar characteristics. The self-consistent field associated with the triplet excited state of the two-electron quantum dot ͑clean as well as impurity doped͒ exhibits a symmetry breaking of Jahn-Teller type, similar to that underlying formation of nonspherical open-shell nuclei and metal clusters. Furthermore, impurity and/or magnetic-field effects can be used to achieve controlled manipulation of the formation and pinning of the discrete orientations of the Wigner molecules. Impurity effects are futher illustrated for the case of a quantum dot with more than two electrons.

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Section: Introductionmentioning

confidence: 77%

Formation and control of electron molecules in artificial atoms: Impurity and magnetic-field effects

Yannouleas

Landman

2000

Phys. Rev. B

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“…The central outcome of the formalism is that for any IBM-1 Hamiltonian a corresponding potential V (β , γ) can be constructed where β and γ parametrize the intrinsic quadrupole deformation of the nucleus [43]. This procedure is known as the classical limit of the IBM.…”

Section: The Classical Limitmentioning

confidence: 99%

“…These have the interpretation of (quadrupole) shape variables and their associated conjugate momenta. If one limits oneself to static problems, the α µ can be taken as real; they specify a shape and are analogous to the shape variables of the droplet model of the nucleus [43]. The α µ can be related to three Euler angles which define the orientation of an intrinsic frame of reference, and two intrinsic shape variables, β and γ, that parametrize quadrupole vibrations of the nuclear surface around an equilibrium shape.…”

Section: The Classical Limitmentioning

confidence: 99%

Symmetries in nuclei

Isacker¹,

Bijker²,

Castaños³

et al. 2011

AIP Conference Proceedings

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A new class of nuclear isomeric states: Mixed symmetry isomeric states in nuclei AIP Conf.Abstract. The use of dynamical symmetries or spectrum generating algebras for the solution of the nuclear many-body problem is reviewed. General notions of symmetry and dynamical symmetry in quantum mechanics are introduced and illustrated with simple examples such as the SO(4) symmetry of the hydrogen atom and the isospin symmetry in nuclei. Two nuclear models, the shell model and the interacting boson model, are reviewed with particular emphasis on their use of group-theoretical techniques.

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“…Finally, we discuss the more realistic case. 10,11 If the system size is small, the surface vibrations and the compressional vibrations couple strongly to each other. In a vibrating state, therefore, the pressure caused by the surface vibrations must be in equilibrium with that caused by the compressional vibrations.…”

Section: Liquid-drop Modelmentioning

confidence: 99%

Surface vibrations of aHe4droplet and the universality of the dispersion relation

Tamura

1996

Phys. Rev. B

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By applying the liquid-drop model to a 4 He droplet, we derive the universal dispersion relation for the droplet vibrations. Considering the eigenvalue equation for the coupled modes of surface vibrations and inner vibrations, the universality is clarified by using an effective wave number. It is shown that our universal dispersion curve for the surface modes traces well the eigenfrequencies obtained by several workers and provides benchmarks for the various methods of computer simulations.

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Nuclear Structure

Cited by 786 publications

References 0 publications

Formation and control of electron molecules in artificial atoms: Impurity and magnetic-field effects

Formation and control of electron molecules in artificial atoms: Impurity and magnetic-field effects

Symmetries in nuclei

Surface vibrations of aHe4droplet and the universality of the dispersion relation

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