ИСТИНА

Direct reactions involving rare isotopes offer an important tool for understanding the structure of such nuclei. Deuteron induced reactions are attractive from the experimental perspective, since deuterated targets are readily available. Theoretically they are attractive, since the scattering problem can be reduced to an effective three-body problem, which can be solved exactly using Faddeev techniques. The momentum space Faddeev equations (here in the Alt-Grassberger-Sandhas form) have successfully been solved for $(d, p)$ reactions involving light nuclei [1]. However, the screening technique employed to handle the Coulomb force encounters technical difficulties, when applied to $(d, p)$ reactions with heavier nuclei [2]. An alternative to the screening procedure is a solution of the Faddeev-AGS equations in the Coulomb basis. This was suggested and carried out in Ref. [3] using real two-body transition operators in separable form neglecting spin degrees of freedom. Casting Faddeev-AGS equations in Coulomb basis requires the evaluation of momentum space partial wave matrix elements of two-body transition operators in the corresponding basis. If these operators take a separable form, this requires the folding of a form factor, which only depends on one momentum variable, with a momentum space partial wave Coulomb function $\psi^C_{l, k_0}(p)$, which is highly oscillatory around the external momentum $k_0$. We developed a regularization scheme to calculate Coulomb distorted form factors as integral over the Coulomb function and complex form factors, as they are needed to describe the $N$-nucleus optical potentials [4]. To do this, we also had to develop the algorithm to compute partial wave Coulomb functions in momentum space [5]. We calculated Coulomb distorted form factors for a set of nuclei ranging from ${}^{12}$C to ${}^{208}$Pb in the energy range from a few to about 50~MeV per nucleon. In principle, our scheme to prepare the two-body input for non-relativistic Faddeev-AGS based $(d, p)$ reactions can be applied to nuclei as heavy as ${}^{208}$Pb. The numerical implementation of the Faddeev-AGS equations in Coulomb basis including spin degrees of freedom is in progress. References [1] M. Viviani et al. Phys. Rev. C 84, 054010 (2011). [2] N. J. Upadhyay et al. Phys. Rev. C 85, 054621 (2012). [3] A. M. Mukhamedzhanov et al. Phys. Rev. C 86, 034001 (2012). [4] N. J. Upadhyay et al. (the TORUS Collaboration), Phys. Rev. C 90, 014615 (2014). [5] V. Eremenko et al. (the TORUS Collaboration), Comp. Phys. Comm. 187, 195 (2015).