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

Abstract

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.

Strangeness and Δ resonance in compact stars with relativistic-mean-field models

“…Meanwhile, it is worth mentioning that the covariant density functional PKDD adopted here is phenomenological, where the nucleon-meson coupling constants are fixed according to the masses of spherical nuclei, the incompressibility, saturation density, and symmetry energy of nuclear matter [70]. In light of the recent developments of microscopic many-body calculations in describing finite nuclei and nuclear matter starting from realistic nucleonnucleon interactions [82][83][84][85][86][87][88], a more refined adjustment of parameters incorporating those results are necessary. A possible way to reach this in RMF model is to intro-duce density-dependent coupling constants derived from self-energies of Dirac-Brueckner calculations of nuclear matter [57,89], which are found decreasing with density and can be reproduced with Eqs.…”

Multi-reference many-body perturbation theory for nuclei III -- Ab initio calculations at second order in PGCM-PT

“…[8,9,10] and Refs. [4,6,7] for vacuum and in-medium IMSRG 1 While the IMSRG constitutes per se a method to solve Schrödinger's equation when the SR-IMSRG implementation can be applied, it is not the case for the MR-IMSRG approach that can only be seen as a pre-processing of the Hamiltonian on top of which an appropriate many-body method must be applied. methods, respectively.…”

Beta Decay in Medium-Mass Nuclei with the In-Medium Similarity Renormalization Group

“…There are several review articles detailing both the free-space SRG [21,22] and the in-medium SRG [15,[23][24][25][26], and so here I will review only what is needed for our present purposes.…”