<i>The Nuclear Shell Model</i>

Heyde, K.; Bertsch, G. F.

doi:10.1063/1.2808133

Cited by 72 publications

(133 citation statements)

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“…The resulting pairing matrix elements can be calculated analytically (see, for example, Ref. [39]) and the ratio R is given by a geometrical factor: R = n a lj n a lj |(1 − P 12 )V3 S 1 |n b lj n b lj J =1,T =0 n a lj n a lj |(1 − P 12 )V1 S 0 |n b lj n b lj J =0,T =1 ,…”

Section: A Spin-orbit Suppressionmentioning

confidence: 99%

Partial-wave contributions to pairing in nuclei

2010

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We present a detailed study of partial-wave contributions of nuclear forces to pairing in nuclei. For T=1, J=0 pairing, partial waves beyond the standard 1S0 channel play an interesting role for the pair formation in nuclei. The additional contributions are dominated by the repulsive 3P1 partial wave. Their effects, and generally spin-triplet nuclear forces between paired nucleons, are influenced by the interplay of spin-orbit partners. We explore the impact of including partial waves beyond the 1S0 channel on neutron-neutron pairing gaps in semi-magic isotopic chains. In addition, we show that nuclear forces favor T=1, J=0 over T=0, J=1 pairing, except in low-j orbitals. This is in contrast to the free-space motivation that suggests the formation of deuteron-like T=0 pairs in N=Z nuclei. The suppression of T=0 pairing is because the 3S1 strength is distributed on spin-orbit partners and because of the effects of the repulsive 1P1 channel and of D waves.Comment: 10 pages, 16 figure

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Section: A Spin-orbit Suppressionmentioning

confidence: 99%

Partial-wave contributions to pairing in nuclei

2010

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“…This might shed light onto the ground state structure of 3 He droplets. Prompted by this experimental possibility, we present here a realistic calculation of the structure of these systems using a reliable density functional and powerful techniques borrowed from the shell model description of the atomic nucleus (see, e.g., [6]). …”

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confidence: 99%

Structure and Stability of3HeDroplets

1997

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We have studied the structure of 3 He droplets at zero temperature using a density functional approach plus a configuration interaction calculation in an harmonic oscillator major shell. The most salient feature of open shell drops is that the valence atoms couple their spins to the maximum value compatible with Pauli's principle, building a large magnetic moment. We have determined that 29 atoms constitute the smallest self-bound droplet. [S0031-9007 (97)03450-9] PACS numbers: 36.40.-cThe structure and dynamical properties of liquid helium drops have been the subject of many experimental and theoretical studies during the past 15 years (for recent reviews, see [1,2]). During this time, a severe experimental limitation has been the impossibility of selecting or detecting and identifying quantitatively small van der Waals clusters [3]. The situation has recently changed, and new scattering deflection methods seem able to determine and select the size of large helium clusters [4]. A new method based on diffracting a molecular beam from a transmission grating looks very promising in doing the same for small-size van der Waals clusters [5]. This might shed light onto the ground state structure of 3 He droplets. Prompted by this experimental possibility, we present here a realistic calculation of the structure of these systems using a reliable density functional and powerful techniques borrowed from the shell model description of the atomic nucleus (see, e.g., [6]).The first systematic calculation of the ground state properties of 4 He and 3 He drops was carried out by Pandharipande and co-workers using a variational Monte Carlo (VMC) technique [7] and by Stringari and Treiner within a local, zero range energy density functional (LDF) approximation [8]. At present, diffusion Monte Carlo calculations are also available for 4 He drops [9,10]. For 3 He, there are also two recent systematic calculations which make use of nonlocal, finite-range density functionals (NLDF) built so as to reproduce a large number of properties of the homogeneous and inhomogeneous liquid [11,12]. Within LDF, a random-phase approximation calculation of the collective spectrum of closed shell 3 He drops is also available [13].One of the more interesting issues of these studies is the existence of a minimum number N min of atoms below which 3 He droplets are unbound. That number was estimated to be between 20 and 40 [7], since for N 20 the system was unbound and weakly bound for N 40. Calculations carried out employing local or nonlocal functionals have reproduced this microscopic feature [8,11,12]. These two numbers belong to the ͑p 1 1͒ ͑p 1 2͒ ͑p 1 3͒͞3 sequence with p 0, 1, 2, ... characteristic of the harmonic oscillator (HO) well, each of them defining a major shell closure.NLDF calculations of large drops show departures from that sequence above N 168 [11,12]. These functionals are fitted to reproduce many properties of the homogeneous liquid and of its free surface, as well as Landau parameters and dynamical properties of the liquid [14],...

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“…The relation (18) between the Hamiltonian and the conserved quantitiesL 2 andR 2 can be rewritten as…”

Section: The Hydrogen Atommentioning

confidence: 99%

“…No review is given here of the nuclear shell model which has been the subject of several comprehensive monographs [15,16,17,18,19]. Instead, after an introductory subsection, describing the model's essential features and assumptions, emphasis is laid on its symmetry structure.…”

Section: The Nuclear Shell Modelmentioning

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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The Nuclear Shell Model

Cited by 72 publications

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Partial-wave contributions to pairing in nuclei

Partial-wave contributions to pairing in nuclei

Structure and Stability of3HeDroplets

Symmetries in nuclei

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