# Deuteron-alpha scattering: separable vs nonseparable Faddeev approach

## TL;DR

This study compares separable and nonseparable Faddeev approaches in deuteron-alpha scattering, demonstrating that separable interactions can accurately reproduce results from nonseparable forces with less computational complexity.

## Contribution

It provides a detailed validation that separable Faddeev interactions yield results nearly identical to nonseparable forces in deuteron-alpha scattering calculations.

## Key findings

- Separable and nonseparable force calculations agree within 1% for cross sections.
- Elastic and breakup observables are in excellent agreement between methods.
- Separable interactions effectively reproduce nonseparable force results.

## 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.