Nuclear Structure from the In-Medium Similarity Renormalization Group

Abstract

Efforts to describe nuclear structure and dynamics from first principles have advanced significantly in recent years. Exact methods for light nuclei are now able to include continuum degrees of freedom and treat structure and reactions on the same footing, and multiple approximate, computationally efficient many-body methods have been developed that can be routinely applied for medium-mass nuclei. This has made it possible to confront modern nuclear interactions from Chiral Effective Field Theory, that are rooted in Quantum Chromodynamics with a wealth of experimental data.Here, we discuss one of these efficient new many-body methods, the In-Medium Similarity Renormalization Group (IMSRG), and its applications in modern nuclear structure theory. The IMSRG evolves the nuclear many-body Hamiltonian in second-quantized form through continuous unitary transformations that can be implemented with polynomial computational effort. Through suitably chosen generators, we drive the matrix representation of the Hamiltonian in configuration space to specific shapes, e.g., to implement a decoupling of lowand high-energy scales, or to extract energy eigenvalues for a given nucleus.We present selected results from Multireference IMSRG (MR-IMSRG) calculations of openshell nuclei, as well as proof-of-principle applications for intrinsically deformed medium-mass nuclei. We discuss the successes and prospects of merging the (MR-)IMSRG with many-body methods ranging from Configuration Interaction to the Density Matrix Renormalization Group, with the goal of achieving an efficient simultaneous description of dynamic and static correlations in atomic nuclei.

Microscopically based energy density functionals for nuclei using the density matrix expansion

“…Ab initio methods employ these realistic interactions and calculate properties of nuclear systems by directly considering the interaction between each pair of nucleons. This approach has been successful in describing light and medium nuclei (up to Z = 50) [5]. The same systematic, order-by-order, improvement from the interaction can be observed in the description of nuclear properties calculated with ab initio methods [6].…”

Generator-coordinate reference states for spectra and 0νββ decay in the in-medium similarity renormalization group

“…In 48 Ti, only projected-HFB reference states with β ≥ 0.2 (and the GCM state) lead to a final energy that is very close to the exact ground-state value. Starting from smaller values of β, we fall short of the correct binding energy.…”

“…. 0.4, 0.5} in 48 Ti. For these axially-deformed HFB states, one-dimensional angularmomentum projection, together with particle-number projection, is sufficient to restore all the broken symmetries.…”

“…For these axially-deformed HFB states, one-dimensional angularmomentum projection, together with particle-number projection, is sufficient to restore all the broken symmetries. Figure 1 presents curves of HFB energy vs, deformation (often referred to as "energy surfaces" even in one dimension) for 48 Ca and 48 Ti, both before and after projection onto states with J = 0 and well-defined particle number. The global energy minimum is at a spherical shape in 48 Ca and a prolate shape in 48 Ti.…”

“…The figure also shows the energies of the lowest lying states after the full calculations, which mix the shapes indicated by the dots. The ground states have GCM energies of −7.12 MeV in 48 Ca and −22.18 MeV in 48 Ti. The results of exact diagonalization are −7.57 MeV and −23.81 MeV, both significantly smaller than the corresponding GCM results.…”