Nd breakup within isospinless AAB model

Abstract

The three-nucleon system (ppn or nnp) may be considered as a system of identical particles within a framework of the isospin formalism (AAA model). Here we propose to treat the system as a system with only two identical particles as a natural way to take into account the charge dependence of the nucleon–nucleon (NN) interaction. We apply the ‘given charge formalism’ to formulate the ‘isospinless’ AAB model. The charge independence breaking effect for Nd scattering is modeled by using a phenomenological adjustment for s-wave NN potential. The modeling is based on the configuration space Faddeev equations. Calculations of the phase shifts, inelasticities, and breakup amplitudes are performed for nd and pd scattering at different energies for both AAA and AAB models. It has found that the numerical differences between the results obtained with these two models are relatively small (about 1%), however, noticeable. In this regard, we consider the numerical accuracy of the calculations and in particular the effect of oscillations of the phase shifts and inelasticities that depend on the asymptotic cutoff parameter. The choice of the cutoff parameter is performed to minimize the impact of oscillations on the accuracy for the phenomenological (MT I–III) and realistic (AV14) potentials.

Three-body model for $K(1460)$ resonance

“…Within s-wave approach the equation for the singlet component corresponding to the KK singlet potential is omitted due to the isospin symmetry. The similar property is demonstrated for equations describing AAB systems like N N K [55,56] and nnp [57].…”

Mass-Energy Equivalence in Bound Three-Nucleon Systems

“…[42] where the mass difference was taken by a perturbative manner using additional operator of the kinetic energy written as The s-wave AAB model for bound states of three-nucleon systems was proposed in Ref. [4][5][6] based on the "charge isospin basis" [44]. The basis allows us to "separate" isospin variables.…”

“…However, this effect for the 3 H bound energy, evaluated in early works [2,3] is significant and amounts to 12 keV. Recently, we proposed an AAB model, where the n-p mass difference and the charge dependence of nucleon-nucleon potential were taken into account [4][5][6]. The results of Ref.…”

Mass-Energy Equivalence in Bound Three-Nucleon Systems

“…The s-wave AAB model for bound states of three-nucleon systems was proposed in Ref. [4][5][6] based on the "charge isospin basis" [46]. The basis allows us to "separate" isospin variables.…”

“…However, this effect for the 3 H bound energy, evaluated in early works [2,3] is significant and amounts to 12 keV. Recently, we proposed an AAB model, where the n-p mass difference and the charge dependence of nucleon-nucleon potential were taken into account [4][5][6]. The results of Ref.…”