# Irreducible 3-body forces contributions to the self-energy

## TL;DR

This paper derives equations for including fully irreducible three-nucleon force contributions in the self-energy within ab initio many-body methods, addressing computational challenges and highlighting the importance of specific diagrams.

## Contribution

It introduces ADC equations for a key Feynman diagram involving irreducible three-nucleon forces, advancing the treatment of 3NFs in many-body calculations.

## Key findings

- Derivation of ADC equations for a specific 3NF diagram
- Identification of the diagram's significance in many-body calculations
- Potential for improved accuracy in nuclear structure modeling

## Abstract

The inclusion of the three-nucleon forces (3NFs) in \textit{ab initio} many-body approaches is a formidable task, due to the computational load implied by the treatment of their matrix elements. For this reason, practical applications have mostly been limited to contributions where 3NFs enter as effective two-nucleon interactions. In this contribution, we derive the algebraic diagrammatic construction (ADC) working equations for a specific Feynman diagram of the self-energy that contains a fully irreducible three-nucleon force. This diagram is expected to be the most important among those previously neglected, because it connects dominant excited intermediate state configurations.