Quantum Monte Carlo Calculations of Light Nuclei

Pieper, Steven C.

doi:10.1016/j.nuclphysa.2005.02.018

Cited by 139 publications

(230 citation statements)

References 28 publications

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“…In that case the main numerical effort goes into calculating the matrix elements of the Hamiltonian. Examples are the exact Faddeev and Faddeev-Yakubovsky equations for the 3-and 4-body system [15], the hyperspherical harmonics basis [16], or the Green's Function Monte Carlo method (GFMC) [17,18,19,20,21]. The other possibility is to represent the eigenstates of the Hamiltonian with many-body basis states |Φ [ν] which are chosen such that the numerical effort for calculating the matrix elements…”

Section: Effective Potentialsmentioning

confidence: 99%

Nuclear structure in the framework of the Unitary Correlation Operator Method

Roth¹,

Neff²,

Feldmeier³

2010

Progress in Particle and Nuclear Physics

161

217

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Correlations play a crucial role in the nuclear many-body problem. We give an overview of recent developments in nuclear structure theory aiming at the description of these interactioninduced correlations by unitary transformations. We focus on the Unitary Correlation Operator Method (UCOM), which offers a very intuitive, universal and robust approach for the treatment of short-range correlations. We discuss the UCOM formalism in detail and highlight the connections to other methods for the description of short-range correlations and the construction of effective interactions. In particular, we juxtapose UCOM with the Similarity Renormalization Group (SRG) approach, which implements the unitary transformation of the Hamiltonian through a very flexible flow-equation formulation. The UCOM-and SRG-transformed interactions are compared on the level of matrix elements and in many-body calculations within the no-core shell model and with Hartree-Fock plus perturbation theory for a variety of nuclei and observables. These calculations provide a detailed picture of the similarities and differences as well as the advantages and limitations of unitary transformation methods.

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Section: Effective Potentialsmentioning

confidence: 99%

Nuclear structure in the framework of the Unitary Correlation Operator Method

Roth¹,

Neff²,

Feldmeier³

2010

Progress in Particle and Nuclear Physics

161

217

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“…At the same time, it is known that details of the NNN interaction are important for nuclear structure applications. For example, the Urbana IX [19] and the Tucson-Melbourne [20,21,22] NNN interactions perform differently in mid-p-shell nuclei [16,23,24] although their differences appear to be minor. In the Green's function Monte Carlo (GFMC) calculations with the AV18 NN potential [25], the best results for p-shell nuclei up to A = 10 are found using the Illinois NNN interaction that augments the Urbana IX by a two-pion term from the Tucson-Melbourne NNN interaction and by three-pion terms that in the χEFT appear beyond the N 3 LO [26,27].…”

Section: Introductionmentioning

confidence: 99%

Local three-nucleon interaction from chiral effective field theory

2007

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The three-nucleon (NNN) interaction derived within the chiral effective field theory at the nextto-next-to-leading order (N 2 LO) is regulated with a function depending on the magnitude of the momentum transfer. The regulated NNN interaction is then local in the coordinate space, which is advantages for some many-body techniques. Matrix elements of the local chiral NNN interaction are evaluated in a three-nucleon basis. Using the ab initio no-core shell model (NCSM) the NNN matrix elements are employed in 3 H and 4 He bound-state calculations.

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“…In view of the overall good agreement between the χEFT NN+NNN and AV18+UIX calculations, the photo-absorption cross section at low energy appears to be more sensitive to change in the α-particle size, than to the details of the spin-orbit component of the NNN interaction. In this regard, a more substantial role of the NNN force can be expected in the photo-disintegration of p-shell nuclei, for which differences in the spin-orbit strength have crucial effects on the spectrum [41,10]. Finally, the rather contained width of the theoretical band embracing the χEFT NN+NNN, AV18+UIX and UCOM results within 15 MeV from threshold is remarkable compared to the large discrepancies still present among the different experimental data.…”

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confidence: 99%

The 4He total photo-absorption cross section with two- plus three-nucleon interactions from chiral effective field theory

Quaglioni

Navrátil

2007

Physics Letters B

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The total photo-absorption cross section of 4 He is evaluated microscopically using two-(NN) and three-nucleon (NNN) interactions based upon chiral effective field theory (χEFT). The calculation is performed using the Lorentz integral transform method along with the ab initio no-core shell model approach. An important feature of the present study is the consistency of the NN and NNN interactions and also, through the Siegert theorem, of the two-and three-body current operators. This is due to the application of the χEFT framework. The inclusion of the NNN interaction produces a suppression of the low-energy peak and enhancement of the high-energy tail of the cross section. We compare to calculations obtained using other interactions and to representative experiments. The rather confused experimental situation in the giant resonance region prevents discrimination among different interaction models.Key words: PACS: 25.20.Dc, 21.60.Cs, 27.10.+h Interactions among nucleons are governed by quantum chromodynamics (QCD). In the low-energy regime relevant to nuclear structure and reactions, this theory is nonperturbative, and, therefore, hard to solve. Thus, theory has been forced to resort to models for the interaction, which have limited physical basis. New theoretical developments, however, allow us to connect QCD with low-energy nuclear physics. Chiral effective field theory (χEFT) [1,2] provides a promising bridge to the underlying theory, QCD. Beginning with the pionic or the nucleon-pion system [3] one works consistently with systems of increasing number of nucleons [4]. One makes use of spontaneous breaking of chiral symmetry to systematically expand the strong interaction in terms of a generic small momentum and takes the explicit breaking of chiral symmetry into account by expanding in the pion mass. Nuclear interactions are nonperturbative, because diagrams with purely nucleonic intermediate states are enhanced [1,2]. Therefore, the chiral perturbation expansion is performed for the potential. The χEFT predicts, along with the nucleon-nucleon (NN) interaction at the leading order, a three-nucleon (NNN) interaction at the next-to-next-to-leading order or N 2 LO [2,5,6], and even a four-nucleon (NNNN) interaction at the fourth Email addresses: quaglioni1@llnl.gov (Sofia Quaglioni), navratil1@llnl.gov (Petr Navrátil). order (N 3 LO) [7]. The details of QCD dynamics are contained in parameters, low-energy constants (LECs), not fixed by the symmetry, but can be constrained by experiment. At present, high-quality NN potentials have been determined at N 3 LO [8]. A crucial feature of χEFT is the consistency between the NN, NNN and NNNN parts. As a consequence, at N 2 LO and N 3 LO, except for two parameters assigned to two NNN diagrams, the potential is fully constrained by the parameters defining the NN interaction. The full interaction up to N 2 LO was first applied to the analysis of nd scattering [6] and later the N 3 LO NN potential was combined with the available NNN at N 2 LO to study the 7 Li stru...

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Quantum Monte Carlo Calculations of Light Nuclei

Cited by 139 publications

References 28 publications

Nuclear structure in the framework of the Unitary Correlation Operator Method

Nuclear structure in the framework of the Unitary Correlation Operator Method

Local three-nucleon interaction from chiral effective field theory

The 4He total photo-absorption cross section with two- plus three-nucleon interactions from chiral effective field theory

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