Pseudospin-orbit splitting and its consequences for the central depression in nuclear density

Li, Jia Jie; Long, Wen Hui; Song, Junlei; Zhao, Qiang

doi:10.1103/physrevc.93.054312

Cited by 49 publications

(52 citation statements)

References 122 publications

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“…It was found that the angular momentum of the pseudospin doubletsl is nothing but the orbital angular momentum of the lower component of the Dirac spinor (61), and the pseudospin symmetry is exact when the sum of vector and scalar potentials V +S vanishes [369], or a more general condition d(V +S )/dr = 0 which can be approximately fulfilled in exotic nuclei [370,371]. Since then, pseudospin symmetry as a relativistic symmetry has been realized and much work has been done for investigating its origin and its properties using phenomenological single-particle Hamiltonians, relativistic mean field theory, or relativistic Hartree-Fock (RHF) theory [212,213,[372][373][374][375][376][377][378][379][380][381][382][383][384].…”

Section: Pseudospin and Spin Symmetriesmentioning

confidence: 99%

Towards an ab initio covariant density functional theory for nuclear structure

Shen

Liang

Long

et al. 2019

Progress in Particle and Nuclear Physics

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Nuclear structure models built from phenomenological mean fields, the effective nucleon-nucleon interactions (or Lagrangians), and the realistic bare nucleon-nucleon interactions are reviewed. The success of covariant density functional theory (CDFT) to describe nuclear properties and its influence on Brueckner theory within the relativistic framework are focused upon. The challenges and ambiguities of predictions for unstable nuclei without data or for high-density nuclear matter, arising from relativistic density functionals, are discussed. The basic ideas in building an ab initio relativistic density functional for nuclear structure from ab initio calculations with realistic nucleon-nucleon interactions for both nuclear matter and finite nuclei are presented. The current status of fully self-consistent relativistic Brueckner-Hartree-Fock (RBHF) calculations for finite nuclei or neutron drops (ideal systems composed of a finite number of neutrons and confined within an external field) is reviewed. The guidance and perspectives towards an ab initio covariant density functional theory for nuclear structure derived from the RBHF results are provided. Summary and Perspectives 521. Introduction Brief introduction on nuclear theoryThe discoveries of radioactivity by Becquerel [1] and the Curies [2, 3] and the existence of a compact nucleus at the center of an atom by Rutherford et al. [4] opened the door of nuclear physics. During the hundred years of development in nuclear physics, there emerged several significant milestones, including the discovery of the neutron by Chadwick [5] which verified the composition of the nucleus as protons and neutrons, the meson-exchange theory for the strong interaction between nucleons by Yukawa [6], the independent-particle shell model of the nucleus by Goeppert-Mayer [7], Haxel, Jensen, and Suess [8], and the collective Hamiltonian for nuclear rotation and vibration by Rainwater [9], Bohr and Mottelson [10,11], etc.With the understanding of the composition of a nucleus as protons and neutrons [5] and the meson-exchange theory for the strong interaction between the nucleons [6], nuclear physicists hoped to describe the nucleus, a quantum many-body system, from the underlying nucleon-nucleon interaction. Euler, a student of Heisenberg, assumed the nuclear force as a two-body (2N) interaction with a Gaussian shape and calculated the infinite nuclear system, i.e., homogeneous nuclear matter, using second-order perturbation theory [12]. However, the strong repulsive core of the realistic nuclear force [13] prevents the application of perturbation theory.On the other hand, the nuclear structure model with a phenomenological mean field achieved great success. Goeppert-Mayer [7], Haxel, Jensen, and Suess [8] introduced a strong spin-orbit potential and proposed the nuclear independentparticle shell model that successfully explained the conventional magic numbers in nuclei. Rainwater [9], Bohr and Mottelson [10, 11] explored the nuclear deformation and proposed the nuclear collective mode...

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Section: Pseudospin and Spin Symmetriesmentioning

confidence: 99%

Towards an ab initio covariant density functional theory for nuclear structure

Shen

Liang

Long

et al. 2019

Progress in Particle and Nuclear Physics

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“…Recently, indication of the core swelling phenomenon was observed for neutron-rich Ca isotopes, suggesting that it crucially affects the density profile near the nuclear surface [5,6]. Another exotic phenomenon, a central depression of nuclear density profile, was reported [7,8]. The vacancy in the s-orbit plays an essential role in bubble formation, resulting in a depletion of the central part of the nuclear density profile.…”

Section: Introductionmentioning

confidence: 99%

Enormous nuclear surface diffuseness in the exotic Ne and Mg isotopes

Choudhary¹,

Horiuchi²,

Kimura³

et al. 2021

Preprint

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Background: The density profile of exotic nuclei can be a rich source of information on the nuclear surface. In particular, the nuclear surface diffuseness parameter is correlated with the occupation probability of nucleons in distinct nuclear orbits, especially those with low angular momenta.Purpose: The aim of this paper is to investigate the relationship between the nuclear surface diffuseness and spectroscopic information of neutron rich Ne and Mg isotopes both at the cusp and inside the island of inversion.Method: We use the microscopic antisymmetrized molecular dynamics model to calculate the densities and other spectroscopic information related to Ne and Mg isotopes. A two-parameter Fermi density distribution is then used to define the diffuseness parameter and the matter radius. These quantities are extracted by minimizing the difference between these two densities. To relate them with observables, the two densities are given as inputs to a Glauber model calculation of nucleon-nucleus elastic scattering differential cross section, with the demand that they reproduce the first peak position and its magnitude.Results: A marked increase in the occupation of neutrons in the pf -orbit is noted in Ne and Mg isotopes from N = 19 onwards. We observed that the nuclear diffuseness is strongly correlated with the nuclear deformation, in the island of inversion, and gradually increases with the occupation of neutrons in the 1p 3/2 orbit. This result is also confirmed by a single-particle estimate of the valence neutron density distribution, with 29 Ne as a test case. An exception is noted for 35−37 Mg, where the filling up of the holes in the sd-shell partially compensates the increase in diffuseness due to filling up of the 1p 3/2 orbit. Conclusion:Information on nuclear density profile of neutron rich medium mass nuclei can be reliably extracted by studying the first diffraction peak of the nucleon-nucleus elastic scattering differential cross section. The enormous surface diffuseness of Ne and Mg isotopes, in the island of inversion, could be attributed to the increasing neutron occupation of the 1p 3/2 orbit.

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“…The amplitude of this central depletion in 205 Tl is of order 11%. A much larger central depletion of protons, of about 40% compared to stable 36 S, was proposed in 34 Si [10,14] using various mean field approaches, arising from the proton occupancy of the 2s 1/2 orbital. However, recent theoretical calculations suggest that nuclear correlations act to smoothen these orbital occupancies in both the heavy and superheavy nuclei [15,16] and in 34 Si [17].…”

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confidence: 99%

A proton density bubble in the doubly magic 34Si nucleus

et al. 2016

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PACS numbers: to be definedMany properties of the atomic nucleus, such as vibrations, rotations and incompressibility can be interpreted as due to a two-component quantum liquid of protons and neutrons. Electron scattering measurements on stable nuclei demonstrate that their central densities are saturated, as for liquid drops. In exotic nuclei near the limits of mass and charge, with large imbalances in their proton and neutron numbers, the possibility of a depleted central density, or a "bubble" structure, was discussed in a recurrent manner since the seventies. Here we report first experimental evidence that points to a depletion of the central density of protons in the short-lived nucleus 34 Si. The proton-to-neutron density asymmetry in 34 Si offers the possibility to place constraints on the density and isospin dependence of the spin-orbit force -on which nuclear models have disagreed for decades-and on its stabilizing effect towards limits of nuclear existence.Microscopic systems composed of atoms or clusters can exhibit intrinsic structures that are bubble-like, with small or depleted central densities. For example, the fullerene molecules, composed of C atoms, are structures with extreme central depletion [1]. In nuclear physics, depletions also arise in nuclei with well-developed cluster structures when clusters are arranged in a triangle or ring-like structure -such as in the triple-α Hoyle state [2,3]. Unlike such a non-homogeneous, clustered system, central density depletions or bubble-like structures would be much more surprising in homogeneous systems, such as typical atomic nuclei with properties characteristic of a quantum liquid [4].This hindrance of bubble formation in atomic nuclei is inherent in the nature of the strong force between nucleons, which is strongly repulsive at short distances (below 0.7 fm), attractive at medium range (≈1.0 fm) and vanishes at distances beyond 2 fm. In a classical picture, the medium-ranged attraction of nuclear forces implies that nucleons interact strongly and attractively only with immediate neighbors, leading to a saturation of the nuclear central density, ρ 0 . Quantum mechanically, the delocalization of nucleons [5] leads to a further homogeneity of the density. Extensive precision electron scattering studies from stable nuclei [6] confirm that their central densities are essentially constant, with ρ 0 ≈ 0.16 fm −3 , independent of the number of nucleons A. As a consequence, like a liquid drop, the nuclear radii and volumes increase as A 1/3 and as A, respectively. Thus, a priori, bubble-like nuclei with depleted central densities are unexpected.Historically, the possibility of forming bubble nuclei was investigated theoretically in intermediate-mass [7][8][9][10], superheavy [11] and hyperheavy systems [12]. In general, central depletions will arise from a reduced occupation of single particle orbits with low angular momentum . These wave functions extend throughout the nuclear interior whereas those with high-are more excluded by centrifugal forces. For...

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Pseudospin-orbit splitting and its consequences for the central depression in nuclear density

Cited by 49 publications

References 122 publications

Towards an ab initio covariant density functional theory for nuclear structure

Towards an ab initio covariant density functional theory for nuclear structure

Enormous nuclear surface diffuseness in the exotic Ne and Mg isotopes

A proton density bubble in the doubly magic 34Si nucleus

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