Three-Body Monopole Corrections to Realistic Interactions

Zuker, A. P.

doi:10.1103/physrevlett.90.042502

Cited by 137 publications

(188 citation statements)

References 25 publications

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“…9, first CC results with 3N forces show that low-momentum 3N interactions are accurately treated as effective 0-, 1-and 2-body terms, and that residual 3N interactions can be neglected [19]. This is very promising and supports the idea that phenomenological monopole shifts in shell model interactions are due to 3N contributions [20], see also the talk by T. Otsuka and Ref. [21].…”

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confidence: 52%

Three-nucleon interactions: A frontier in nuclear structure

Schwenk¹,

Holt²,

Sakai³

et al. 2008

AIP Conference Proceedings

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Abstract. Three-nucleon interactions are a frontier in understanding and predicting the structure of strongly-interacting matter in laboratory nuclei and in the cosmos. We present results and discuss the status of first calculations with microscopic three-nucleon interactions beyond light nuclei. This coherent effort is possible due to advances based on effective field theory and renormalization group methods in nuclear physics.The physics of strong interactions extends over extremes in density, neutron-to-proton imbalance and temperature (see Fig. 1). Understanding and predicting the properties of these fascinating forms of matter requires progress on fundamental problems in the theory of nuclear forces and in many-body physics. In this talk, we highlight the key role of three-nucleon (3N) interactions for nuclear structure.Nuclear interactions depend on a resolution scale, which we denote by a generic momentum cutoff Λ, and the Hamiltonian is always given by an effective theory for nucleon-nucleon (NN) and corresponding many-nucleon interactions (with corresponding effective operators) [1,2,3]:This scale dependence is similar to the scale dependence of parton distribution functions, and shows that the effect of 3N interactions depends on this scale and the theoretical convention that enters all parts of the Hamiltonian. At very low momenta Q ≪ m π ≈ 140 MeV, the details of pion exchanges are not resolved and nuclear forces can be systematically expanded in contact interactions and their derivatives [1]. The corresponding pionless effective field theory (EFT) is extremely successful for capturing universal large scattering-length physics (with improvements by including effective range and higher-order terms) in loosely-bound or halo nuclei, reactions at astrophysical energies and in dilute neutron matter (see e.g., Ref.[4]).For most nuclei, the typical Fermi momenta are Q ∼ m π and therefore pion exchanges have to be included explicitly. In chiral EFT, nuclear interactions are then organized in an expansion in powers of Q/Λ b , where Λ b denotes the breakdown scale, roughly Λ b ∼ m ρ [1,2]. The great advantage is that up to next-to-next-to-next-to-leading order (N 3 LO) only two new 3N couplings enter, since parts of the 3N force can be consistently determined by πN and NN couplings. The two 3N couplings, as well as the short-ranged NN couplings, depend on the resolution scale Λ and for each Λ can be fit to data.Using the renormalization group (RG), we can evolve an initial potential to lower resolution by integrating out high momenta through discretized RG flow equations

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confidence: 52%

Three-nucleon interactions: A frontier in nuclear structure

Schwenk¹,

Holt²,

Sakai³

et al. 2008

AIP Conference Proceedings

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“…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 full circles, respectively. The monopole matrix elements of the GXPF1A interaction [6] for p f shell and JUN45 [7] for p f 5/2 g 9/2 shell are also shown for comparison.…”

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confidence: 80%

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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“…On the other hand, large-scale shell-model calculations have allowed one to describe more and more exotic systems using renormalized interactions from realistic NN potentials. The appearance and disappearance of shell closures have their origin in the nature of the nucleus and its study brings an insight into the nuclear force, such as the monopole evolution due to the NNN forces [1] and its tensor character [2]. In the last decades, experimental studies have clearly shown that well-established shell closures disappear [3], such as N = 8, N = 20, N = 28 and new ones appear such as N = 16 [4] and N = 32 [5].…”

Section: Introductionmentioning

confidence: 99%

Lifetime measurements in neutron-rich63,65Co isotopes using the AGATA demonstrator

Modamio¹,

Valiente-Dobón²,

Lunardi³

et al. 2013

Phys. Rev. C

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Lifetimes of the low-lying (11/2 − ) states in 63,65 Co have been measured employing the recoil distance doppler shift method (RDDS) with the AGATA γ -ray array and the PRISMA mass spectrometer. These nuclei were populated via a multinucleon transfer reaction by bombarding a 238 U target with a beam of 64 Ni. The experimental B(E2) reduced transition probabilities for 63,65 Co are well reproduced by large-scale shell-model calculations that predict a constant trend of the B(E2) values up to the N = 40 67 Co isotope.

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Three-Body Monopole Corrections to Realistic Interactions

Cited by 137 publications

References 25 publications

Three-nucleon interactions: A frontier in nuclear structure

Three-nucleon interactions: A frontier in nuclear structure

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

Lifetime measurements in neutron-rich63,65Co isotopes using the AGATA demonstrator

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