Deuteron-alpha scattering: separable vs nonseparable Faddeev approach

Abstract

{\bf Background} Deuteron induced reactions are widely used to probe nuclear structure and astrophysical information. Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques. {\bf Purpose} Faddeev-AGS equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. However, it needs to be demonstrated that observables calculated based on separable interactions agree exactly with those based on nonseparable forces. {\bf Methods} Momentum space AGS equations are solved with separable and nonseparable forces as coupled integral equations. {\bf Results} Deuteron-alpha scattering is calculated via momentum space AGS equations using the CD-Bonn neutron-proton force and a Woods-Saxon type neutron(proton)-${}^4$He force, for which the Pauli-forbidden S-wave bound state is projected out. Elastic as well as breakup observables are calculated and compared to results in which the interactions in the two-body sub-systems are represented by separable interactions derived in the Ernst-Shakin-Thaler (EST) framework. {\bf Conclusions} We find that the calculations based on the separable representation of the interactions and the original interactions give results that are in excellent agreement. Specifically, integrated cross sections and angular distributions for elastic scattering agree within $\approx$ 1\%, which is well below typical experimental errors. In addition, the five-fold differential cross sections corresponding to breakup of the deuteron agree extremely well.

References in corpus (12)

• The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)
• Three-body Faddeev-Alt-Grassberger-Sandhas approach to direct nuclear reactions
• Coulomb force effects in low-energy $\alpha$-deuteron scattering
• Generalized Faddeev equations in the AGS form for deuteron stripping with explicit inclusion of target excitations and Coulomb interaction
• Separable Representation of Phenomenological Optical Potentials of Woods-Saxon Type
• A New Approach to the 3D Faddeev Equation for Three-Body Scattering
• Breakup of three particles within the adiabatic expansion method
• Separable Representation of Proton-Nucleus Optical Potentials
• A new form of three-body Faddeev equations in the continuum
• Core-excitation effects in ${}^{20}\mathrm{O}(d,p){}^{21}\mathrm{O}$ transfer reactions: Suppression or enhancement?
• ${}^6$Li in a Three-Body Model with Realistic Forces: Separable vs. Non-separable Approach
• Separable Representation of Multichannel Nucleon-Nucleus Optical Potentials

Cited by in corpus (6)

• Toward emulating nuclear reactions using eigenvector continuation
• Fermion Pair Dynamics in Open Quantum Systems
• Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
• Prediction of (p,n) Charge-Exchange Reactions with Uncertainty Quantification
• Quantifying uncertainties due to irreducible three-body forces in deuteron-nucleus reactions
• Uncertainty Quantification in Breakup Reactions