Pairing in the framework of the unitary correlation operator method (UCOM): Hartree-Fock-Bogoliubov calculations

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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“…[149]. In this calculation step, 3N interactions can be included exactly (up to e max and E 3max truncations).…”

Section: Interactions and Implementationmentioning

confidence: 99%

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

Hergert¹

2016

Phys. Scr.

145

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“…Alternative methods for the inclusion of correlations beyond Hartree-Fock, such as ring-, ladder-, or Padé-resummed perturbation theory [93,94] as well as Brueckner-Hartree-Fock schemes and Green's function methods [95,96] are also feasible. The Hartree-Fock or the corresponding Hartree-Fock-Bogoliubov [97,98] solutions also form the basis for the description of collective excitations in the Random Phase Approximation at different orders [52,99,100].…”

Section: Hartree-fock and Beyondmentioning

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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“…To obtain reference states for the MR-IM-SRG(2), we solve HFB equations in 15 major HO shells, and project the resulting state on proton and neutron numbers [10,11,49]. The intrinsic NN+3N Hamiltonian is normalordered with respect to the reference state, and the residual 3N interaction term is discarded.…”

mentioning

confidence: 99%

Ab initiomultireference in-medium similarity renormalization group calculations of even calcium and nickel isotopes

et al. 2014

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We use the newly developed Multi-Reference In-Medium Similarity Renormalization Group to study all even isotopes of the calcium and nickel isotopic chains, based on two-plus three-nucleon interactions derived from chiral effective field theory. We present results for ground-state and twoneutron separation energies and quantify their theoretical uncertainties. At shell closures, we find excellent agreement with Coupled Cluster results obtained with the same Hamiltonians. Our results confirm the importance of chiral 3N interactions to obtain a correct reproduction of experimental energy trends, and their subtle impact in neutron-rich Ca and Ni isotopes. At the same time, we uncover and discuss deficiencies of the input Hamiltonians which need to be addressed by the next generation of chiral interactions.

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Pairing in the framework of the unitary correlation operator method (UCOM): Hartree-Fock-Bogoliubov calculations

Cited by 30 publications

References 81 publications

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

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

Nuclear structure in the framework of the Unitary Correlation Operator Method

Ab initiomultireference in-medium similarity renormalization group calculations of even calcium and nickel isotopes

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