Abstract
Nuclear structure theory has recently gone through a major renewal with the development of ab initio techniques that can be applied to a large number of atomic nuclei, well beyond the light sector that had been traditionally targeted in the past. Self-consistent Green's function theory is one among these techniques. The present work aims to give an overview of the self-consistent Green's function approach for atomic nuclei, including examples of recent applications and a discussion on the perspectives for extending the method to nuclear reactions, doubly open-shell systems and heavy nuclei.
Highlights
The theoretical description of atomic nuclei is challenging, for several reasons
In standard many-body Green’s function theory, this is realized by rewriting the Schrödinger equation in terms of one, two, ..., A-body objects gI(= g), gII, ..., gA named propagators or, Green’s functions (GFs)
Self-consistent GF approximation schemes are defined by the content of the irreducible self-energy, which is expressed as a function of the exact GFs and encodes its perturbative expansion
Summary
The theoretical description of atomic nuclei is challenging, for several reasons. Approaches in the first category do not impose any formal approximation on the solution of the many-body Schrödinger equation, which is affected only by basis truncation and numerical errors Typical examples of such methods are Quantum Monte Carlo [7, 8], no-core shell model (or configuration interaction) [9] or nuclear lattice EFT [10]. In 2018, working equations for the state-of-the-art many-body truncation used in nuclear structure calculations (algebraic diagrammatic construction at third order, see section 3.1) were derived [34] Building on these formal advances, several applications (based on either Dyson or Gorkov frameworks) have been carried out in the past decade.
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