3D calculation of Tucson-Melbourne 3NF effect in triton binding energy

TL;DR

This paper introduces a three-dimensional formalism for calculating the effects of three-nucleon forces on triton binding energy, demonstrating improved efficiency over traditional partial wave methods.

Contribution

It develops a non partial wave approach to include 3NFs in three-nucleon bound state calculations, simplifying the angular momentum algebra involved.

Findings

Non PW calculations are more efficient and less cumbersome.

The formalism successfully incorporates 3NFs using vector Jacobi momenta.

Results agree with standard partial wave schemes, validating the approach.

Abstract

As an application of the new realistic three-dimensional (3D) formalism reported recently for three-nucleon (3N) bound states, an attempt is made to study the effect of three-nucleon forces (3NFs) in triton binding energy in a non partial wave (PW) approach. The spin-isospin dependent 3N Faddeev integral equations with the inclusion of 3NFs, which are formulated as function of vector Jacobi momenta, specifically the magnitudes of the momenta and the angle between them, are solved with Bonn-B and Tucson-Melbourne NN and 3N forces in operator forms which can be incorporated in our 3D formalism. The comparison with numerical results in both, novel 3D and standard PW schemes, shows that non PW calculations avoid the very involved angular momentum algebra occurring for the permutations and transformations and it is more efficient and less cumbersome for considering the 3NF.