H. Hergert

Ab Initio Calculations of Even Oxygen Isotopes with Chiral Two-Plus-Three-Nucleon Interactions

We formulate the in-medium similarity renormalization group (IM-SRG) for open-shell nuclei using a multireference formalism based on a generalized Wick theorem introduced in quantum chemistry. The resulting multireference IM-SRG (MR-IM-SRG) is used to perform the first ab initio study of all even oxygen isotopes with chiral nucleon-nucleon and three-nucleon interactions, from the proton to the neutron drip lines. We obtain an excellent reproduction of experimental ground-state energies with quantified uncertainties, which is validated by results from the importance-truncated no-core shell model and the coupled cluster method. The agreement between conceptually different many-body approaches and experiment highlights the predictive power of current chiral two- and three-nucleon interactions, and establishes the MR-IM-SRG as a promising new tool for ab initio calculations of medium-mass nuclei far from shell closures.

The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei

Abstract We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab initio method for nuclei. The IM-SRG employs a continuous unitary transformation of the many-body Hamiltonian to decouple the ground state from all excitations, thereby solving the many-body problem. Starting from a pedagogical introduction of the underlying concepts, the IM-SRG flow equations are developed for systems with and without explicit spherical symmetry. We study different IM-SRG generators that achieve the desired decoupling, and how they affect the details of the IM-SRG flow. Based on calculations of closed-shell nuclei, we assess possible truncations for closing the system of flow equations in practical applications, as well as choices of the reference state. We discuss the issue of center-of-mass factorization and demonstrate that the IM-SRG ground-state wave function exhibits an approximate decoupling of intrinsic and center-of-mass degrees of freedom, similar to Coupled Cluster (CC) wave functions. To put the IM-SRG in context with other many-body methods, in particular many-body perturbation theory and non-perturbative approaches like CC, a detailed perturbative analysis of the IM-SRG flow equations is carried out. We conclude with a discussion of ongoing developments, including IM-SRG calculations with three-nucleon forces, the multi-reference IM-SRG for open-shell nuclei, first non-perturbative derivations of shell-model interactions, and the consistent evolution of operators in the IM-SRG. We dedicate this review to the memory of Gerry Brown, one of the pioneers of many-body calculations of nuclei.

Matrix elements and few-body calculations within the unitary correlation operator method

We employ the unitary correlation operator method (UCOM) to construct correlated, low-momentum matrix elements of realistic nucleon-nucleon interactions. The dominant short-range central and tensor correlations induced by the interaction are included explicitly by an unitary transformation. Using correlated momentum-space matrix elements of the Argonne V18 potential, we show that the unitary transformation eliminates the strong off-diagonal contributions caused by the short-range repulsion and the tensor interaction and leaves a correlated interaction dominated by low-momentum contributions. We use correlated harmonic oscillator matrix elements as input for no-core shell model calculations for few-nucleon systems. Compared to the bare interaction, the convergence properties are dramatically improved. The bulk of the binding energy can already be obtained in very small model spaces or even with a single Slater determinant. Residual long-range correlations, not treated explicitly by the unitary transformation, can easily be described in model spaces of moderate size allowing for fast convergence. By varying the range of the tensor correlator we are able to map out the Tjon line and can in turn constrain the optimal correlator ranges.

Hartree-Fock and many body perturbation theory with correlated realistic NN interactions

We employ correlated realistic nucleon-nucleon interactions for the description of nuclear ground states throughout the nuclear chart within the Hartree-Fock approximation. The crucial short-range central and tensor correlations, which are induced by the realistic interaction and cannot be described by the Hartree-Fock many-body state itself, are included explicitly by a state-independent unitary transformation in the framework of the unitary correlation operator method (UCOM). Using the correlated realistic interaction

Nonperturbative Shell-Model Interactions from the In-Medium Similarity Renormalization Group

\VO_{; ; \UCOM}; ;

In-medium similarity renormalization group with chiral two- plus three-nucleon interactions

resulting from the Argonne V18 potential, bound nuclei are obtained already on the Hartree-Fock level. However, the binding energies are smaller than the experimental values because long-range correlations have not been accounted for. Their inclusion by means of many-body perturbation theory leads to a remarkable agreement with experimental binding energies over the whole mass range from \elem{; ; He}; ; {; ; 4}; ; to \elem{; ; Pb}; ; {; ; 208}; ; , even far off the valley of stability. The observed perturbative character of the residual long-range correlations and the apparently small net effect of three-body forces provides promising perspectives for a unified nuclear structure description.

Nuclear structure based on correlated realistic nucleon–nucleon potentials

We present the first ab initio construction of valence-space Hamiltonians for medium-mass nuclei based on chiral two- and three-nucleon interactions using the in-medium similarity renormalization group. When applied to the oxygen isotopes, we find experimental ground-state energies are well reproduced, including the flat trend beyond the drip line at (24)O. Similarly, natural-parity spectra in (21,22,23,24)O are in agreement with experiment, and we present predictions for excited states in (25,26)O. The results exhibit a weak dependence on the harmonic-oscillator basis parameter and reproduce spectroscopy within the standard sd valence space.

Unitary Correlation Operator Method and Similarity Renormalization Group: Connections and Differences

We use the recently proposed In-Medium Similarity Renormalization Group (IM-SRG) to carry out a systematic study of closed-shell nuclei up to

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

\nuc{Ni}{56}

Ground and excited states of doubly open-shell nuclei from ab initio valence-space Hamiltonians

, based on chiral two- plus three-nucleon interactions. We analyze the capabilities of the IM-SRG by comparing our results for the ground-state energy to Coupled Cluster calculations, as well as to quasi-exact results from the Importance-Truncated No-Core Shell Model. Using chiral two- plus three-nucleon Hamiltonians whose resolution scales are lowered by free-space SRG evolution, we obtain good agreement with experimental binding energies in