The Pairing-Plus-Quadrupole Model

Bès, D.R.; Sorensen, Raymond A.

doi:10.1007/978-1-4684-8343-7_3

Cited by 130 publications

(88 citation statements)

References 111 publications

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“…Our strength parameters g 0 and χ 2 agree, respectively, with g 0 = 20/A and χ 2 = 240/A 5/3 of Bes and Sorensen [28]. We may also compare our strengths with those derived from the GXPF1A interaction using the prescription of Dufour and Zuker [9].…”

supporting

confidence: 78%

Toward a unified realistic shell-model Hamiltonian with the monopole-based universal force

et al. 2014

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We propose a unified realistic shell-model Hamiltonian employing the pairing plus multipole Hamiltonian combined with the monopole interaction constructed starting from the monopole-based universal force by Otsuka et al. (Phys. Rev. Lett. 104, 012501 (2010)). It is demonstrated that the proposed PMMU model can consistently describe a large amount of spectroscopic data as well as binding energies in the p f and p f 5/2 g 9/2 shell spaces, and could serve as a practical shell model for even heavier mass regions. PACS numbers: 21.30.Fe, 21.60.Cs, 21.10.Dr, 27.50.+e The nuclear shell-model interaction can in principle be derived microscopically from the free nucleon-nucleon force. In fact, such attempts were made in the early years for the beginning of the shell [1,2]. However, it was soon after realized that such an interaction fail to describe binding energies, excitation spectra, and transitions if many valence nucleons were considered. To reproduce experimental data, considerable efforts have been put forward to construct the so-called effective interactions, such as USD [3] and USDA/B [4] for the sd shell, KB3G [5] and GXPF1A [6] for the p f shell, and JUN45 [7] and jj4b [8] for the p f 5/2 g 9/2 model space. Each of these interactions is applicable to a given model space while mutual relations among them are obscure. On the other hand, it has been shown [9] that realistic effective interactions are dominated by the pairing plus quadrupole-quadrupole (P + QQ) terms with the monopole interaction. This finding not only makes the understanding of effective interactions in nuclei intuitive, but may also be used to unify effective interactions for different model spaces. In particular, one may begin to talk about universality for shell models.Along the lines of this thought, we have carried out shellmodel calculations using the extended P + QQ Hamiltonian combined with the monopole terms (EPQQM), which are regarded as corrections for the average monopole interaction. It has been demonstrated that despite of its simplicity, this EPQQM model works surprisingly well for different mass regions, for example, the proton-rich p f shell [10] and the p f 5/2 g 9/2 shell [11], the neutron-rich f pg shell [12], and the sd-p f shell region [13]. It has also been successfully applied to the neutron-rich nuclei around 132 Sn [14,15]. However, these calculations rely heavily on phenomenological adjustments on the monopole corrections. Consequently, the EPQQM model cannot describe binding energies or unusual structures such as the first excited 0 + state of Zn and Ge isotopes around N = 40 [16], and it essentially provides no information about the unconventional shell evolution in neutronrich nuclei.The monopole interaction is a crucial ingredient for successful shell-model calculations. It is defined as [17]where V JT ab,ab are the interaction matrix elements. The connection between the monopole interaction and the tensor force [18] was confirmed, which explains the shell evolution [19]. It was shown [20,21] shown by open and ...

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confidence: 78%

Toward a unified realistic shell-model Hamiltonian with the monopole-based universal force

et al. 2014

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“…Here, we use the symbol ↔ instead of = because it is obtained by applying the high-spin formula (20) to the low-spin limit. For simplicity, we omit the argument (−π/2) of the d function.…”

Section: Generalized Intensity Relationsmentioning

confidence: 99%

“…According to the LO high-spin formula (20), the intraband B(E2; ∆I = 2) strengths are proportional to the quadrupole deformation (Q 22 ) 2 . The ∆I = 1 transitions, which are associated with the wobbling transitions, appear in the NLO with respect to 1/I; B(E2; ∆I = 1)/B(E2; ∆I = 2) ∼ 1/I.…”

Section: Rotor Model Analysis Of the Wobbling In The High-spin Limitmentioning

confidence: 99%

Quantal rotation and its coupling to intrinsic motion in nuclei

et al. 2016

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Abstract. Symmetry breaking is an importance concept in nuclear physics and other fields of physics. Self-consistent coupling between the mean-field potential and the single-particle motion is a key ingredient in the unified model of Bohr and Mottelson, which could lead to a deformed nucleus as a consequence of spontaneous breaking of the rotational symmetry. Some remarks on the finite-size quantum effects are given. In finite nuclei, the deformation inevitably introduces the rotation as a symmetry-restoring collective motion (Anderson-Nambu-Goldstone mode), and the rotation affects the intrinsic motion. In order to investigate the interplay between the rotational and intrinsic motions in a variety of collective phenomena, we use the cranking prescription together with the quasiparticle random phase approximation. At low spin, the coupling effect can be seen in the generalized intensity relation. A feasible quantization of the cranking model is presented, which provides a microscopic approach to the higher-order intensity relation. At high spin, the semiclassical cranking prescription works well. We discuss properties of collective vibrational motions under rapid rotation and/or large deformation. The superdeformed shell structure plays a key role in emergence of a new soft mode which could lead to instability toward the K π = 1 − octupole shape. A wobbling mode of excitation, which is a clear signature of the triaxiality, is discussed in terms of a microscopic point of view. A crucial role played by the quasiparticle alignment is presented.

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“…The Agassi model is a schematic version of the paring-plus-quadrupole model [32] extensively used in nuclear physics to describe deformed superconducting nuclei. It combines the Lipkin model with the two-level pairing model [33].…”

Section: Introductionmentioning

confidence: 99%

Combining symmetry collective states with coupled-cluster theory: Lessons from the Agassi model Hamiltonian

2017

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The failures of single-reference coupled cluster for strongly correlated many-body systems is flagged at the mean-field level by the spontaneous breaking of one or more physical symmetries of the Hamiltonian. Restoring the symmetry of the mean-field determinant by projection reveals that coupled cluster fails because it factorizes high-order excitation amplitudes incorrectly. However, symmetry-projected mean-field wave functions do not account sufficiently for dynamic (or weak) correlation. Here we pursue a merger of symmetry projection and coupled cluster theory, following previous work along these lines that utilized the simple Lipkin model system as a testbed [J. Chem. Phys. 146, 054110 (2017)]. We generalize the concept of a symmetry-projected meanfield wave function to the concept of a symmetry projected state, in which the factorization of high-order excitation amplitudes in terms of low-order ones is guided by symmetry projection and is not exponential, and combine them with coupled cluster theory in order to model the ground state of the Agassi Hamiltonian. This model has two separate channels of correlation and two separate physical symmetries which are broken under strong correlation. We show how the combination of symmetry collective states and coupled cluster is effective in obtaining correlation energies and order parameters of the Agassi model throughout its phase diagram.

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The Pairing-Plus-Quadrupole Model

Cited by 130 publications

References 111 publications

Toward a unified realistic shell-model Hamiltonian with the monopole-based universal force

Toward a unified realistic shell-model Hamiltonian with the monopole-based universal force

Quantal rotation and its coupling to intrinsic motion in nuclei

Combining symmetry collective states with coupled-cluster theory: Lessons from the Agassi model Hamiltonian

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