Three-nucleon force in relativistic three-nucleon Faddeev calculations

TL;DR

This paper develops a relativistic three-nucleon Faddeev framework incorporating both pairwise and three-nucleon forces, ensuring Poincare invariance and enabling accurate analysis of high-energy nuclear interactions.

Contribution

It introduces methods to include three-nucleon forces in relativistic Faddeev equations while maintaining Poincare invariance, advancing the theoretical modeling of nuclear systems.

Findings

Relativistic effects and three-nucleon forces are significant at higher energies.

The proposed methods allow calculation of three-nucleon force matrix elements with Poincare invariance.

A consistent treatment of relativity and three-nucleon forces is essential for accurate data analysis.

Abstract

We extend our formulation of relativistic three-nucleon Faddeev equations to include both pairwise interactions and a three-nucleon force. Exact Poincare invariance is realized by adding interactions to the mass Casimir operator (rest Hamiltonian) of the non-interacting system without changing the spin Casimir operator. This is achieved by using interactions defined by rotationally invariant kernels that are functions of internal momentum variables and single-particle spins that undergo identical Wigner rotations. To solve the resulting equations one needs matrix elements of the three-nucleon force with these properties in a momentum-space partial-wave basis. We present two methods to calculate matrix elements of three-nucleon forces with these properties. For a number of examples we show that at higher energies, where effects of relativity and of three-nucleon forces are non-negligible, a consistent treatment of both is required to properly analyze the data.