Similarity renormalization group evolution of three-nucleon forces in a hyperspherical momentum representation

Wendt, Kyle

doi:10.1103/physrevc.87.061001

Cited by 29 publications

(39 citation statements)

References 26 publications

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“…The figure shows contour plots of the matrix elements as a function of λ in the lowest hyperspherical partial wave, both for the 3N interaction (top panel) and the embedded N N interaction in that partial wave (lower panel). See [109] for additional details. partial waves of the four-body system has been carried out by A. Calci and co-workers [105], again working in Jacobi HO representation.…”

Section: Srg Evolution Of Nuclear Interactionsmentioning

confidence: 99%

In-medium similarity renormalization group for closed and open-shell nuclei

Hergert¹

2016

Phys. Scr.

145

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Abstract. We present a pedagogical introduction to the In-Medium Similarity Renormalization Group (IMSRG) framework for ab initio calculations of nuclei. The IMSRG performs continuous unitary transformations of the nuclear many-body Hamiltonian in second-quantized form, which can be implemented with polynomial computational effort. Through suitably chosen generators, it is possible to extract eigenvalues of the Hamiltonian in a given nucleus, or drive the Hamiltonian matrix in configuration space to specific structures, e.g., band-or block-diagonal form.Exploiting this flexibility, we describe two complementary approaches for the description of closed-and open-shell nuclei: The first is the Multireference IMSRG (MR-IMSRG), which is designed for the efficient calculation of nuclear ground-state properties. The second is the derivation of nonempirical valence-space interactions that can be used as input for nuclear Shell model (i.e., configuration interaction (CI)) calculations. This IMSRG+Shell model approach provides immediate access to excitation spectra, transitions, etc., but is limited in applicability by the factorial cost of the CI calculations.We review applications of the MR-IMSRG and IMSRG+Shell model approaches to the calculation of ground-state properties for the oxygen, calcium, and nickel isotopic chains or the spectroscopy of nuclei in the lower sd shell, respectively, and present selected new results, e.g., for the ground-and excited state properties of neon isotopes.Submitted to: Phys. Scr.

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Section: Srg Evolution Of Nuclear Interactionsmentioning

confidence: 99%

In-medium similarity renormalization group for closed and open-shell nuclei

Hergert¹

2016

Phys. Scr.

145

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“…. interactions and to general observables [23,[91][92][93][94][95][96]. Moreover, we could easily achieve a block decoupling as in Fig.…”

Section: Srg In the Two-nucleon Systemmentioning

confidence: 99%

“…In the process, we also encounter a new type of contraction, 96) as expected from the canonical anti-commutator algebra. ρ is the so-called hole density matrix.…”

Section: Wick's Theoremmentioning

confidence: 99%

In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem

Hergert

Bogner

Lietz

et al. 2017

An Advanced Course in Computational Nuclear Physics

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We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear manybody problem. These methods use continuous unitary transformations to evolve the nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the many-body Schrödinger equation. We discuss the IM-SRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory (Chapter 8), Configuration-Interaction Monte Carlo (Chapter 9), and the SelfConsistent Green's Function approach discussed in Chapter 11. The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.

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“…On the other hand, the SRG evolution of the A=3 system has been first accomplished using the HO basis [26,27] although later a momentum space implementation [34] and also hyperspherical momentum implementation [35] have been achieved.…”

Section: A Backgroundmentioning

confidence: 99%

Alternative similarity renormalization group generators in nuclear structure calculations

2014

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The similarity renormalization group (SRG) has been successfully applied to soften interactions for ab initio nuclear calculations. In almost all practical applications in nuclear physics, an SRG generator with the kinetic energy operator is used. With this choice, a fast convergence of manybody calculations can be achieved, but at the same time substantial three-body interactions are induced even if one starts from a purely two-nucleon (N N ) Hamiltonian. Three-nucleon (3N ) interactions can be handled by modern many-body methods. However, it has been observed that when including initial chiral 3N forces in the Hamiltonian, the SRG transformations induce a nonnegligible four-nucleon interaction that cannot be currently included in the calculations for technical reasons. Consequently, it is essential to investigate alternative SRG generators that might suppress the induction of many-body forces while at the same time might preserve the good convergence. In this work we test two alternative generators with operators of block structure in the harmonic oscillator basis. In the no-core shell model calculations for 3 H, 4 He and 6 Li with chiral N N force, we demonstrate that their performances appear quite promising.

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Similarity renormalization group evolution of three-nucleon forces in a hyperspherical momentum representation

Cited by 29 publications

References 26 publications

In-medium similarity renormalization group for closed and open-shell nuclei

In-medium similarity renormalization group for closed and open-shell nuclei

In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem

Alternative similarity renormalization group generators in nuclear structure calculations

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