Background: Self-consistent Green's function theory has recently been extended to the basic formalism needed to account for three-body interactions [Carbone, Cipollone, Barbieri, Rios, and Polls, Phys. Rev. C 88, 054326 (2013)PRVCAN0556-281310.1103/PhysRevC.88.054326]. The contribution of three-nucleon forces has so far been included in ab initio calculations on nuclear matter and finite nuclei only as averaged two-nucleon forces. Purpose: We derive the working equations for all possible two- and three-nucleon terms that enter the expansion of the self-energy up to the third order, thus including the interaction-irreducible (i.e., not averaged) diagrams with three-nucleon forces that have been previously neglected. Methods: We employ the algebraic diagrammatic construction up to the third order as an organization scheme for generating a nonperturbative self-energy, in which ring (particle-hole) and ladder (particle-particle) diagrams are resummed to all orders. Results: We derive expressions of the static and dynamic self-energy up to the third order, by taking into account the set of diagrams required when either the skeleton or nonskeleton expansions of the single-particle propagator are assumed. A hierarchy of importance among different diagrams is revealed, and a particular emphasis is given to a third-order diagram [see Fig. 2(c)] that is expected to play a significant role among those featuring an interaction-irreducible three-nucleon force. Conclusion: A consistent formalism to resum at infinite order correlations induced by three-nucleon forces in the self-consistent Green's function theory is now available and ready to be implemented in the many-body solvers.
Algebraic diagrammatic construction formalism with three-body interactions / F. Raimondi, C. Barbieri. - In: PHYSICAL REVIEW C. - ISSN 2469-9985. - 97:5(2018), pp. 054308.1-054308.31.
|Titolo:||Algebraic diagrammatic construction formalism with three-body interactions|
|Parole Chiave:||greens-function; forces; approximation; nuclei|
|Settore Scientifico Disciplinare:||Settore FIS/04 - Fisica Nucleare e Subnucleare|
|Data di pubblicazione:||2018|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1103/PhysRevC.97.054308|
|Appare nelle tipologie:||01 - Articolo su periodico|