Comparison of Pauli projection and supersymetric transformation methods for three-body nuclear structure and reactions

TL;DR

This paper compares two methods for handling Pauli-forbidden states in three-body nuclear calculations, analyzing their effectiveness in bound, resonant, and scattering states within a momentum-space framework.

Contribution

It provides a systematic comparison of Pauli projection and supersymmetric transformation methods for eliminating forbidden states in three-body nuclear systems.

Findings

The projection method aligns better with experimental data for deuteron-Helium-4 scattering.

No clear superiority of either method for bound and resonant states.

Systematic differences between the two approaches are identified.

Abstract

Three-body Faddeev-type equations for bound, resonant, and scattering states in the systems with a nuclear core and two nucleons are solved using the momentum-space framework. Two approaches for eliminating the Pauli-forbidden deeply-bound states are compared: projecting out those states by a nonlocal term in the potential, and by using a supersymmetric transformation of the potential. While the former method is preferred by the experimental data for the deuteron-${}^4${He} scattering, the results for bound and resonant states do not indicate a clear superiority of a single method. Instead, systematic differences between them are found.