Li6 in a three-body model with realistic Forces: Separable versus nonseparable approach

Abstract

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. Purpose: Faddeev 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 their solution based on separable interactions agrees exactly with solutions based on nonseparable forces. Methods: Momentum space Faddeev equations are solved with nonseparable and separable forces as coupled integral equations. Results: The ground state of 6 Li is calculated via momentum space Faddeev equations using the CD-Bonn neutron-proton force and a Woods-Saxon type neutron(proton)-4 He force. For the latter the Pauli-forbidden S-wave bound state is projected out. This result is compared to a calculation in which the interactions in the two-body subsystems are represented by separable interactions derived in the Ernst-Shakin-Thaler (EST) framework. Conclusions: We find that calculations based on the separable representation of the interactions and the original interactions give results that agree to four significant figures for the binding energy, provided that energy and momentum support points of the EST expansion are chosen independently. The momentum distributions computed in both approaches also fully agree with each other.

New developments in reaction theory: preparing for the FRIB era

“…Separable forms for the optical potentials were developed ( [9] and references therein). Recently, the three-body problem with separable interactions was implemented and applied to 6 Li [10]. The main conclusion in that work is that separable interactions can reproduce the exact solutions to very high accuracy.…”

“…Note that only the NN interaction is varied, the 4 He-N system is kept fixed with the parameters described in Ref. [10]. The dashed line serves to guide the eye and suggests that there is a linear correlation between the three-body binding energy and the deuteron d-state probability.…”

“…This method was used to explore the role of core excitation in (d,p) reactions, and understand the origin of the dynamical effects [3]. Based on the particle-rotor model of n+ 10 Be, a number of 11 Belike models were generated with a range of separation energies, while maintaining a significant coreexcited component. We used the n+ 10 Be system as a toy model, included the first two states of 10 Be and coupled the additional neutron to a total spin J = 1 2 just as in 11 Be(g.s.…”

“…Based on the particle-rotor model of n+ 10 Be, a number of 11 Belike models were generated with a range of separation energies, while maintaining a significant coreexcited component. We used the n+ 10 Be system as a toy model, included the first two states of 10 Be and coupled the additional neutron to a total spin J = 1 2 just as in 11 Be(g.s. ), but then adjusted the interaction to produce a number of models with different separation energies ranging S n = 0.1 − 5.0 MeV.…”

Deuteron- α scattering: Separable versus nonseparable Faddeev approach

“…Our work represents an important stepping stone for using Faddeev techniques for nuclear reactions with heavy nuclei. Starting from the non-relativistic AGS equations [4], we make use of the formulation derived by Lovelace [9], and introduce pair-wise separable interactions as previously developed [10][11][12]. For the treatment of the singularities in the free three-body propagator above the breakup threshold, we implement a procedure proposed in [13,14], which allows one to cast the so-called moving singularities (see e.g.…”