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

Abstract

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.

Nonempirical Interactions for the Nuclear Shell Model: An Update

“…At the conceptual level, these interactions validate the independent-particle picture underlying the shell model. They provide sufficient binding already at the mean-field level, and allow us to use it as the starting point for the treatment of correlations, either through rapidly converging non-perturbative many-body methods (127,145,146), or possibly even through finite-order perturbation theory (116,147). Furthermore, novel approaches like the valence-space IMSRG (VS-IMSRG) or shell model Coupled Cluster (SMCC), both discussed below, provide both the conceptual framework and practical tools to relate no-core and valence-space methods, as shown by the consistent ground-and excited-state results obtained thus far (see (129,143) and Sec.…”

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

“…In the nuclei shown, the agreement is quite satisfactory given that the chiral input Hamiltonian is entirely fixed by A ≤ 4 data. The IMSRG interactions turn out to perform quite well in the entire lower sd−shell, achieving an rms deviation of ∼ 580 keV in about 150 states [73,160]. The chiral 3N interactions are found to be of crucial importance for the correct reproduction of level orderings and spacings.…”

“…The former has become maybe the most popular tool for pre-processing nuclear interactions and operators, leading to vast improvements in the rate of convergence of many-body calculations, and extending the range of nuclei that can be tackled in ab initio approaches [44,48,49,53,73,108].…”

“…10.3.4 and Refs. [53,73]). The RG property will matter in our discussion of SRGevolved nuclear interactions in the next section.…”

“…This only leaves diagram (IV), which vanishes if matrix elements of the type Γ pp vh vanish. Thus, we define [73,121] compared to results with the phenomenological USDB interaction [162] and experimental data, see [73,163] for full details. Hamiltonian at all stages of a calculation [86,160,161].…”