Many-Body Perturbation Theories for Finite Nuclei

Abstract

In recent years many-body perturbation theory encountered a renaissance in the field of ab initio nuclear structure theory. In various applications it was shown that perturbation theory, including novel flavors of it, constitutes a useful tool to describe atomic nuclei, either as a full-fledged many-body approach or as an auxiliary method to support more sophisticated non-perturbative many-body schemes. In this work the current status of many-body perturbation theory in the field of nuclear structure is discussed and novel results are provided that highlight its power as a efficient and yet accurate (pre-processing) approach to systematically investigate medium-mass nuclei. Eventually a new generation of chiral nuclear Hamiltonians is benchmarked using several state-of-the-art flavors of many-body perturbation theory.

ADG: Automated generation and evaluation of many-body diagrams I. Bogoliubov many-body perturbation theory

“…This code development took place in the context of the rapidly evolving field of quantum many-body calculations for fermionic systems, i.e., atomic nuclei, molecules, atoms or solids. In nuclear physics in particular, the past decade has witnessed the development and/or the application of formalisms [2][3][4][5][6][7][8][9][10][11][12][13] among which is Bogoliubov many-body perturbation theory [12,14]. This profusion of diagrammatic methods, along with the rapid progress of computational power allowing for high-order implementations, welcomes the development of a versatile code capable of both generating and evaluating many-body diagrams.…”

Self-Consistent Green's Function Theory for Atomic Nuclei

“…After analysing the ADC convergence behavior, one expects ADC(4) corrections to be small for total energies and negligible for charge radii. The accuracy of the ADC(3) scheme is also confirmed by a direct benchmark against no-core shell model in 16 O, with total energies computed in the two approaches differing by less than 1% for any tested interaction [40].…”

“…The third point implies that the EFT error can (and should) be subsequently propagated to many-body observables. This has been done in practice only very recently (see e.g., [16,[87][88][89][90][91][92]) and more formal and technical developments along these lines will be required in the future. Mainly three different χ-EFT Hamiltonians have been employed in recent GF calculations, all of which are discussed here.…”

“…Only relatively recently, with the advent of EFTs and, specially, SRG techniques applied to nuclear Hamiltonians, MBPT was revived [12,13] and it is now considered as a convenient approach for large-scale systematic calculations. Moreover, it can be easily complemented with resummation techniques like Padé or eigenvector continuation [14,15] (see [16] for a recent review). Other methods rely on the MBPT concept but are built such that infinite subsets of MBPT contributions are resummed by construction.…”

“…Excited states of even-even systems were addressed in the form of the electromagnetic dipole response in [42]. In [43], ab initio optical potentials were computed and applied in elastic scattering off 16 O and 40 Ca. Barbieri et al [44] instead discussed lepton-nucleus scattering, with particular attention to neutrino scattering off 40 Ar.…”