Faddeev Calculations for $Nd$ Breakup Scattering within Isospin and Given Charge Formalism: Numerical Stability

The isospin and given charge models are applied for studying the $Nd$ breakup scattering problem based on the configuration space Faddeev equations. The models are differ by the isospin basis used. The given charge formalism allows us to implement charge dependence of $NN$ interaction for phenomenological $s$-wave $NN$ potentials with adjusted parameters to define the spin singlet $nn$, $pp$ and $np$ components. Calculations of the phase shifts, in elasticities and breakup amplitudes are performed for the $nd$ and $pd$ scattering at $E_{lab}$=4.0 and 14.1~MeV for the both models. We study numerical stability of the calculations for both models with relation to known effect of oscillations of break up amplitudes with dependence on asymptotical cutoff parameter. This effect was recently predicted for quadruplet state of $nd$ scattering in [1]. The oscillations affect at numerical solution accuracy. It was found that new approach based on the given charge formalism brings in more stable numerical solution. Preliminary results for realistic AV14 potential are presented. [1] P.A. Belov and S.L. Yakovlev, Physics of Atomic Nuclei, 76, 126-38 (2013).