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

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.Comment: 4 pages, 1 figure, 1 table

Three-nucleon bound state in a spin-isospin dependent three dimensional approach

“…The calculations of three-nucleon bound state, with the phenomenological TucsonMelbourne (TM) 2π exchange three nucleon potential, and the formulation of the fournucleon bound state is currently underway and they will be reported before long [48].…”

“…The comparison of Eqs. ( 21) and (24) shows that new 3D formalism avoids the highly involved angular momentum algebra occurring for the permutations and additionally it will be more efficient especially for the three-body forces [48].…”

Zero-energy neutron–triton and proton–Helium-3 scattering with EFT(π̸)

“…FIG.1:The singlet S-wave neutron triton scattering length as a function of the triton binding energy. The correlations for EFT( π) with regulators from 400 MeV to 1.6 GeV are compared to R-matrix data[31] (red solid lines), and to the MT-I/III[40], v14[41], and the v18+UIX[5] force models with as(t-n) from[25].…”

Bound-state calculations of the three-dimensional Yakubovsky equations with the inclusion of three-body forces

“…To this aim the first step for realistic calculations of three-nucleon bound state in a realistic Three-Dimensional approach has already been taken by calculation of Triton binding energy with Bonn-B potential [44,45] and formulation of four-nucleon bound state is currently underway and it will be reported elsewhere [46]. They will be the first steps for realistic calculations of three-and four-nucleon bound states in a Three-Dimensional scheme.…”